jgrizou/ILOGMM.ipynb

## ILOGMM.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**The following serves as a simple introduction to ILO-GMM. It also illustrate, using carefully selected examples, problems we might encounter when learning forward and, especially, inverse models.**\n",
    "\n",
    "# Overview\n",
    "\n",
    "We compare different inference method for ILO-GMM:\n",
    "- Weighted mean of the Gaussian center by their relative importance\n",
    "- Max of the probability distribution\n",
    "- Mean of the most important (bigger weight) Gaussian\n",
    "- Sampling the probability distribution\n",
    "\n",
    "The data are sampled from a 1 period sinus with a small Gaussian noise.\n",
    "\n",
    "We investigate the forward and inverse model. We show that the inverse problem, which illustrates the redundancy/multimodal/multimodes problem, poses problem to some infering methods.\n",
    "\n",
    "We conclude that, for most practical robotic problems involving inverse models, the order of inference methods to use is as follow:\n",
    "- Max of the probability distribution\n",
    "- Mean of the most important (bigger weight) Gaussian\n",
    "- Sampling the probability distribution\n",
    "- Weighted mean of the Gaussian center by their relative importance\n",
    "\n",
    "\n",
    "We then consider the problem of redundancy using a 3 period sinus. This problem helps visualizing a limitation of ILO-GMM that is the fixed number of Gaussian. We explore briefly two options:\n",
    "- DPGMM: http://scikit-learn.org/stable/modules/generated/sklearn.mixture.DPGMM.html#sklearn.mixture.DPGMM\n",
    "- use of a clustering algortihm to identify the number of modes. DPGMM, wile showing promises in theroy, is not convincing experimentally on our simple example. The clustering shows more practical promises.\n",
    "\n",
    "\n",
    "# Before starting\n",
    "\n",
    "The code below requires the following python modules:\n",
    "- http://www.numpy.org/\n",
    "- http://scikit-learn.org/stable/index.html\n",
    "- https://github.com/AlexanderFabisch/gmr\n",
    "- http://matplotlib.org/\n",
    "\n",
    "\n",
    "# Simple 1 period Sinus\n",
    "\n",
    "## Generate data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "rng = np.random.RandomState(10)\n",
    "X = np.linspace(0, 2 * np.pi, 500)[:, np.newaxis]\n",
    "Y = np.sin(X).ravel() + rng.normal(0, 0.1, X.shape[0])\n",
    "Y = Y[:, np.newaxis]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1.5, 1.5)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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qEFMXlM39LvPzLahqyg9kaxOK0pQ+VCXnF1CRLH/EfAhdPL163cX77+/E7z+O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\nM3t3GAUAQgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fedf9d89e90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(0)\n",
    "ax = fig.add_subplot(111, aspect='equal')\n",
    "ax.scatter(X, Y)\n",
    "plt.xlim([-0.1,2 * np.pi + 0.1])\n",
    "plt.ylim([-1.5,1.5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Build Tree to find NN"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn.neighbors import KDTree\n",
    "X_tree = KDTree(X, leaf_size=2)\n",
    "Y_tree = KDTree(Y, leaf_size=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Forward Model: example of unimodal/grouped data\n",
    "\n",
    "## Find local data for x=1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "_, ind = X_tree.query(1, k=50)     \n",
    "local_X = X[ind]\n",
    "local_Y = Y[ind]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot local data at x=1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1.5, 1.5)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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PKSIiDYg03IcA+4BDQBXwIjCxVpkvAUvc7c1Ae6BrhMcVEZF6RBrumcD7NZ4fdV9rqEz3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\nEREREREREZFm9f+AocFpiObpNgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fedf0ce7d50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(0)\n",
    "ax = fig.add_subplot(111, aspect='equal')\n",
    "ax.scatter(local_X, local_Y)\n",
    "plt.xlim([-0.1,2 * np.pi + 0.1])\n",
    "plt.ylim([-1.5,1.5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fit local GMM with 3 components"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn.mixture import GMM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "GMM(covariance_type='full', init_params='wmc', min_covar=0.001,\n",
       "  n_components=3, n_init=1, n_iter=100, params='wmc', random_state=None,\n",
       "  thresh=None, tol=0.001)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "local_gmm = GMM(n_components=3, covariance_type='full')\n",
    "local_data = np.squeeze(np.concatenate((local_X, local_Y), axis=2))\n",
    "local_gmm.fit(local_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot local GMM\n",
    "\n",
    "Here I switch to https://github.com/AlexanderFabisch/gmr because there is a simple interface for conditional distribution and ellipse drawing\n",
    "\n",
    "However I fit the GMM using sklearn because I will later use the DPGMM from sklearn, so it is all consistent and it help see where to find the code to reimplement all this in a uniform python module."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import gmr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "local_gmminf = gmr.gmm.GMM(3, \n",
    "                           local_gmm.weights_, \n",
    "                           local_gmm.means_, \n",
    "                           local_gmm.covars_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "ellipses = local_gmminf.to_ellipses(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1.5, 1.5)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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rC0I4j7OIOnpL8+vtwMHerLAvhvsEogu1H9uR36a+ZwrRp5KXKtyOOKqIflntIRpuequy\nzYntB8A3gWylG5KQUG6CPAd4D/gZ0bTx+/jkU2Ov6Ivhnqt0A1SSM4nGD79O1IPvr7JEw0wTgcuJ\nvgepv/oT4F2i8ekQersQ3QQ5G1gAfI2o99sfVRN9weI9+ffDwLd6s8K+GO47iS7afayeqPeuvmMw\n8F/AfwKPVbgtSTlINIX39yvdkBguARYRjVMvB64C/r2iLYpvd/79PeBRevjlg33Ijvzrlfz6w3T/\nbbpBqga2EH3kr6H/X1CF6FxCuaCaIgqMH1S6IQkYRTSDAWAo0TecXl255iTqCvr/bJnQboJ8Dpie\nX24Avl+5plTOAqJZGE30/xuflgO7gI+IriV8sbLNiW0+0VDGOqKP/2uJpq72RzOJxj/XEU23+2Zl\nm5OoK+j/s2XOIaybIGcR9dwbgUfo5dkykiRJkiRJkiRJkiRJkiRJkiRJktSr/h9XMWQnKY/0ogAA\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fededdc2890>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib.patches import Ellipse\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111, aspect='equal')\n",
    "\n",
    "for ellipse in ellipses:\n",
    "    e = Ellipse(xy=ellipse[0], angle=ellipse[1][0]*180/np.pi, width=ellipse[1][1], height=ellipse[1][2])\n",
    "    ax.add_artist(e)\n",
    "    e.set_clip_box(ax.bbox)\n",
    "    e.set_alpha(0.5)\n",
    "    e.set_facecolor(rng.rand(3))\n",
    "\n",
    "plt.xlim([-0.1,2 * np.pi + 0.1])\n",
    "plt.ylim([-1.5,1.5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## We compute and plot the conditional for x=1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "conditional_gmm = local_gmminf.condition([0], [1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fedf0a6f350>]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fededdab690>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "YY = np.linspace(-1.5, 1.5, 500)[:, np.newaxis]\n",
    "proba = conditional_gmm.to_probability_density(YY)\n",
    "plt.plot(proba, YY)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Method 1: Find the Max"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "max_proba = np.max(proba)\n",
    "max_id = np.where(proba == max_proba)[0]\n",
    "max_value = YY[max_id][0,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fedf0a84e90>]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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fl1hmNtCdHZ8DfBbYlGCdkqSEkhzxLwL+E/g4Ey/nXAr8K/AF4Ezgv7PLdwH/AfzDJJ/n\nEb8k1WgqR/ytdLWNwS9JNWp0V48kaQYy+CUpMga/JEXG4JekyBj8khQZg1+SImPwS1JkDH5JiozB\nL0mRMfglKTIGvyRFxuCXpMgY/JIUGYNfkiJj8EtSZAx+SYqMwS9JkTH4JSkyBr8kRcbgl6TIGPyS\nFBmDX5IiY/BLUmQMfkmKjMEvSZEx+CUpMga/JEXG4JekyCQJ/huAl4HjwIVllrsaGAJeA76TYH2S\npDpIEvybgOuB35RZphO4ixD+/cBNwOoE65QkJdSV4L1DVSwzAGwFtmWnHwCuA15NsF5JUgLT3cff\nC+womB7OzpMkNUmlI/7HgCUl5n8X+EUVn5+puUaSpGlVKfj/OOHn7wSWF0wvJxz1lzQ4OPjheCqV\nIpVKJVy9JLWXdDpNOp1O9BkddajHr4G/AZ4v8VoXsBm4EngL+D3hBG+pPv5MJuMXBEmqRUdHB9SY\n5Un6+K8n9N+vBR4GfpmdvzQ7DTAG3AI8CrwCPIgndiWpqepxxF8vHvFLUo0afcQvSZqBDH5JiozB\nL0mRMfglKTIGvyRFxuCXpMgY/JIUGYNfkiJj8EtSZAx+SYqMwS9JkTH4JSkyBr8kRcbgl6TIGPyS\nFBmDX5IiY/BLUmQMfkmKjMEvSZEx+CUpMga/JEXG4JekyBj8khQZg1+SImPwS1JkDH5JiozBL0mR\nMfglKTJJgv8G4GXgOHBhmeW2AS8BLwC/T7A+SVIdJAn+TcD1wG8qLJcBUsAFwECC9UUjnU43uwot\nw22R57bIc1skkyT4h4AtVS7bkWA90XGnznNb5Lkt8twWyTSijz8DPA48B3y9AeuTJJXRVeH1x4Al\nJeZ/F/hFleu4FNgFnJb9vCHgyWorKEmqr3p0wfwa+GtgQxXLrgMOAbeXeG0rsLIO9ZGkmLwOnFXL\nGyod8VdrsgZkNtAJHATmAJ8F/m6SZWuquCSp8a4HdgBHgN3AL7PzlwIPZ8fPBF7Mlv8DbmtwHSVJ\nkiQ10tWEk7uvAd+ZZJk7s69vJFz7364qbYsUsJ9w49sLwPcaVrPGuxfYQ7g3ZDKx7BeVtkWKOPaL\n5YTzhy8Tegu+NclyMewX1WyLFC26X3QSTuD2AbMI3T+ri5b5PPBIdvzTwP82qnINVs22SAHrG1qr\n5rmc8J92srCLZb+AytsiRRz7xRJgTXZ8LrCZePOimm2Roob9opHP6hkghN02YBR4ALiuaJlrgfuy\n488AC4CeBtWvkarZFhDPjW9PAu+XeT2W/QIqbwuIY7/YTTgggnAl4KuE84eFYtkvqtkWUMN+0cjg\n7yWcDM4Zzs6rtMyyaa5XM1SzLTLAJYSvsI8A/Y2pWkuKZb+oRoz7RR/hW9AzRfNj3C/6KL0tatov\n6nU5ZzUyVS5X3GpV+76ZpJq/aQOhb28EuAb4ObBqOivV4mLYL6oR234xF/gv4NuEo91iMe0X5bZF\nTftFI4/4dxIqlrOc0EKXW2ZZdl67qWZbHCT8I0K4VHYWsGj6q9aSYtkvqhHTfjEL+Bnw74QgKxbT\nflFpW7TsftFFuMOsDziRyid319K+J2uq2RY95I9mBgjnA9pZH9Wd3G3n/SKnj8m3RSz7RQfwU+Af\nyywTy35RzbZo6f3iGsIZ6a3kb+b6Rrbk3JV9fSPln/M/01XaFn9JuHTrReB3hB27Xd0PvAUcI/TZ\n/jnx7heVtkUs+8VlwDjh78xdongNce4X1WyLWPYLSZIkSZIkSZIkSZIkSZIkSZIkSWpt/w8zSkSe\nBYjBjgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fededb71190>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(proba, YY)\n",
    "plt.plot([0, max_proba], [max_value, max_value], 'r')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1.5, 1.5)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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PRZrndOEUjDKPA8mYwtMtAHC5zmTAgKpUq1aNEiVK0LFjR1vI+TCydOlS5syZ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\ncDgcDofD4XA4HA6Hw+FwOBwOh8NRo/w/+aDX2nwKMdUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fededa9e410>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(0)\n",
    "ax = fig.add_subplot(111, aspect='equal')\n",
    "ax.scatter(X, Y)\n",
    "ax.scatter(1, max_value, 50, 'r')\n",
    "plt.xlim([-0.1,2 * np.pi + 0.1])\n",
    "plt.ylim([-1.5,1.5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Method 2: Sample from distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "sampled_values = conditional_gmm.sample(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1.5, 1.5)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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iRo1dtGnTjIkTZyGywejC9ShlHgTCUIWnVWE8k6kLQ4ZUpFKlShQtWpR27drp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\n4XA4HA6Ho1b5f8U/H1Oju9boAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7feded9b58d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(0)\n",
    "ax = fig.add_subplot(111, aspect='equal')\n",
    "ax.scatter(X, Y)\n",
    "ax.scatter(np.ones(sampled_values.shape), sampled_values, 50, 'r')\n",
    "plt.xlim([-0.1,2 * np.pi + 0.1])\n",
    "plt.ylim([-1.5,1.5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Method 3: Weighted mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "weighted_mean = conditional_gmm.priors.dot(conditional_gmm.means)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7feded8ef210>]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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s+Bzgc8D6BOuUJCWU5Ix/IfCfwMeZfDnnEuBfgS8CZwD/nV2+B/gP4B/KfJ5n/JJUp6mc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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fededd9fa10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(proba, YY)\n",
    "plt.plot([0, max_proba], [weighted_mean, weighted_mean], 'r')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note that it is not the max.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1.5, 1.5)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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gGXgbaAOAy3U6gwfXpFatWpQpU4bu3bvjdtuwgEPFsmXLmDVrFmPHvsSyZRdj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\n4XA4HA6Hw+Fw1Cj/D6cch2k/XSlyAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7feded9ed550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(0)\n",
    "ax = fig.add_subplot(111, aspect='equal')\n",
    "ax.scatter(X, Y)\n",
    "ax.scatter(1, weighted_mean, 50, 'r')\n",
    "plt.xlim([-0.1,2 * np.pi + 0.1])\n",
    "plt.ylim([-1.5,1.5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Method 4: Mean of most important Gaussian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1.5, 1.5)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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CG4DfALexb28gAmXn3o/dbsHl6ozFshCnMxa3ewoVKw7gttsiOXDgABkZHtSoGaA2dnsN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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7feded8b6f50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "max_weight = np.max(conditional_gmm.priors)\n",
    "max_ind = np.where(conditional_gmm.priors == max_weight)[0][0]\n",
    "\n",
    "fig = plt.figure(0)\n",
    "ax = fig.add_subplot(111, aspect='equal')\n",
    "ax.scatter(X, Y)\n",
    "ax.scatter(1, conditional_gmm.means[max_ind], 50, 'r')\n",
    "plt.xlim([-0.1,2 * np.pi + 0.1])\n",
    "plt.ylim([-1.5,1.5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Ranking\n",
    "\n",
    "- Max\n",
    "- Mean of most weighted Gaussian\n",
    "- Weighted Mean\n",
    "- Sample"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Inverse Model: example of redundancy/multimodality/multimodes\n",
    "\n",
    "## Find local data for y=0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "_, ind = Y_tree.query(0.5, k=50)     \n",
    "local_X = X[ind]\n",
    "local_Y = Y[ind]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot local data at y=0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1.5, 1.5)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAC8CAYAAACDmO49AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7feded9056d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(0)\n",
    "ax = fig.add_subplot(111, aspect='equal')\n",
    "ax.scatter(local_X, local_Y)\n",
    "plt.xlim([-0.1,2 * np.pi + 0.1])\n",
    "plt.ylim([-1.5,1.5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**This is the problem of redundancy**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fit local GMM with 3 components"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "GMM(covariance_type='full', init_params='wmc', min_covar=0.001,\n",
       "  n_components=3, n_init=1, n_iter=100, params='wmc', random_state=None,\n",
       "  thresh=None, tol=0.001)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "local_gmm = GMM(n_components=3, covariance_type='full')\n",
    "local_data = np.squeeze(np.concatenate((local_X, local_Y), axis=2))\n",
    "local_gmm.fit(local_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot local GMM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "local_gmminf = gmr.gmm.GMM(3, \n",
    "                           local_gmm.weights_, \n",
    "                           local_gmm.means_, \n",
    "                           local_gmm.covars_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ellipses = local_gmminf.to_ellipses(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1.5, 1.5)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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HN9OA55jcfz8NyXsN8Bvg4gq2pVg+CXwb2FjphhTBi0BzpRtRJHcAH062a4DppaxsIv62\nzEricG8H+oC7gCsr2aCUNgGHKt2IItpL/D9ciGc+bSV+zjJZdSfvdcQdi4MVbEsxtACXAV+nOLPh\nJoIQ7mM6cUfv9mS/HzhcygonYrjPJ35Q+7pdyTFNPIuIP5U8WuF2pFFF/D+rfcTDTc9Wtjmp3Qxc\nD+Qr3ZAiCeVLkIuB/cA3iaeN38YbnxpLYiKGe1TpBmhUphGPH36CuAc/WeWJh5lagPcQ/w7SZHUF\n8Arx+HQIvV2IvwS5AlgH/B1x73cyqiH+gcVbkvcu4NOlrHAihvtu4od2r1tA3HvXxFEL3A38N/Cj\nCrelWA4TT+E9v9INSeHdwHriceo7gT8FvlXRFqW3J3nfD/yQMf744ASyK3k9nux/n+F/TTdINcDv\niD/y1zH5H6hCfC+hPFDNEAfGzZVuSBGcRjyDAWAq8S+cXlq55hTVKib/bJnQvgT5MLA02W4Fbqpc\nUypnHfEsjB1M/i8+3Qm8DBwlfpZwTWWbk9rFxEMZm4k//j9FPHV1MlpGPP65mXi63fWVbU5RrWLy\nz5ZZTFhfglxO3HNvA35AiWfLSJIkSZIkSZIkSZIkSZIkSZIkSVJJ/T/9i3nrEXL2YwAAAABJRU5E\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7feded8e1210>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib.patches import Ellipse\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111, aspect='equal')\n",
    "\n",
    "for ellipse in ellipses:\n",
    "    e = Ellipse(xy=ellipse[0], angle=ellipse[1][0]*180/np.pi, width=ellipse[1][1], height=ellipse[1][2])\n",
    "    ax.add_artist(e)\n",
    "    e.set_clip_box(ax.bbox)\n",
    "    e.set_alpha(0.5)\n",
    "    e.set_facecolor(rng.rand(3))\n",
    "\n",
    "plt.xlim([-0.1,2 * np.pi + 0.1])\n",
    "plt.ylim([-1.5,1.5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note that the GMM model well the bi-modality of the data**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## We compute and plot the conditional for y=0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "conditional_gmm = local_gmminf.condition([1], [0.5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7feded920d90>]"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7feded95ce10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "proba = conditional_gmm.to_probability_density(X)\n",
    "plt.plot(X, proba)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note that the GMM model well the bi-modality of the data**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Method 1: Find the Max"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "max_proba = np.max(proba)\n",
    "max_id = np.where(proba == max_proba)[0]\n",
    "max_value = X[max_id][0,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fededadab10>]"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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BrptLuKUgF0mfN0Ee5axOUGi4FvUWfNq5itjjTZCrtZJNqshF0udFkPf2Qnt7tPeqteKW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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fededa68cd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X, proba)\n",
    "plt.plot([max_value, max_value], [0, max_proba] , 'r')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1.5, 1.5)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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aTc5zpUFMHVE29/vNz3egqik/mqlNKEpT+lCVnCegIln+iPkQuny6d7+fDz/c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\nOGqU/wcSzXlt0iEqKQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fededb06d90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(0)\n",
    "ax = fig.add_subplot(111, aspect='equal')\n",
    "ax.scatter(X, Y)\n",
    "ax.scatter(max_value, 0.5, 50, 'r')\n",
    "plt.xlim([-0.1,2 * np.pi + 0.1])\n",
    "plt.ylim([-1.5,1.5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Method 2: Sample from distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sampled_values = conditional_gmm.sample(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1.5, 1.5)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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3xDGYRQOvxC+//LKXVpZ/S8+ePfnss5mMGnUkDRpUxQQ61cXNrXQka4/77L5v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\nHA6Hw+FwOBwOR43y/4uja2hnCRhvAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7feded764450>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(0)\n",
    "ax = fig.add_subplot(111, aspect='equal')\n",
    "ax.scatter(X, Y)\n",
    "ax.scatter(sampled_values, 0.5 * np.ones(sampled_values.shape), 50, 'r')\n",
    "plt.xlim([-0.1,2 * np.pi + 0.1])\n",
    "plt.ylim([-1.5,1.5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Method 3: Weighted mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "weighted_mean = conditional_gmm.priors.dot(conditional_gmm.means)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7feded6a4510>]"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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BrptLuKXLC4ukb8wHuW4u4ZaCXCR93gR5lLM6QaHhWtRb8GnnKmKPN0Gu1ko2qSIXSZ8X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\nRERERERERERExoL/B6/JUZKBKB9YAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7feded7c39d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X, proba)\n",
    "plt.plot([weighted_mean, weighted_mean],[0, max_proba], 'r')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "** This is not desired **"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1.5, 1.5)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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VCND4D993Asqmp7No0ZVMlK4fZs2ahMvVHpfrIczmwcAjwCaU6+lQoDMWywCs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\n8t9h6p0UAE/h97fE5/MhvYHZdc/i66/3UVKyF5/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EtBho8C2vTwEWHOc9egI7gDT7eRuB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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7feded79e3d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(0)\n",
    "ax = fig.add_subplot(111, aspect='equal')\n",
    "ax.scatter(X, Y)\n",
    "ax.scatter(weighted_mean, 0.5, 50, 'r')\n",
    "plt.xlim([-0.1,2 * np.pi + 0.1])\n",
    "plt.ylim([-1.5,1.5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "** This is not desired **"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Method 4: Mean of most important Gaussian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1.5, 1.5)"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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bFe5/OdOB9agMUT5UJee5qEiWLKdZsxv5+OO78fuPo4o934Xf35q5c6exZ88M\n+vRpx4svTiT+Evs3JpmvOICfmVgsnRg8uDRlypQhX77baNWqlS7kfJXo0KEDa9eWYvny5UyevJ2t\nW8ugxgxVUT+xQxhGOOnpZ4BUVKzAAlTQUwjwPCooqgvQAYBgcDqLFkUhIueDPDSa/xRXqtyPoBT3\neQqjRu+ZOZfp/QJgChAFnP7jwUaOHJnxPj4+nvj4+H/UmalTJ7BixQ0cONActXb7FADBYHV27y5E\nsWL5gOosZzMXgm0usBzwsxvoSp486xky5E0iIyP/UR80/45KlSpRqVIlKlSoQKtWt+LzDUb9RHYA\nB0lLWwgMw2JpgsgNqOWen4BqqFG+A/gZFVR2L/ADwaCbjRs3XnMJ1zSaK2Hp0qUsXbr0b9td6ZDG\nhqp+fCMqTn8tKh3gjkxt8qHi7AWojaqgXOwixzLNR1fGqFGjefrpFQQCh1Fh7L2AxYAFiyWASAVc\n7GIuqbTItN/3QHPspFAHi2U1W7ZsoGLFilfcH80/Z/Xq1bz++rts2bKejRvjCQbPolIW3Ay8jIr0\n7YnKthlj7uVHPbDTUco9L7CGkJBF7Nu3k5iYmD+dR6O5Hrha6Qf8wEPAV6icth+hFHtv8wXKELoF\nZRR9Geh2hee8JCLC2rWbCQTWAWdQ4e1FgP8BbkRsgI0UoumAgxbAWKAtFprjJYUvge9wu0uRmpp6\ntbqp+Rvq1KnDO++8xuDBA3E6FwKfoHLM1EONJ6qjJoANUWOLuahJ5CLUWskS1PJONImJ6UyaNCkH\npNBocpZryRj5r0bufr+fCRMmsmLFemJiQpkx4wuSkzegvC97o5R8WeB9oD9qZPcQKtFVOAYWAhwG\n3kQlwJpDRMRDHDr00zVXHOO/RjAYpFWrjixa9ANKefczt3wBvI0avR81X4VRo/vqqCRvX6J+3suI\nirqTX389kN3d12iyhUuN3HO9cu/SpSfz5x/G57sTu30WgcAegsHd5tbCwIdAU1ScVX9gFdAClX0w\nDLVA1x41oTiCxeJizZpvqFWr1pVLpLliUlNTKV68IidO3EUw+AtqspiAsrMXQcXOlQJKo5Z0rKj7\n+bJ5hFO43aXx+c5kf+c1mmzguswKefLkST77bC4+3+dAT9LTZyNyEqt1HMoeG4kKoHWhXPLrA8NQ\nKWa3ocq/TQeOA3Nxu+vTt29vrdivIZxOJ6tXf0PFip9jtX4AvAcko8wzq1DLOLVR9zNIsWIGNtv7\nKOU/BYg9v5kHAAAgAElEQVTDbg/jvffezyEJNBrNP3beP3LkiLhc0aKyN6p4pJCQGlK4cGkzEKaZ\nqFwxxQSaZopZWijgFZutmVitt4jFEinR0cVlwIChkpaWloXhBZqsYNOmTWY2yvfNoCaved/yCXyU\n6b5+JdWrx8vYsWPFbg8z7/0zAm+I1RojnTrdqis5aa47uB6LdYgI9es3Z/36WFJT78VqnYzFshgR\nP8HgSGAUylkn3HwtMvc8g9Waj0mTXuHs2bPceOON1KxZMytl0WQhw4eP4Nln0xEZgwpSGwe0QaUp\n2oyapVlxOO7E41lGWpodn+8wqvj2SNSMrQQQgtO5gBEjhtK7d2+ioqJyRB6NJiu57mzuqampnDlz\nBrfbzcCBT/Dtt8s4ePAwgcBM4HaUOSYvyuY+DuUX0wyog8Uynvvua8DUqROvghiarOaZZ55l1Khj\n+P2TUK6P21AP7WSgGnb7WRwON3Z7gKSktqSnP4DKetEL9VD/GWWDbwI4sFpdREb+zOrV31KqVKkc\nkUmjySquG5v7kiVLqFixFm53OEWKVKBixVoMGtSX227rSDD4EEqp34wKjA1HLbp9DixD2Wmfo0YN\nL6+99vIlz6G5trjrrp6EhHyK1ToMFSIxArWwehS3O5kpU56mX7/uGIad9PSuqAVWJ8oD6lugMiqg\nrSKwimBwKWfO9OPBBwfniDwaTXaQq5T7t99+S5s2Xdi+fR8im0lPX86RI/WJj2+Fx+PCbj9qtpyM\nSj8wDhVf9SNQHadzPuXKuVi4cK5OJZCLKFSoEBs2rKR3bx+33FKOsmV/wGr14HBUZcyYx5gy5V0m\nTNjEr79GATO5kJ7AigpPG4Nyha0HDABKEgy+xubNG/jmm28oW7Ym0dFF6Ny5J+fOnbtUNzSaXEWu\nMsu0b9+DefPsqECVVijXxghgL2DB7Q7H7+9IenoxPJ7JPP30IH766QA+XwoNG9akWrVqVKtWDbvd\nftWF0VxdUlNTsdvtfP7559x++/MkJn6PSlfQFDiNx2OjWLFotm/fhco/0wHlHx8G/IpKSpaAylT9\nIVAVp3METZr4WLDgfzkik0bzb7iUWeZKc8tkK0qISFSAyhxUUeZTqODXZILBprRo8QtlykTRvv0s\nGjVqlIO91VxNnE5VaPzs2bOoeAYryh6/Bqs1jO+/X0OHDj1QC6lHUaact1D/A15U5skQVOCTSjaW\nmvo6X38dSTAYxGq1cn6woROPaXIjuco2MWDAfbhcHwJu1Oh9J/AoKkVvNKmpA7DZwhg/fpxW7P8R\nGjdujEpN8DGwH4djIHXrNiU2NpbTp0+j0hrVBl5ExTvEAAeAQag1mcNc8CQ7hNPpxWKx8OKLL+P1\nRuFwuOnYsQc+ny+7RdNorohcpdyPHj1OIJCE+ueMQaUSWJOx3W5fS9GiBXKod5qcoEiRIixa9Bll\ny75AZGQDmjc/w7hxT1GuXBypqZEoM8wBVP6ZZGAfSqmvBW5BzfzaAM2wWhtRo0ZNZs6cyYgRk0lO\nXofff5KFC9Po23dQDkmo0fw7rqX5ZobN3efzsWHDBtxuN9WqVcNqtbJnzx6qVq2Hz7cYFWXaHJiI\nmnI3wGLxUajQSTZsWEl0dHTOSaHJcerXb8mqVR0QuRPl6z4Lw7BSvHhpDh06SmpqK5RpLz9wEosl\nBcO4Ab//fhyOxbjdX5CQMAA1ugfYSsGCnTl8eMclzqjR5By5xuZ+8OBB6tW7iXPnwggEfqNatZK8\n8soYtm3bhs1WD6iCSvD1FDAVOILV2heLxc+RIwFaterM/PkfkSdPnhyVQ5NzHDly1Mz57gHeBarh\ndj/PgQNNSU+vhPKY8aDMNVUReQK//3PARVrarYgUwGJZj8hUYD5wjtBQb06Jo9HkekRE5KabOohh\njDbDyWcIeMRqzWtWvc8j8Ju5baRYLJFStGgFcTgKCPwk4BebbYDEx9+cI2HAmmuDO+/sLU7nbQKp\nAifE5SopLlcVszi6CEwUuMF8f1wg0qzXKgLLzfq54WY93f8JjBWPJ1r27duX06JpNH+Cq1RDNcvZ\ntWs3gcBNwIOoeqZ9CQbTUbOOFFT63huxWl9i9OhH8fuTSUvrihqJdcLvn8OyZd+zd+/eHJNBk7NM\nnvwiDRsmYRhh2GxF6NixHnZ75llrOBBqvo8B6qDs74uAO1BeNaEoj6xOwBDS07sya9YsfvnlF53r\nX5PlLFu2jOrV4ylZsjpDhjyF3++/4mNeczb3tm278cUXPwLFUYtdR1HRiDZUBse8qLogj+N0JpOa\n2hnlNfMbKtXrHcCn5M//Bnv2bMbr1dPp/yrJycnYbDZEhLi4BuzZU5m0tJa4XG+Snr6KQKA8qrbM\nOSCEUqXKcujQAVJTV6CC374GygFgGLcTGrqU5ORkRFJ5+ulRxMbmw2az0bp1a8LCwnJMTk3uZsuW\nLdSp0xSfbxJQHI9nMPfeW5tXXnn+svbPNbllVq9eTb16bRFZj6qPGUSNtI4AZ1F1M9ui/iFbomyq\nDVC1M49xXqSwsFosWPAK9erVy3ZBNNceCQkJDB/+DNu3/0zdutU4ffo0U6Z8gLK/PwaswG6/hVat\nWvLVVxZSU0ujRu6jsFj2AM8AoxDpjyrb2B63uxmGkUpExF7Wr1+u13k0/4rRo59m1KhzBIPnlfke\nIiObcPr0ocva/2rmlmmJGjrvBoZcos1Ec/sm4C+rFUdHR+N2O1EjcQuqXuYJVMDJJFTg0hhUIqiz\nqMLI5VBubknmUVJJTT2uKylpMggPD2fixBdYvPhTnn76Kdat24oy8w1D/YaaEAzWJSYmhEBgIUqZ\n/0SxYqNo23YDkITII+bRpgJPkZw8l8TEBZw40YLRo8fmiFya3I/b7cIwTmf65jROpwuAyZNfJza2\nLPnzl2LEiGcIBoPZ1i8D2IPK5mRHhYqW/0Ob1ii/M4AbgNWXOJaIiAQCAalXr5lYLEUEJgkcEOgg\n4DIXuqzmwthZgfICtwsUFegoUEdgnEADKViwrASDwZxb5dBc03TqdIf5m9ptLqSmitUaK05nAYEN\nAqfE4egmXbrcJe+8856AW2CZ2baewLeZ8si/Kzff3D2nRdLkUo4fPy7R0YXEMPoLvCIeTxF5443p\nMm3aG+J0FhdYK7BZPJ4a8sILE/60P5dYUL1S6gILM30ear4y8zpquH2enah8rX8ko7NJSUnicsUI\n/Czwnum1ECNVqtwgkZEFBRaY/1T7xG6PloiIogKvCbwtMEAMo4488cTw7Lw/mlzGvn37xOOJEogW\nuFugnBQtWkZgeCalvU+83khxOKIEpgnECLQWiBLDuEkgUeCkeDy15dVXp+S0SJpczJEjR2TQoKHS\nq1cfmTdvngwdOlQslghTp2UuRtPkT/tyCeV+pX7uBYHMhqHDqNH537UphLK1XBSPx0P9+vX59tsn\nCAaXAx8Bedm58x7at2/MggV3YhhlSUvbw7333s099/SgYcPmBINNsFh+JV8+H4899ugViqa5nilW\nrBj79+/k1VdfZd++fTRvPozDhw8zfPgaAgFBmQSHkpQUBGqiPLeaA99jGEupXj2N9eujsFgs3H33\nQzz4YO+cFEeTy4mNjeWFF55DRGjdujNffbUUkerA/kytDhIWdvmm5itV7pc7Hfijsf+i+40cOTLj\nfZ8+d/DDD4+YkYJqUTQt7WVWr76Dffu2s2XLFvLnz0/58soKtGPHehYvXozb7aZNmzbaS0bzt+TJ\nk4fRo0cDsHbtWh544DECAVCWxDCUa+T9KC+t6cA0YBeBQHl27rQQG1ucNWu+pUABnfJCkzV8+umn\nLF68GhEfSrH/iMpi6sRieZ1x475h6dKlLF269Kr3pQ6/N8s8zp8XVV8HumX6/LdmmfMMGTJMDKNv\npmnJp1KxYt1smCRp/kv89NNP4nJFCOQXSBCYLvCAQAlR9XdbmOab1gKPZvwe7fYB0qvXgzndfc11\nwu7du8XtDheoLlBRoKbAfoEepknQJtWrN5LDhw//bj+uUhDTD0Bp1IKqA2Vbn/eHNvOAO833dVBu\nMJc0yWSmf/+HiYr6HIfjHqzWx/F4evPyy6OvsMsazQUSExNp0aItKSn1Ud4zbuBuVHqLkyg3yWjg\neZRbbnzGvunptVm+fDnPPfcc69aty+6ua64Tzp49y6JFixgxYjQpKXeh4nvigFRgC8ol90PgDBs2\nNKBly06Xddys8HNvhfJLNFBz1+eA8wbIqebfSSiXySRUYcv1FzmO+RD6PSdOnODdd9/F50umfft2\nxMX9pSelRvOP6N27H2+9tRK//wxKsZdETTTn4HQuIjX1blQRkMoo19t1QGNgBbAMq7UWUAWn80Pe\needVunTpnDOCaHIl+/bto06dpqSkFCE5+SfS0+9F1YC+FWWWsaIK0Mwx9xAMw8OZM78QGqqirHNN\nENN5tm/fzogRz3PmzFluv70DPXveoYsmaLKcSpXqs23bEOAulMfuImAzcJoGDWDz5h2cPRuBCpIb\nDLwBFECluzCAJah/o1XExHTj5MkDOSCFJjdx7Ngx5s6di8ViYebMz1m+vCHB4FBgA2rg8CAqBcY4\n1CyyKmpQYQd+xjAqkZqaiGEYQC7KCgnw888/c8MN8SQlPYZIEVatGsmvv57h0Uf75XTXNNcZpUoV\nY+fOH818Rm8Dr6EmoAP44YfSpKX5MIxKBALns5CeQFkji6GqOZ3/nypDQsJpNmzYQNGiRYmKisp+\nYTTXPD///DM1azYkNfUmQEhNXU0wOMrc+gtQCqt1GsHgcJSR41nUQKIxymtrBn379slQ7LmFjAWC\nkSNHiWEMyLSQ+qMUKFA6O9c2NP8RDh06JLGxpSQ0tI5YrTECYWbA0nbzt+cVOCngE6gs4DADn6IF\n8pqBTScE6ovF4pGwsMridkfKxx//L6dF01wD+P1+2b9/v5w+fVrOnj0rhQqVFzif9fY3gUICPQU+\nMN9PFKgk8KTZZo1AtFgssWKzeaVbtzv+dA6ukp/7VSEYFEQyP5kMgsGrEoSl+Y9TqFAhdu5cz8qV\nK7Farfz222/cc884zp07H2jtRrmifQ9EobJHDgCc5vu7UTmNBJHpnD37GRBDjx530aRJY2JiYv50\nTr/fz6uvTmHNmk1UrlyaRx/tj8vlygZpNdnJqlWraNWqM4mJKVgsKRQsWJwjR9JRNSkE9ftpjEqE\nOBf4BJiJCgV61TxKDC6XwejR/enUqRMlSpTIAUmunIwn0c6dO8XrjRF4VeAz8Xgqy7PPjsvOB67m\nP8qJEyfE7Y4S2GiOnB4ViDVHVy0FUsz3ecxRvV1UrYHSprvaJIFPBIrIoEGD/3T8YDAoHTrcJh5P\nE4Gp4nJ1kDp1bhS/358D0mquFgcOHBDDiDRH4EGBYwKGqPQodczfV6SA39xeSqCZOSP8TmCnQD+x\nWitInz59/vJcXKX0A1nJ7zq8YcMGadWqs9Sr10omT35d54nRZBszZ34kbnekhIVVFo8nSgYNGixd\nu/YUpzNSYKT5D/iOwAYxjHKmT7xH4AnzgXBK4F2JjS0rx44dk169+kjlyjdIw4ZNZdSoUeJ0Rptm\nHhHwi9dbRtauXZvTYmuykMcff9I08R0V+Mj0XXcI7BEYLBBiDgoSTNNeqPm7KmD6tiuTtNU6VEaO\nHPWX5yI3mWUAqlWrxpdffpzT3dD8B+nWrQvNm9/EgQMHKFasGJGRkYDy4Grfvis//9wUkZ4ABALd\nUNk1bkT5wb8PPALk5+jRg1SqVJvTp0sichJoxYoVC1GLsE7zbAaGEaYLgFxn+HwpqEIwL6FMLe+g\nvLEaAQ/hcrXCbl9OWtqNpKbu4UKm22bAQ8AEYB8Ox5u0bv3lxU7xt1xzlZg0mmuBqKgo4uLiMhQ7\nQIUKFRgxYggeT2KmlhZgBio272XgYWAW0A6I49dfYxFZA3wHjCAY/A4RsNkeAtZhGCMICztL9erV\ns0s0TTbQqVM7HI4zwJuooP14VKxEebzel6hfP5GUFB/B4D7Uus79gAtVuyIEqIfN1p0PP5xKrVq1\n/lUfriXHcXOGodFcuyQmJlKlSh2OHKlFWloRVOTqvcAXwE3AKlRk613Az6giM5uARM6PpUJC2lCp\nUgq//HKGcuVKMXXqSxQqVCj7hdFkGX6/n6SkJMLCwjh8+DANG7bkxIkEUlISgL6oRdOzQEMsljcw\nDAO/vzSwFRXbuQGVz6g3FstyGjasx8yZbxAbG/u3576Un/u1RLbYwjSaK+XMmTMyYsQoKVSorEAR\nMw/IaoF9pp31IYFqpl3VI1BSoK+o2gTvi8sVJi+88ILs2rUrp0XRZAHTpk0XpzNE7HavlCkTJ3Xr\nNhPDGGnazbeYrrUl5UIR9rGmu+MdAukCzwiEitMZL253Pnn22Rf+0fm5hM39WtL2Zj81mtxB0aKV\nOXjwKBCJMs3UACqgIle7o8wzd6My+60ATuFweDCM4lgsFYD5zJ79Pi1btswZATRXzI8//kijRm3x\n+ZYCpbFax2KxvEAgsBooY7a6Fav1BMHg9xmfYRnwMfApygUyAsM4zOzZH9K+fft/1IerWWZPo/lP\nUrp0SSyWjqjIwi5cSH66G7UothPlEz8D2IzVmg+/vyTJyavx+d7B5/uInj37kJKSkiP911w5a9as\nQaQtSpGvIhhcSCAQAP5ntkjB7T6Kw7ENlVKgP/AZEItao1mKqgu9k0DgFQYPzrrEiFq5azT/kmnT\nXiImZjEhIVWx29NQ2a+/QP3jrgCKAAtQNtUGBIM2gsGaqH+7M8DT/PLLEbzeMNq27ciRI0dySBLN\nv6VgwYJYretQ2Rvbo5J+haG8ZCoAhahUycG8eR9hsw1ALbAaqGS5K4AmZnuAW9m3b2eW9U0rd43m\nX1KiRAl2797E//73JIsWzTCjUZNQ7pB3o8w1XUwTTDiQgBrRfQA0RBUkq04wWIsvvkihdOkqbNiw\nIWeE0VwWfr+fJ54YRZUqDWnatB2xsbE0aVIah6MZKuL0HMrd8RDK/fEFDh8+yvTpHyBSE7gZVQxm\nCPAoMB/laQUWyyxKlaqYZX3VNneNJouYOHEyjz/+Mj7fEGAl8DE2W1VEjhEIlEdluu6KSlDmRpU5\n2IuyuVqAt4iLe5f165flkASav+P++x/hgw+2kJwcBXwOBGnZsj0lSxZg2rQTpKcXQiX66oF6wG8B\nghhGJIHAnaiZ3DJUvYClwH6cTjsORwFcrkSWLVuQUV3ucsl1KX81mtzIxx9/wqxZn/PNN0tISGgP\nTEHl5a4KBFBT9QeAQagsf81QBUEAdhAT04pHHrmX9HQ/3bp1oUKFChc9T3p6Oq+99jrbt++hVq0q\n9OrVC6tVT8SvNi5XGKmpg7lggnNgt3ekd+9KzJr1MadOnUbVLXKj1l1eApajApjmomZzx4Aq2Gzz\nmDJlLC1bNuP06dOUKVMGt9v9j/ukXSE1mmxizZo1Yhh5zUx/IjBNVLm+EIEIM13Breb74mbekXSx\n228Rmy1MDOMRsVoHi9cbI6tXr/7T8QOBgNx0Uztxu5sJjBePp67cdts9OSDpfw+vN0qgjcAMuZC1\n9muJi4uXWrWaCrxm5o8pJbBYoHFGmgm4V8AmVqtDypevKsuWLcuSPnEVyuxFAV+jlnoXARGXaLcf\nVf1gA7D2Cs6n0eQKjh07hs2WF5iMKqr9PPAu8AWGYWCxzEYttn6GKu1XGHDhcKzA7x9IIPAKweA4\nkpKeY+jQZ/90/A0bNrBq1TaSk+cDA/H5FjF79hy9IJsNDBo0EMP4ERWspjCM1RQpEsupU78CtVC2\n97OoUtHbUMFsBtAbtzuEQ4f2sX37Rho1anRV+3olyn0oSrmXQZWjGXqJdoKKvY0Dal/B+TSaXEFc\nXBxW61GU0h6MyhvSCGhMIDCZ2NgIVN34Lijb6xGgDUlJQaBopiMVISEhkT/i8/kwjGhUZR4ALzZb\nKD6f76rJdL2yZcsWJk2axKxZs0hPT//b9iNGDGP8+GG4XDOx2+PxetsSFjaFVq0aUbVqBVyuMShv\nqdYoJV8DqIrDURmPpyUzZrxzWVGnWcGV2Gl2opIRnwDyo1YHyl2k3T6UcfHXvzmeOcPQaHI/CxYs\noGvXnpw7lwKMRZVO2w88SqVKB7jvvjsZOPBVAoHd5h55gWHAK6hKUMew2UZz882VqVSpAvHxjalb\nty533vkAn332CYGADXgCkXbYbO9RvPhXbN++Dpvtms0FeM3x6adzuP323ojcgs22nQoVbCxf/hV2\nu/2i7bdu3Ur37vdz4MDPVKhQiZ49b2XPnp957bV3MYw4UlN/JDw8lDNnjmG1GrRv355q1SpRoEAB\nSpQogd1up2TJkuTPnz9L5bgaNvczmY//h8+Z2YsyyfwA3PcXx8sS+5NGc60QDAblu+++E48nxrSz\nhwv0FIejh0RE5BeXK4+Z8lXMbR3NlK/nUxaEitVaS6CoQLRERBQWp7OjwBmBRWK1xkhERGGpV+8m\nWb9+fU6Lm+uIiioksMK8/gHxehvLBx98cNG2Z86ckaiogmKxvCFwRAxjtBQpUl7sdq+o/P0FBDoL\nNJXo6MJy/PjxjH137twp+fOXkJCQUuJ0hstjjz2ZpXLwL/O5f43y5fnjq91FlPnpSxyjgPk3D7AR\n5eCrlbvmP8OmTZukcOGKoorPqEU4w3hcypSpLl5vFTGMwWK1Rogqs1ZaYIy50FrGVPo3C8wXyCew\nLdNC3iBxu6MlNLScuFxR8vDDj+m6B/8Am80pcC7jejqdD8mECRMu2nbJkiXi8dQReEVU8ZZoc4Hc\nJdBJYHymHOwPSa9eD2QUYKlQobZYLJPN7SfF6y0jX331VZbJcSnl/ndzuGZ/se28Oea4qcB/uUS7\nY+bfk8AclN39+4s1HDlyZMb7+Ph44uPj/6Z7Gs21T5UqVYiKiubQoQv+y4FAOUqX3sfYsV1YvHgx\n06alEwwWQ0UtTgA6oMZW50PZnUBJVBbB8+6RM0lOHoXKOniGt96qT4sWjWnTpk22yZabqVu3KatX\nP0l6+lhgG1brJzRqdPHc6QsWLMTn2wlMAr5C+Y/URKnQnahi1g8CSwkGD/POO0E++eQTZs+ewe7d\nWxC5wzxSDGlprdm8eTPNmzf/V/1eunQpS5cu/Vf7Xi7Po8KsQC2mjr1IGw8Qar73on65l5Ioy55k\nGs21xsiRz4rH00DgkMBP4vFUlLfeekdERO64416BYaJK98UItBPoYo7aQwSSzVHfdwJecTjuEa+3\nnajKPr9ljBhttoEyduzYHJY093Dy5Elp0KClGIZdwsPzyYwZMy/a7vjx46IqJRU3XR39Ai+b92eQ\nec/yC9xm3sO5GffL642RokUrCnxofndOvN4qMnfu3CyTg6tQZi8KWMyfXSFjUTG1ACVQppiNqCHH\n439xvCwTVqO51vD7/dK370DxeKIkNDSvjB49RoLBoKSkpEhYWAGBZwWWC+Q1bew2UWmCowRaCMwW\nuF+iowvL+PHjZfr06VKqVDWBt3+nNObMmZPTouYa9u/fL8uWLZOjR49mfLdu3TqZPHmyzJs3TwKB\ngJw5c0aaN29pKvL7BB4xzTAlBRqZyvwu8yG82TSlScYrPLy+TJs2TSIiCkh4eF3xeApKz54PZKn5\n7FLK/VqKajL7qdH8d1i5ciXNmvXC5zsNjEIlkeqL8n8/C7wBvAD4KFgwFJ8vHZ8vgUaN4rnrrm48\n9NBgAoECpKcfpmvXjrz11uTz3hOav+Dllyfx+OMjcTrLkp6+i/fff4NTp04zYMBwRNpiGOto1KgE\nW7du48gRC4FADMpzfBvKGFESZZH+FJVD5mVgB6ra0kagOPALbnclNm9eSUxMDJs3byY6OpqKFbMu\nfwzoCFWN5ppk5cqVEhJSSWCVQHeBDgKRAnXMz+vMxTqH2O15BNaYI/kwMYxCUqRIOenXb4AULVpF\nihevJi+++LJeVP0bdu/eLW53HrlQiPoHcbsjxOHwCvxkfpciDkceMYyuoiJNY837kVegvoBdIF7g\nJoHHBSLFMOqIKsARKVZrC/F4Csnw4U9fdXnIbQWyNZr/AjVr1qRYMS+7d08lNbUjbvcMihUrxv79\np0lOLgzcARzDas1LevrtwLOoEeNRAgEPBw92Y+LEDxHpAWxn6NCxpKYmM3ToYCwWix7FX4S9e/fi\ncFQmObmo+Y2NQMBGMOhHjc7rAftIS0sASqGKnz8PjASSsNm24PdbUdk9FwJHcTrLcOutpUlJsRAZ\n2ZUGDepQuXJlXRvX5Ko/4TSaa5GEhAR5+OFB0rRpBxk69Cnx+XwyfvwrUrBgOYmMLCAOR0PTBa+F\nadt9PpNdt4MoV8kaAu8LPCIWS6jYbC6x2dzSp08/SUhIyGkRryn2798vbne08P/2zjw86urc459Z\nMsks2YAECIQlICggsoSIghBBUdwoFhWugiwWW2RxgyptLVdcri1eq4hV26tIK1ZERaFS5YIIVZSi\nEKWAoIBSBS4oAZIQssz3/nFOQKoomgkTwvk8T57MTH4zv/ecgfec866s+cpu/Gw7txGZOkA9BNdb\nR+lCwdPy+Xpo6NDReuutt5Sc3FimVd7T8vtvUqNGOdqzZ09cxkMNOFRjTVwmxuGozUybNk2BwHiZ\nPptB68DLF5Ra5d5dkChTfEyCKYKeMv1azxUE5fUmaeTIMaqsrIz3cGoNv/nNNJlksQaCL2T6m54n\n0xP3r4IcwXuCcYKwoLM8nmbq1au/ysrKVFlZqYcemqH+/a/U6NHjtX379riNBafcHY7aybZt2zR7\n9mwtWLBA5eXlR/xt5cqVCgTSZJJlFtromR5WCXWwCt8vk7Uqq/gXyWTEDpNpwLxXodBZmjHj91+7\nd2VlpR555FENHDhUN900SV988cXxGnZc2Lt3rwYPHiGvN2R365fZOTrLRsA0FwyQyTjtLpOs9JCd\n33cVDOZrxowZ8R7GEeCUu8NR+zAO1QwlJw9SJNJNZ57ZRwcPHjzimqysNlbpyDpYWwtQSkqmli1b\nppU2P1kAABdKSURBVAEDrpLP19uabtoI/kvQxTpfq8w3E5Sa2kKtWnXRHXdMPZQ9OXbsLQqFugme\nUCBwvVq0aKf9+/fHYyqqRUFBgebNm6dNmzYd8XpRUZEmTpyo/v0v1znnnCefL2AXxb72NJRhTTOn\nCXbYxTPRzl3Qzvt0GSd3O0GyLr54QJxG+c3glLvDUfs45ZQuMrVJTH2TUKifHn300SOuad26i0zt\n9xX2ug/l9SZr69atkqSDBw/q9NO7y+NpIq+3l1VKmTKx8xKslInTfl6wQqFQd40de7Puu+8+eb0B\na5Ywi0Ak0ldz586Nx1T8YH71q6kKhbKUknKxgsEMzZw5S5L0+eefKxxuKDhDppZ6S8EomQSxBoJc\nwWMCn31NVqmbGkAmQuYimQSm1YcW10AgVV9++WWcR30YaqCeu8PhqCY7d34OdLfPvJSUnMlnn31+\nxDXDh19FINAAU0a2A9CJCROup3nz5kSjUe655x4+/HAH0nSi0TRMYngPTD353pi+nRMwJWi7U1Ly\na2bMeIxf/OKfRKNRTNegKiKUlZVVa0ylpaW89957bNq0CdVQ7kpFRQXRaJT169czbdoMSkpWs2/f\nPA4cuIXrrvsJ8+fPZ9iwn1JcvB9T7eRjTImA9piyDn/DVEKZgNGNSzAt8HIwpZSXY0LHTwWaAJ3s\nnXNJSmrO5s2ba2RcdZV4L4AOx3GnX7/LlZAwXlAp+FShUI4WLlx4xDWVlZWaMuVuZWW1VdOmbfX7\n35udfTQa1aWXXqXExFbWPtxQ0N46ACusnXiuvN40eTxj7M6zXNBRJtsyx+5KLxK8KBioYDBF69ev\n18svv6zLLx+ma6/9qdavX3/M4/n444+VldVaKSkdFAw20uDBI2LqyC0qKtIll1wpny9BCQlBXX31\ntUpN7Wvnb4CMM/lmeb0pdgdeX8bZnGRNMUV2zFvsfBTJRMcMsCatiDXL3CgTTXOKPQltsNevVTCY\nrl27dsVsTNUFZ5ZxOGofu3btUrdu+fL7k5SQENS990475vc+//zzSkhoLiiwtuIbBN1kokD2CIoF\neTJhkqlWYfWVqT7ZWqYF3E2CEVapDZLPd5kikfoKBrMFj8vjuUuRSIY2btx4TDJ1736+vN6qUM1i\nhcNn6qmnnvqh0/M1RowYo6SkKwUlgn8pKekU63B+1C5sZTIlGYIyYaLNrMnlFMGFglOtSeZMa4J5\nWBCS19tMEJTHk6Jx48YpHO4o2GfHMVweT1ipqd0VDNbTn/70dMzGEwtwyt3hqL0UFRV9LVLm29iy\nZYtCoTTBOVYB9bR24uGCCdaePEjQTxCVyca8wiq9hwQemfj4563y+60OO1+bC5bY3epoQSddeumP\nDt07Go1q69at2rx589eyYdPTm+pw5qcEUzVx4m0xm6dmzTrosP1bggfVp8+FCgRCMpFC5fYUk2wX\nuO4yztCQTLGvejK1Ya4QNJbfX08+382HPs/rvVeXXjpYw4f/TMFgI6WkdFX9+k21ePFiLV++/Ig6\nNLUFnM3d4ai9hMPh79VFacyYGykpGQJ8iCkJfBMwz/4MwNiX38R0t/Rg2vf9zj7uh2mv0BBTwnYH\n0BFTA/BZTJnhPZjWgM2ACSxcuIrHHvsD27dvp1mzduTkdKZt2zx69uxHcXHxIbnatj0Nr/c5+6yE\ncPivdOhwuNRxdWnUqCHwrn0mAoF36dXrbDZsWEso9D7GNr4ZSAKewNQzzAQq8HrvACLAHPvzKZWV\nXioru9nPe45o9AUWL/47Awb0Y82aN3j11YfZsmUdffr0oWfPnjRu3BjH9yfeC6DDcULw8MO/l8+X\nYXeibwtOF0Tk84Xl8QRlImsSVK9eUwWDWTLVCosVCIzQqad2Vih0muDnghRBtkzp4FZ2V5stY5+u\nZ002VTvkt9SkyalKS8uyO/4yQbl8vkEaN27iIdmqbO7JycbmftVVw2Nqc3/vvfeUnJypcHiIIpHz\n1arV6SosLJQkXXXVUHsKGSFjNw/ZU0quTGhoijXPRFUVneTxpCsYzLOmnGwZ38PzCoWaaP78+TGT\nuybB7dwdjrrB1KnTqKz8NabeSRHwFH5/a3w+H9JrmF33TL78ch9lZXvw+c7G50unU6fNXH55fwYO\n7MrFF2+lb9+zSU4uByqAf2F68/TB7N7rYxqEVJHEgQP72b/fhzkVJGBqsoxgxYrVh67Kycnh448/\n4I03ZlFQsIxnnnkCr/f7qRlJzJw5ix//+FrGj7+VHTt2ALB3714WL15MZmYW4fAK+vRJ5t13l5Oa\nmgrAli3bMdFErwM/w5xgIpjd+0rM6UTA9ZjImKE0aZLJyJE9MCef32KapFxOSck9TJ/+1PeSu7bh\nCoc5HCcYFRXlwHkY08pEYCd5eW1YubIc6AkUADcCC6isbIfffwMpKUtYtWoNK1d2IiFhI6HQZg4e\njFJaOgdTvrYzJlzwdGASphvmdEzhrCaEw7dzwQXn8txzKzDtGgZaaZ4jEKjggQceID8/n86dO5OU\nlERpaSnvv/8++/bto2vXrkfIv3v3btavX0/Tpk1p2LAhwWDwiAJnU6bczf33z6G4eAJ+/1pmzuxI\ngwaN+eSTj4lGPcA04C3mz19Chw5dGT58CCUlB3j33X9gTEy5GEX+sn1+Gqb411rgILAAr/clsrLS\nKSh4i3r16rFhwxYWLz7wFSkPEAg49Rgr4n26cThOCCZN+qXt57lU8KRCoQZau3atsrJaC2YJ/lsm\nciYqU2QsWSYk8AUbLXKJTLp9v0PmCRMO2FUmjHKXfe+9gjQ1adJOkyf/Snfeeac1dTQXNJGJOklW\nKJSvxMSxCgYzNWfOc/r5z+9QKNRc4fAQJSU11JQpdx2S/bXXXlM43ECRSEdBRB6P6YK0aNEiSVJ5\nebn8/vBXnLJ/konu6SY4XzBWpgbMVTLRL+0EE63cy2UKfWUI1slEBFWVUL7ejnObPJ5Wmjx58hHm\noiVLligUypSJnnlIwWADLV++/Lh/tz8EXLSMw1E3qKys1J133qv27c9Wjx4XasWKFZJMCn5mZnMb\nGthDcLO1nWdYZTxOJlNzm0xRsZaCg1aJLrC29/r2+S1WcY6T15spn6++VaAvWht/C5m0/bO+YsN+\nRykpmUpKypAputVBJgQzJL8/ouHDRysSaSBYbBeImfa9rygQiOjmm29WSkqmTK303fYz+wseseMY\nLxOP3kSwVqb+yzaZFoU+wZf2vffI+B3aCMLyeuvpyAib6br22p9+bV7feOMNDRp0ra68crjefPPN\n4/21/mCoAeV+BaYtSSXwbUWLL8R0kN3E4Z6r30S858jhOOEpLy/Xhg0b1KZNJ7vLbmaV3Gj7+367\no/2loI+ggzye6xQMZqlbt152lz/JKvk9Mg7Jc2Vi5v0yST9Jgs9lnLKjv6I0i+T1+pWa2t2+5yp7\n/8Z2oUi0C8RmGeelZJKJGtmdebpM2YRz7S59mYwz9GqZEgID7bWZMi0J29uxnGoXnJ/KhHpuk6kT\ns0bhcC+1a5cnr7cq1LNSSUmX65576k6vWWrAofoBxvC27Fuu8WFirS7EtGwfgjGAORyOGsDv99O2\nbVtefPFpAoE0TPmBQqABpu3xfZjQwKmYNPw78Hpnc+uto1i3rhBYASzG9LOPYsInfwz8A5Oaf7t9\nfSXwEMb5ugLYDuQSjYq9ewuAVZiwSy/wX5gQzQim1MG7VqaPMOGWecBOTGtBH2aveCbGn7AJeM7K\nX4ZpPVgCjLPv743xDwwGqso29ACeJjHxPpo02c+cOU9Qr950UlL6EIl0oX373dx44/iYzHdtpjrK\nfQMmMPbbyMN8A1uBcuAvGBe2w+GoQdq0aUNWVjpebzbQFuMc/QCfrxjYhdnseYGL8fn8JCQkUF6e\nj9mDdQS+wNSyaQQ8BlwNXAa8hInDGAF0xcTBDwROwezb7ubwRnIv8CmmPsvFGEU+DxiL6UPaERPZ\nE8ZE5iRilPhfMIp6DybS5SWMMzQVuJ2kpPokJHwKnGvlHQo8iNk7ziUQKKNXr79xxx2ns2rVG7Rv\n356PPnqfZ5+dxIIFD7Jixf8SDH61no7jaLzO0c0ygzAdfqu4BvOv7JuI9+nG4ahTfPrpp+rR4wKl\npDTUaad1U8uWHZSQMEqmvO1gwUyFQn10xRXDtGjRIoXDrQSPy8SEr5KJC99k7dcrD5lffL5O1u4d\ntGaaqqzWB6wZZos1m0SsGaaejL0/V6bmTZFg6lf+nmofn2XNQj+TcYB6BdfYz98juFOQqN/97ndW\ntodl/AbvC54RNFNGRhv98Y9PxHvqjyv8QLPMIoz55d9/Lv2O9x1S2Md4ncPhiDHZ2dn8/e9/Y+/e\nHTz55HR274by8j8A7wAt8XpvYdy4M5k9+38477zzuPHGYXi944ALMLvythgTigezQ6+iIR5PKsY8\n48eYegoxIYrXAy0wppHFJCQIE3v+30A6JoTzRswOvyGmSmMUaIoxrazAhGQut/dahMnCTQPSyMjI\n4ssvCzEhm3/GVLrsA4zg4ovz2LbtfUaNGhHLaTxh+a5AzvOr+fmfAdlfeZ6NyZb4RqZMmXLocX5+\nPvn5+dW8vcPhAGwcedVeKxm4k8TEmYwefd2hsgd33XUHOTlNGTv2QQ4cuB1zyL4Qk9B0Hcb+vpFA\nYBWJiQEKCzMxtvEtGBPJa5jFQJgFYQv16zeiqGg/RUVeTHz8BIxSzsVYdf8CXIsx3fwZGAksxOcb\nT1paCYWFKVRWVsXJV3L33Q/x2Wfb8XrziEYzMGae1tSrt40FC6rKHtRtli5dytKlS4/LvV7HLPPf\nhB+zDLcAAsAaju5QjffpxuGos5SVlal9+zwlJo4SvKikpCvUs+cFXyv8FY1GbeXFDCUnt1dGRjPd\ne++9ys/vr/T0bLVseboWLlyoTz75RIMGDZXfn2nNKOda00yeTAGvqwVhPf7448rLO1fB4EUybf9S\nbFTM69ak0l8mbDLbRsEE5fPVV3p6MwWDzZSQ0E4mHj5Z4fBlCoVaaMiQ4YpEMuTxTBM8q1DoNP32\ntw/EaWbjDzVgIRkIbAMOYNLAFtrXszBLdBX9MeeqjzCu9qMR7zlyOOo0hYWFGjPmJp1zziW69dbJ\nKikpkSSVlpbq8ccf19SpU7V06VJJpurk6tWrD13zyiuvKBKpL78/pMaNW6mgoECS1LHjOTLJUWfI\n1JMfLbhLHs8Fys5uq9LSUpWWlmrUqFHyehsIRtrQxdsEe2XCMRPk84V1ww3jtXTpUr3wwgsKhVrI\ndEnqJhN6ucaGNw4QpCgnp4POP/9H6tPnR3riiZlfW6ROJmpCuceaeM+Rw3HScfDgQXXt2kuhUD95\nvbcpFMrWjBmH2/zt379fP/nJGHm9ydZJKsEsZWQ0V1lZmWbN+rOCwWbWQdtCEFFmZhsNHHiNduzY\nIcksDD5fut2djxZcKhP33lmmkFdExcXFh+45Z84cJSXl2ZPAc9bhWmkV/a2CjfJ4pqt+/abas2fP\ncZ+z2gZOuTscjn9n7ty5ikR6WOVp+rMmJSUrGo2qvLxcnTv3lN+fb80u/5CpuHiNEhPrHerhmpvb\ny/ZufUqBwGCdccbZWrduncaMuVHDhl2v3NxzZTJHn5ZJQmooU3HyDgUCrTRp0i+PkGnjxo02q3SW\nTAZrK8E0+96qbFgpJaW3XnvttXhMW62Coyh3VxnH4TiJKSwsRGrF4cC5lpSVlVJRUUFBQQGbNu2m\nouJpjHW1PzAZCHPw4ALefvttAoEAH3zwAdHoZ0CQsrJr2LTpNHJzz+HAgZ8htcDjqXJ0XoJJZHoY\nmEVOTjaTJt3G6NGjjpDplFNOITf3DFau3I1xzM7DRNkUYmLn04AKotGdRCKRGp2fExmn3B2Ok5je\nvXsj3Qa8AnQlIWEqeXnnkpCQQGVlJR6PH1MxsikmSegm+84GTJv2CGeddRYeTwImXgLAS3l5CRUV\n1yFNBUAqB/4Tk8h0K9CZtLS1rFq1hPT09G+U69FH76dnz36UlOwDEggGK8jPv4g33uhLScmVBINL\n6NKlJXl5eTUzMXUAp9wdjpOY1q1bM3/+s4wcOZ7du3fQo0cvZs+eDUDnzp1p3DiB0tLxlJc3wnQ3\nqiKJyspKsrOz6dixPQUF13Hw4Ej8/r8RCJRRXl7vK9f2oHHjRqSnl7Jjx6107nwqM2euPKpir7r3\n228v4bHHniQajTJq1Kt06dKF2bNn884779G27WWMHj0an89XI/PiiC3xNl05HI5/Y/fu3Ro6dLRa\nt+5knaKzBS8pFMrRk0+axtd79+7ViBFj1K7dWRo48BrNmzdPoVBD6wz9hfz+Rho2bESNyFdcXKz/\n+I9RSk1trOzsdnrppZdq5D61GY5ic/d804txwsrpcDhqI6+++ipTpz5IWVkFY8cOY9iwa4567Suv\nvMKQIdezf38m0oWEwy8wZswgfvObqTGVafDgkbz00n5KS+8HPiIUGsKyZa98rUFIXcY2OvmaLnfK\n3eFwxJx33nmHvn2HUly8FmOP30UgkMPOndtIS0uL2X2SkzMoKirApNeAzzeJO+9MY/LkyTG7R23n\naMrd9VB1OBwxp7CwEJ8vm8OO1gb4/cns27cvpvcJh1MxRWcNgcCWQz1VT3accnc4HDEnNzcXj2cd\n8CdgJz7fXTRq1IAmTZrE9D4PPngPweCP8Xh+SVLSYBo2XMfQoUNjeo8TFWeWcTgcNcLq1au5+urr\n+fTTzXTs2IVnn/0fsrOzv/uN35O33nqLV199jfT0NEaOHElKSkrM71GbcTZ3h8PhqIM4m7vD4XCc\nRDjl7nA4HHUQp9wdDoejDuKUu8PhcNRBnHJ3OByOOohT7g6Hw1EHqY5yvwL4J1AJdPmW67YC7wOr\ngZXVuJ/D4XA4jpHqKPcPMH1Ul33HdQLyMUWhv1fx5ePV4ft4UZfGU5fGAnVrPHVpLODG80OpjnLf\nAGw8xmt/ULKU+1JrL3VpLFC3xlOXxgJuPD+U42FzF/C/wCrgJ8fhfg6Hw3HS812dmBYBjb7h9cnA\n/GO8Rw9gO5BhP28DsPxYBXQ4HA7H9ycWtWVeB24B3juGa38NFAH3f8Pf1gBnxEAeh8PhOJkoADrV\nxAe/Dhyt7UkISLaPw8CbQL+aEMLhcDgcsWEgsA04AOwAFtrXs4C/2sc5mB35GmAtcPtxltHhcDgc\nDofD4XDUJBdiHK+bgJ/HWZbq8gSwE5MXUBfIxpji/ok5jY2PrzjVIgl4B3OyXAfcG19xYoYPkzR4\nrEEPtZmt1J0kyDRgLrAe8++te3zFOf74gI+AFkAC5j/eafEUqJqcg0ngqivKvRGHnTcR4ENO7O8n\nZH/7gbeBnnGUJVbcDDwNvBxvQWLAFqBevIWIEU8BI+1jP1CjzV5rY22ZPIxy3wqUA38BBsRToGqy\nHNgTbyFiyA7Mggsm8mk9Va3nT0xK7O8AZmPxZRxliQVNgYuAP1K7Oq1Vh7owjlTMRu8J+7wC2FuT\nN6yNyr0JxlFbxb/sa47aRwvMqeSdOMtRHbyYxWonxty0Lr7iVJsHgIlANN6CxIi6kgTZEtgFPIkJ\nG/8Dh0+NNUJtVO6ukeqJQQRjP5yA2cGfqEQxZqamQC9MHaQTlUuA/8PYp+vCbhdMEmRnoD9wA2b3\neyLixxRYfMT+LgZuq8kb1kbl/hnGaVdFNmb37qg9JADPA38G5sVZllixFxPCmxtvQarB2cBlGDv1\nM0AfYFZcJao+2+3vXcCLfM/ig7WIf9mff9jnc/n2arp1Ej/wMebIH+DEd6iCGUtdcah6MArjgXgL\nEgMaYCIYAIKYCqd94ydOTOnNiR8tU9eSIJcBbezjKcB98RMlfvTHRGF8xImf+PQM8DlwEONLGBFf\ncapNT4wpYw3m+L8aE7p6InI6xv65BhNuNzG+4sSU3pz40TItqVtJkGdgdu4FwAvUcLSMw+FwOBwO\nh8PhcDgcDofD4XA4HA6Hw+FwOBwOh8PhcDgcDofD4XA4HA6Hw+Fw1Cj/D1e3dccSCqvYAAAAAElF\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7feded7a9e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "max_weight = np.max(conditional_gmm.priors)\n",
    "max_ind = np.where(conditional_gmm.priors == max_weight)[0][0]\n",
    "\n",
    "fig = plt.figure(0)\n",
    "ax = fig.add_subplot(111, aspect='equal')\n",
    "ax.scatter(X, Y)\n",
    "ax.scatter(conditional_gmm.means[max_ind], 0.5, 50, 'r')\n",
    "plt.xlim([-0.1,2 * np.pi + 0.1])\n",
    "plt.ylim([-1.5,1.5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Ranking\n",
    "\n",
    "- Max\n",
    "- Mean of most weighted Gaussian\n",
    "- Sample\n",
    "- Weighted Mean"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bigger redundancy: the need to adapt the number of gaussian"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generate more redundant data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "rng = np.random.RandomState(10)\n",
    "X = np.linspace(0, 6 * np.pi, 1000)[:, np.newaxis]\n",
    "Y = 6*np.sin(X).ravel() + rng.normal(0, 0.5, X.shape[0])\n",
    "Y = Y[:, np.newaxis]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-6.5, 6.5)"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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gqx0pj8LCtSQkJJTZsUX53/hbs0pBQYEcDq9M6mfQbp9S7Db3n4IY+XwnCC6Xx9NGrVp1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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7feded849ed0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(0)\n",
    "ax = fig.add_subplot(111, aspect='equal')\n",
    "ax.scatter(X, Y)\n",
    "plt.xlim([-0.1, 6 * np.pi + 0.1])\n",
    "plt.ylim([-6.5,6.5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Build Tree to find NN"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.neighbors import KDTree\n",
    "X_tree = KDTree(X, leaf_size=2)\n",
    "Y_tree = KDTree(Y, leaf_size=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Inverse Model\n",
    "\n",
    "## Find local data for y=3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "_, ind = Y_tree.query(3, k=100)     \n",
    "local_X = X[ind]\n",
    "local_Y = Y[ind]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot local data at y=3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-6.5, 6.5)"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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xCmYREY9RMIuIeIyCWUTEYxTMIiIek2gw/wr4EvgMeDDxckREJJDA354NXAic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\nYgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7feded614a50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(0)\n",
    "ax = fig.add_subplot(111, aspect='equal')\n",
    "ax.scatter(local_X, local_Y)\n",
    "plt.xlim([-0.1, 6 * np.pi + 0.1])\n",
    "plt.ylim([-6.5,6.5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fit local GMM with 3 components"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "GMM(covariance_type='full', init_params='wmc', min_covar=0.001,\n",
       "  n_components=3, n_init=1, n_iter=100, params='wmc', random_state=None,\n",
       "  thresh=None, tol=0.001)"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "local_gmm = GMM(n_components=3, covariance_type='full')\n",
    "local_data = np.squeeze(np.concatenate((local_X, local_Y), axis=2))\n",
    "local_gmm.fit(local_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot local GMM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "local_gmminf = gmr.gmm.GMM(3, \n",
    "                           local_gmm.weights_, \n",
    "                           local_gmm.means_, \n",
    "                           local_gmm.covars_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ellipses = local_gmminf.to_ellipses(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-6.5, 6.5)"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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2Y445hmXL5jFuXDvGjWvNkiXf06lTp2iXVaM6d+7MmDF34fV2w+UajGV1p2/f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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7feded743210>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib.patches import Ellipse\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111, aspect='equal')\n",
    "ax.scatter(local_X, local_Y)\n",
    "\n",
    "\n",
    "for ellipse in ellipses:\n",
    "    e = Ellipse(xy=ellipse[0], angle=ellipse[1][0]*180/np.pi, width=ellipse[1][1], height=ellipse[1][2])\n",
    "    ax.add_artist(e)\n",
    "    e.set_clip_box(ax.bbox)\n",
    "    e.set_alpha(0.5)\n",
    "    e.set_facecolor(rng.rand(3))\n",
    "\n",
    "plt.xlim([-0.1, 6 * np.pi + 0.1])\n",
    "plt.ylim([-6.5,6.5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**There is not enough gaussian to model this properly**\n",
    "\n",
    "Such problem are arise quite often in our simple example, e.g. multidimensional arm\n",
    "\n",
    "**Note that the same problem might arise with a simple NN model if we take the weighted mean of more than 1 neigborh**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## We compute and plot the conditional for y=3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "conditional_gmm = local_gmminf.condition([1], [3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7feded68de50>]"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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uYt+vH/TvHx8P0u9Qd3VAVUdU7MPDCrF/4414eCUdGT9e/i/X2L1bimmNGGHa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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7feded71c050>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "proba = conditional_gmm.to_probability_density(X)\n",
    "plt.plot(X, proba)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Find the Max"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "max_proba = np.max(proba)\n",
    "max_id = np.where(proba == max_proba)[0]\n",
    "max_value = X[max_id][0,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7feded72b9d0>]"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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11nS5siDuYj9gAAwcGB8P0k+ou9qhKhMV+/CwQuxfeSUeXkkmEyfK/+Uae/fK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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7feded871690>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X, proba)\n",
    "plt.plot([max_value, max_value], [0, max_proba] , 'r')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-6.5, 6.5)"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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KYIiMigsAfsDp0zfw1Vdf4euvP0Nqahrs9o0Q2TQ+EDGcugC+B1AJohDlGoCTAILk32oB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GKxNopG5wneUCRylwoLO+rdd9/N9LRbBVOnfs49SPe6436Mc1H0cw/TO2X+zW3u338sS7Fb5LbU\nX5Y1Xf2sIFAQ5Oqmm27J9LRaFVu2bFFpaQ9FIoWyprZVgl6Cupzz1xSGfQ/oM8+ePdfdV0lZ38WX\n3ULpWMF49/uzZfGfutjPozrxxIpGjdMb5iOMHj0GCJ5SXbqNrbh6uYvhFPfkvsEZbMmE9NsL+go+\nKRPUqTPcXxHc7j7jCsFvnYGvFwnPyxviA4JNxODBZ7pjPdqdj2xZ9V6BzEcpWTPVce4Gv9zd2P8l\nK+vNFZQoFmurT3xigq/ObCb279+v2bOvUxgOkO1S8gXLZcVdWYKY8vPbKD+/kyAqGCuL1XQQrJLt\nVvNVLzY2Rg0rdqPRGzVx4rmNGuPBDLP3MWeAUaOGk0x+C9iN+SdTWLPP3ViK3BrMx1yL+aDvAkZg\n/q//wSQjl2OpWyuAyzG/9M1YA9ZdmEQhQBW1tW+Qn39wgXfPR6O8vAem7/sc8FmsF+B7WFrjTOAt\nYAZZWU+RSp1GJHI3sBCYhUmyjgPOJxYLGTly+CFJUXo+OtFolHnz5jJz5iRycydhMZxLMK3yfCDK\nzp017Nx5KWYG6+6Pblh8YBswFFgCfBP4vXt9GtHoSNq0+QG33DK/JafU5DTRM7D1sHfvXp199meU\nlRWX+Ym7yXxYKcGfBN9zK+hvyPxcZTI/WbnMB1bcYKs8wq0AkoK/ut9dIXNrXKucnNM0fvx0L2jU\nRGzcuFGxWDu39U3LpFU7uZVYV0G2Uql2Wrz4Tl199dUyN5RkWTXjGmyFX1IYFmR6Oq2W3bt3a82a\nNXrkkUc0a9Y1gpPcDrRI8Cm3c6lr7TXE/Zxyr9urvnS+XHU9Gc1t9VllZQ1R58699N577zVqjDSj\nK+My4AXgeeA/vGE+NGpqapweRpGsSqm7uyjOkanO5auwsEwDBw5WEHSQ+bxCt+06X/C2zN853H11\nlQUKB6l79z6aM+daLV269KCKdZ5D57rr5rsHap2W9i4lEh01c+ZMvfbaa5KsKWskErpztldwlTuv\ndYZ5p2KxhH9gNgOVlZU65pjeyssbotzcU1Ra2k1ZWeZCMvdTXVC9Ls6zTRbjScr8/8ucS2O5e8/f\nnVGvb56bkzOm0brZzWWYz8DK1OrKzP5Z8NQb5o/EmjVrNHLkJI0YMUmdO/dWLDZIkchVCsNumjdv\ngfbu3asuXY53T+wit1orFkScgXhSFqRICZKaMGHCBwp/e5qOhQtvVnZ2OyWTn1MQdFRRUQ9ddNFX\ntH37di1fvkJBELob71xZvnmezA/9E8EzgtEaNWpipqfRKjnvvEsUi13pjGhaQXCpBg8e6naWeW4X\nk+POx2WqD/zlymQRpsqC7hJcLVOWC2R1BXVKdBdp8eLFjRpncxnmn1Kv8H0wmuhwtz7S6bTOO+8S\nJRJFSqV6qKSks8Kwj0xbQYI3FARJLViwQEEwTBb93y7Tce7rVs+lzkjPEgxXWVlvH1BqIZ5++mkd\nf/zJisfHClYpCC5V5869lEwWyUSO2srcUsvcTb9RVkx0vGKxXlq6dGmmp9AqGTx4lN4v3blSQ4ee\npVgszy1e/iAL6PVz5+V5wedkGRlzVd+tpr6zUDxeqHh8ivvbZcrJKdbLL7/cqHEezDA3Jvh3LHA6\n8BTWAXRgIz7rqOS+++7j5z/fRFXVX9i1awWVlXvZs6eI+k1ILbW1WcyePZeamq5AKaansQwLDE7E\nAoc/ARJABZWVrxGJRDIwm6OLJ598kvnzF/HCCy+wb99KYCI1Nd/l7bdFNNoLuBArOLkRuAILzqaB\ntcBjxOO76d2794d+vufwGTZsIMnkD4FqoIpk8m6OPbYT0WgKKzpZghX47MDWlsdjPQInAddjuhpP\nE42OIwiuIAwXsnz53Zx7bjtKS6fQr9/tPProg3Tv3r3Z5vCvRIwexVrD/iNz3HsLsDbPJ2Mr6G4f\n9CHXX3/9gdcVFRVUVFQc+khbIc88s5nduycBNcAYTBhnPlYJ2BcYitQFqQh4CDO+P8aehW2BXOyi\nGk19W/XvsHPnToqLi1t0LkcT69ev56yzprJnzwzsvNQ/CKPRBDU1L2BZMU8CXwHWMnLkCJ54YjxB\nUE5NzQtceunnGTjQr2Wag3nzvsHmzeeydm0JkKZnz948/fT/UVPzHpZ9cSdmoNtjlZqvYPfWD7Cs\npkoSia6MGhUwZEgHRo/+FeXl5UyaNKlR41q3bh3r1q1r1Gd8FH4JDG/w88vYcu4faaINSuvj7rvv\nVhgOk7UqGua2TU+5gFFclivb2wUi5rttV+j8XT1VX9zwW1mGwK3q3Lm3Dyg1M5/85FRZbnlaFogd\nJ3hQ8fgMde3aV/PmLVAy2U55eWcoO7tAd9xxp7Zt26b7779fd955p7Zs2ZLpKRwVvP3221q06BaF\n4bGyPPJJzoVxpfMzD3YxgBx3Dts4X3OJotFcVVSM07333t9s46OZfMxfBG5wr3sCr33I3zXbxD7u\n1NbWasKETyuRqOv/tkeW3J6SKZFNlImoXOaM9t9lanN9ZO1u6oIWCUFM3bv309atWzM9rVbPGWdM\nlFX0nX3gHMRiJRo8+HSFYYGysuI6+eShKizspOzsdoJQkUiOwvB0hWGpZsy4KtNTOGro3fsUmah9\nnb+4nyxNbocsA6pI8HUX4OsoKxIqlYnk/0hheJxuvvk7zTK25jLMAebc3Aw8DVR4w3zopNNpPfvs\ns6qoGKOcnIEuYHSbTGqwkyzbYpALOpS6VXKBTNGsUvC0giD3QJqWp/n52c9WKhYrkklCVgl2Kxbr\npyAolaXQ7VIk0lHwVVlgto3qWxjtUBh2PdDeyNO89O07RPDfDQzzhcrKKpapAU51hnm04HR3vm6S\ntQ+r+/tnVVTUuVnGdjDD3JjgXw1wHuZFH4AFAD2HSCQSoby8nF//+iHuuutKYC/m/2oLPA7sJhLZ\nSiQyAjgJaIP5NE/EXP1jmDZtCmVlZRmawdHHlCln06lTGfBVrIFBSG1tkpqaSzA1wAlIlViF5iws\nCHW6e3cbotFTeOWVVzIx9KOOOXMuIwy/CNwD3EJOzkMsXHgNPXteSzy+AVNpfA5rfrAWq5oNG3xC\nyP79tS0+7hYryW4Jp/fHmWg0yjnnnEMqlY0Z3J9jz7rfcfrp/cjJycICFYOBczBZwnJgLM8882KG\nRt16+VfX66BB/YnF6v7md8Az2MbxdGAsFgd/E3vIlmKZNAB/Jp1eR3l5edMP+ggnEzbg05+ezrJl\n32PcuEeZNu05Hn/8ES644AKGDz+V4uI87MFaiMkbVGD31Q+wRVAp0egwpkyZ0OLjbgkkSXPnzm2W\n7UBr4xe/+IXi8Vy3FQ4ViXxGWVmnuO1wB1l3k4UNtlqXqHPnvpkedqvjX12vmzdvVirVTrHYYGVl\ndZQJ3BTJRNb3CAY633+erKw3FBQrEklo0aJbW2YSRxhHgg2oqqpSz54nKggukhWRFMmEqNrIgutJ\nRSK5LpbziiKRRWrXrkujy68/CLyI0ceHsWPHsmXLH+jfvyuRyA1It7N//xZgPZbqsxpYBGwAXiIr\naw1Tp47P5JCPOnbt2sX48dOpqjqL2tqBmADVevd9DyasXga8iu1w2mGiOI+RnT2CbdveytDIj27W\nrVvHrFmzePXV96ip+SXwGyxNLgv4MvBtIBspH8s/74Z0JVVVxTz33HMtOlbfjPUIpEePHsTjIVIf\nzE9ZgLny/wjcTyTyNbKzzyaZzKZHjzIWLLjhoJ/naVoefvhhtm/vRG3tEgD27w+AxZj7YgBwN+aO\naodtlT8P5AF9qKr6Ehs2fC8Twz6qmTPnBm69dSk1NX3Zt+/vwHcxFbl7gPswBbk/Y+drL+ZrzgWq\n2bfvTVKpVIuOtyVKxNbx/nxnj8fj8cBjfHg2m8fj8Xg8Ho/H4/F4PB6Pp57RwJ+Al7Ce4p6m4S9Y\nZvwmrN+U5/D4EVCJVbDWUYgJeG0FHsGqejyHxgcd1+uB17FrdhP1ylueFiYLEzfqgpVwPwN4rcOm\n4c+YAfE0jmFYGWVDA7IQuMq9vhpY0NKDagV80HGdC1yZmeF8vGjuPOZBmGH+C1bC/QAmIuxpGrzw\ncuN5HBPmbcgETF8V971xeo9HJx90XMFfsx+J5jbMHYG/Nvj5dfc7T+MR8Cusfe/FGR5La6ME24bj\nvpdkcCytjcuAZ7Fkb+8i+hCa2zA3i6ydB4Ah2FbxLOBSbOvoaXqaTZ7xKOQOoCvQHyuFXJTZ4Ry5\nNLdhfgOrTa2jDFs1exrPNvf9beA/MbeRp2mopL5zTwfA11A3DW9R/6D7If6a/VCa2zD/HusN2AWI\nA9OBB5v5/zwaCLF6UTD5slG8P8jiaRwPAue71+cDqzI4ltZEhwavJ+Ov2YxyFvAiFgS8JsNjaS10\nxTJcngGexx/XxrAM+BvWLfWvWBfVQsx/79PlDp9/PK4XAUuxFM9nsYed9917PB6Px+PxeDwej8fj\n8Xg8Ho/H4/F4PB6Px+PxeDwej8fj8Xg8Ho/H4/F4PB/E/wMl6e3s0VRWzgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7feded892710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(0)\n",
    "ax = fig.add_subplot(111, aspect='equal')\n",
    "ax.scatter(X, Y)\n",
    "ax.scatter(max_value, 3, 50, 'r')\n",
    "plt.xlim([-0.1, 6 * np.pi + 0.1])\n",
    "plt.ylim([-6.5,6.5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "** This is not desired **"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Would DPGMM solve the problem?\n",
    "\n",
    "Short answer: I did'nt succeed, on paper it is what we look for but in pratice it did not work on this simple example.\n",
    "\n",
    "I tried as above, simply replace GMM by DPGMM. It looked to me some prior was pulling Gaussians towards [0,0] but I am not sure at all..\n",
    "\n",
    "So I tried scaling the data, but this didn't help.\n",
    "\n",
    "## Fit local DPGMM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DPGMM(alpha=1, covariance_type='full', init_params='wmc', min_covar=None,\n",
       "   n_components=10, n_iter=10, params='wmc', random_state=None,\n",
       "   thresh=None, tol=0.001, verbose=False)"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.mixture import DPGMM\n",
    "local_gmm = DPGMM(n_components=10, \n",
    "                  covariance_type='full', \n",
    "                  alpha=1,\n",
    "                  tol=1e-3, \n",
    "                  params='wmc',\n",
    "                  init_params='wmc')\n",
    "local_data = np.squeeze(np.concatenate((local_X, local_Y), axis=2))\n",
    "local_gmm.fit(local_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Play a bit with the parameter to get a sense of what is a happening: http://scikit-learn.org/stable/modules/generated/sklearn.mixture.DPGMM.html#sklearn.mixture.DPGMM**\n",
    "\n",
    "## Plot local GMM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "local_gmminf = gmr.gmm.GMM(local_gmm.weights_.shape[0], \n",
    "                           local_gmm.weights_, \n",
    "                           local_gmm.means_, \n",
    "                           local_gmm._get_covars())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "ellipses = local_gmminf.to_ellipses(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-6.5, 6.5)"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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i4rYx6KRhnD74XPr06dNlr5OoKArDhg3BZssgErkY+B/My8ydBozmxRdf5Pbb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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7feded655490>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib.patches import Ellipse\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111) ##, aspect='equal')\n",
    "ax.scatter(local_X, local_Y)\n",
    "\n",
    "\n",
    "for ellipse in ellipses:\n",
    "    e = Ellipse(xy=ellipse[0], angle=ellipse[1][0]*180/np.pi, width=ellipse[1][1], height=ellipse[1][2])\n",
    "    ax.add_artist(e)\n",
    "    e.set_clip_box(ax.bbox)\n",
    "    e.set_alpha(0.5)\n",
    "    e.set_facecolor(rng.rand(3))\n",
    "\n",
    "plt.xlim([-0.1, 6 * np.pi + 0.1])\n",
    "plt.ylim([-6.5,6.5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note that the Gaussian you see at [0,0] are the ones that are not in use, there is a way to know this. See here: http://scikit-learn.org/stable/auto_examples/mixture/plot_gmm_sin.html#example-mixture-plot-gmm-sin-py**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Let's try to estimate the number of clusters with a clustering algorithm\n",
    "\n",
    "See: http://scikit-learn.org/stable/modules/clustering.html\n",
    "\n",
    "I picked: http://scikit-learn.org/stable/modules/generated/sklearn.cluster.AffinityPropagation.html#sklearn.cluster.AffinityPropagation\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "We found 6 clusters\n"
     ]
    }
   ],
   "source": [
    "from sklearn.cluster import AffinityPropagation\n",
    "\n",
    "af = AffinityPropagation(damping=0.6)\n",
    "af.fit(local_data)\n",
    "n_clusters = len(af.cluster_centers_)\n",
    "print(\"We found {} clusters\".format(n_clusters))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot the clusters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-6.5, 6.5)"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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dyq233snJk8fZunUrRUVNOOecHPbt2054eMWrTmqDefPmMWzYcG76zWgaNzzzvIjcvOO8\nPfdFbr31Jv7y6F+CUo8xBperLgXeVBxRS4iLO4eWycnce1c61113HRERZS8VrA1KP7gtM6NDdsRd\nWFjIa6+9RnR0NA0bNiEzcxpwnAEDrg9qHcePHyfC6aowtAEauuI5cuxIkKqqvpo1a8bDj0zkib8+\nTo/YDjSM+nFlQF5RPl8e20KdhDjGjRsXkvqSk5NZsWIpWVlZ/OpXyRQU/IMjR/qSm5sbtOu6V2e9\nevWiT58rmP7aYzRLakfHdik4HU727N/Ohq9XkJaWxqS/TApqTeee25jvv2+Is8jFvaPuYdu270hJ\nSanVoX02ITviHjv2IZ5/fgmWlU1Gxm04HA6aN2/OwIEDz7pEyJ8KCwuJq1efD9xfUT+y/P7n6u8/\n45nDE/hyk26qANC1S0++XLsKlyOc+pHn4A3z8n3BMW6+aShPP/t3YmJigl6T1+vlk08+IT4+ng4d\nOvDww39h+vTXuf76/rzwwjNB/b2qrlJT+/Hpp59T8k+/BZGRW3G7U+ncOYVRo+6iSZPgr+D47rvv\nePvtt6lTpw5jxz7FiRPX0q7dF2zc+J+g11KdVMsj7v37D3DyZEccjoPk5p4gI0S94/DwcAZdP5i5\nG/7JHS3vK3fcmzueZ/DdwevZVnfbtu+i0LuYsPARZIfncPx4U5zOLYybMD4koQ1wzz3388orH+L1\nZjFmzCiefHIyxcUOXn/9PWJjz+WxxzJCUld1sWvXLlauXA20BUYTHj6OZ599lpEjQ7vSpmnTpowd\nOxaPx4MxhRjj4cCBI+Tn5+tU93KErOv/xBN/5sorv6dvXyepqZcG9Eyts7nv/nt5Y/ezfH2k7KPp\n+ftms+zgIpo2rfgsr9pk0qSHcLkG0KlTEg5HOEVFd+JwnEtW1s9XdQTL8uVryM1Nx5gevP76v0s/\nN+nHiRM9Wbw48Fe7q+5uvnkUJ0/eDPyAZY3k7bf/EfLQPp3b7aZDh+ZYVluys5vx/PMvhLqkaitk\nwZ2QkMC0aZP59FMPV1/9W0aMCN0a6Y4dO/LKGy+Tvu56Jm8ez5ZjG/nh5CHWHV7On1bdysS1aRiH\nxfLlK9m0SffDA0hP/x0nThzjP/9ZwKxZr9Kly1uMHj2Unj17hqymKVMeISHhaVq02E9+/gksaxiW\nNZ+4uCU89ljtXlECEBkZQVhYNlFRFkOGDOGjj5Zw6NChUJd1ho4d2xMefgyH4zjR0VGhLqfaCumq\nkjlz5jBs2BRycx+lceORZGZuDUI55du1axfTnp/GrJnvkJ1zjMYN4uk/sB/Nmifxpz9NJD9/OA0b\nvktW1q6Q1ikVS0npxdq1g3C5PuDxx/szZsyYUJdULWRlZfHkk1M5cGA/7767lcLCVlxzTTHvvvtG\nqEs7JScnh8mTpxIXdw7p6aMDfsGr6qyiHncwlHuHh+PHj5uLL77UREbGmJdemhHQu0n4YvPmzcbl\namBgiqlXr0Goy5GzuPPO35s6dTqZqKgG5rPPPjPGGLNs2TLTunUXc+21Q01eXl6IKwwdr9drOne+\nzEC4gUamS5ee1fIOQfPmzTOpqdeYadOmh7qUkKGCO+CEfB13dbdq1SqWLl0KhPH552sZN+5uevTo\nEeqypAJFRUXMmzePxMTEU9eV7tDhEr766maio2fzwgu3M3x48O5lWp3s3LmT5OQLKS4uBOrjcjmZ\nO/cl+vYt/8JTwWSMobi4mDp1YikoeBaX609s2rSGpKSkUJcWdBUdceuUpArs378ft7sfDzzwFVOn\nvkiHDhfwu9+NZ86c2nsnla1bt/Lmm29y5Ej1XdPudDoZOHDgGTcDaN++NXXqvIkxX9fqmwiff/75\nWFYk8DbQBq+3mBMnToS6LKDkIlgxMfVp3LgZ0dF1CAtbiWWZWn/ji7LoiLsCmzdvplMnNydO/A2H\n4y7CwqIoLHwRl6vkg7naJjMzkxYt2gIX0bx5Hl99tSLUJVVaQUEB7777Ls2bN6dr166hLiek7r77\nj8yY8TbFxce4++6RPP305GpxWnn//jcyf74by/qWUaOKSEiIp0+fPnTr1i3UpYVERUfc/gjuJsA/\ngYaU9GReAp457XnbBjfA5Ml/5/nnX2L//jAKCqJwOPJISnKwbdv6UJcWdAMH3sR7730ChBEZmUd+\nfk6oS5JfwBjDunXriI+PJz4+PtTlnDJjxmukp4/Fsor56KM5pKamhrqkkAp0cDcu/foSiAHWANcB\n/103Z+vgBpg48c88/viXeL31SUnZznvvzaJRo0ahLivozjuvKYcP/xvLupN77rmCp56aHOqSpIbZ\nvn07LpeLhISEUJcScoEO7p+aCzwLLCr93vbBnZ2dTVrafeTlneDFFyfTuHHjUJcUElOmPMO4cffR\npk0nli//hLp1K76+i4j8csEM7iRgKdAO+O/7aNsHt/zI6/VWi36oSE0XrFUlMcBsYAw/hrbUMApt\nkdDz10WmwoF/A29Q0io5w+nXZXa73bjdbj9NKyJSM3g8HjweT6XG+qNVYgGvA4eBe8t4Xq0SEZEq\nCnSPuyfwKbCBH0/RnADML91WcIuIVFGwV5X8lIJbRKSKdMq7iEgNouAWEbEZBbeIiM0ouEVEbEbB\nLSJiMwpuERGbUXCLiNiMgltExGYU3CIiNqPgFhGxGQW3iIjNKLhFRGxGwS0iYjMKbhERm1Fwi4jY\njIJbRMRmFNwiIjaj4BYRsRkFt4iIzSi4RURsRsEtImIzCm4REZtRcIuI2IyCW0TEZhTcIiI2o+AW\nEbEZfwR3P2AzsBUY74fXExGRClg+/rwD+Ba4AtgHrAKGAptOG2OMMT5OIyJSu1iWBeVktK9H3F2B\nbcAuoBB4Cxjo42uKiEgFfA3uBGDPad/vLX1MREQCxOnjz1eqB5KRkXFq2+1243a7fZxWRKRm8Xg8\neDyeSo31tcfdHcig5ANKgAmAF/jbaWPU4xYRqaJA9rhXA8lAEhABDAHe8/E1RUSkAr62SoqAdOBj\nSlaYzODMFSUiIuJnvrZKKkOtEhGRKgpkq0RERIJMwS0iYjMKbhERm1Fwi4jYjIJbRMRmFNwiIjaj\n4BYRsRkFt4iIzSi4RURsRsEtImIzCm4REZtRcIuI2IyCW0TEZhTcIiI2o+AWEbEZBbeIiM0ouEVE\nbEbBLSJiMwpuERGbUXCLiNiMgltExGYU3CIiNqPgFhGxGQW3iIjNKLhFRGzG1+B+EtgErAfeBc7x\nuSIREamQr8G9AGgHXAhsASb4XJGIiFTI1+BeCHhLt1cAiT6+noiInIU/e9x3AB/68fVERKQMzkqM\nWQg0LuPxB4D3S7cfBAqAmX6qS0REylGZ4O5zludvBwYAl5c3ICMj49S22+3G7XZXYloRkdrD4/Hg\n8XgqNdbyca5+wBQgFfi+nDHGGOPjNCIitYtlWVBORvsa3FuBCOCH0u+XA3f/ZIyCW0SkigIZ3JWh\n4BYRqaKKgltnToqI2IyCW0TEZhTcIiI2o+AWEbEZBbeIiM0ouEVEbEbBLSJiMwpuERGbUXCLiNiM\ngltExGYU3CIiNqPgFhGxGQW3iIjNKLhFRGxGwS0iYjMKbhERm1Fwi4jYjIJbRMRmFNwiIjaj4BYR\nsRkFt4iIzSi4RURsRsEtImIzCm4REZtRcIuI2Iw/gvs+wAvU98NriYjIWfga3E2APsB3fqhFREQq\nwdfgfgoY549CRESkcnwJ7oHAXmCDn2oREZFKcJ7l+YVA4zIefxCYAFx52mOWv4oSEZHynS24+5Tz\neHugGbC+9PtEYA3QFTj408EZGRmntt1uN263u4pliojUbB6PB4/HU6mx/jpK3gmkAD+U8Zwxxvhp\nGhGR2sGyLCgno/21jlvJLCISJMHoS+uIW0SkioJxxC0iIkGi4BYRsRkFt4iIzSi4RURsRsEtImIz\nCm4REZtRcIuI2IyCW0TEZhTcIiI2o+AWEbEZBbeIiM0ouEVEbEbBLSJiMwpuERGbUXCLiNiMgltE\nxGYU3CIiNqPgFhGxGQW3iIjNKLhFRGxGwS0iYjMKbhERm1Fwi4jYjIJbRMRmFNwiIjaj4BYRsRlf\ng/v3wCbgK+BvvpcjIiJn4/ThZ3sB1wIdgUKggV8qEhGRCvlyxJ0GPEZJaAMc8r0cERE5G1+COxm4\nDPgC8ACd/VGQiIhU7GytkoVA4zIef7D0Z+OA7kAX4G2geVkvkpGRcWrb7XbjdrurXqmISA3m8Xjw\neDyVGmv5MM9HwOPA0tLvtwHdgMM/GWeMMT5MIyJS+1iWBeVktC+tkrlA79LtVkAEPw9tERHxM19W\nlbxS+rURKABu80tFIiJSIV9aJZWlVomISBUFqlVSJZVtussvo/0bWNq/gaX9WzUK7hpC+zewtH8D\nS/u3anStEhERm1Fwi4jYTDA+nPQAqUGYR0SkJlkKuENdhIiIiIiIiIiI0A/YDGwFxoe4lppqF7AB\nWAesDG0ptvcKkEXJGcH/VZ+SC65tARYAsSGoq6Yoa/9mAHsp+f1dR0lmSAg5KLn4VBIQDnwJtAll\nQTXUTkrCRXx3KXAxZwbLE8C40u3xlFxcTX6ZsvbvI8AfQ1OOPQV6OWBXSoJ7FyU3XHgLGBjgOWur\nYKwQqg0+A4785LFrgddLt18HrgtqRTVLWfsX9PtbJYEO7gRgz2nf7y19TPzLAJ8Aq4GRIa6lJmpE\nydt7Sv/bKIS11FS/B9YDM1Ar6qwCHdy6ulRwXELJ28/+wGhK3o5KYBj0e+1vLwLNgIuATGBKaMup\n/gId3PuAJqd934SSo27xr8zS/x4C5lDSohL/yeLHO0HFAwdDWEtNdJAf/yC+jH5/zyrQwb2akntT\nJlFyo4UhwHsBnrO2iQbqlm7XAa7kzA9+xHfvAcNLt4dTchMR8Z/407avR7+/1UJ/4FtKPqScEOJa\naqJmlKzW+RL4Cu1jX/0vsJ+Sm4PsAUZQsmLnE7Qc0B9+un/vAP5JyXLW9ZT8UdRnCCIiIiIiIiIi\nIiIiIiIiIiIiIiIiIiIiIiLyy/0/pQ8KejRAVy0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7feded709ed0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111) ##, aspect='equal')\n",
    "ax.scatter(local_X, local_Y, 5)\n",
    "\n",
    "for cs in af.cluster_centers_:\n",
    "    ax.scatter(cs[0], cs[1], 100, rng.rand(3))\n",
    "\n",
    "plt.xlim([-0.1, 6 * np.pi + 0.1])\n",
    "plt.ylim([-6.5,6.5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Let's use this number ot fit the GMM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "GMM(covariance_type='full', init_params='wmc', min_covar=0.001,\n",
       "  n_components=6, n_init=1, n_iter=100, params='wmc', random_state=None,\n",
       "  thresh=None, tol=0.001)"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "local_gmm = GMM(n_components=n_clusters, covariance_type='full')\n",
    "local_gmm.fit(local_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "local_gmminf = gmr.gmm.GMM(n_clusters, \n",
    "                           local_gmm.weights_, \n",
    "                           local_gmm.means_, \n",
    "                           local_gmm.covars_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "ellipses = local_gmminf.to_ellipses(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-6.5, 6.5)"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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650doxsEciUQYP/4ennvuFbzeDMaPv5FTTz011WUlTSAQ4Oyzf8MHH0zFshwM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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7feded5d0d50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "from matplotlib.patches import Ellipse\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111, aspect='equal')\n",
    "ax.scatter(local_X, local_Y)\n",
    "\n",
    "\n",
    "for ellipse in ellipses:\n",
    "    e = Ellipse(xy=ellipse[0], angle=ellipse[1][0]*180/np.pi, width=ellipse[1][1], height=ellipse[1][2])\n",
    "    ax.add_artist(e)\n",
    "    e.set_clip_box(ax.bbox)\n",
    "    e.set_alpha(0.5)\n",
    "    e.set_facecolor(rng.rand(3))\n",
    "\n",
    "plt.xlim([-0.1, 6 * np.pi + 0.1])\n",
    "plt.ylim([-6.5,6.5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compute the conditional for y=3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "conditional_gmm = local_gmminf.condition([1], [3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7feded512650>]"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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v8oYbam/ztrfB+9+fvcRvujh4EB59FP7+77O3/c3fhG99C97+9qkZy+AgfOMb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\nRM7d/wfxYTx6JMGvzgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fededb3cd10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "proba = conditional_gmm.to_probability_density(X)\n",
    "plt.plot(X, proba)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Find the max"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "max_proba = np.max(proba)\n",
    "max_id = np.where(proba == max_proba)[0]\n",
    "max_value = X[max_id][0,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7feded52e910>]"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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461unZiwDA/D1r1u1mufuu+FjH7O2nYeJvNFRaxsdO2YtpKNHrcp++WWbVzpw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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fedf0a49850>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X, proba)\n",
    "plt.plot([max_value, max_value], [0, max_proba] , 'r')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-6.5, 6.5)"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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UbLfEXWVijC+15zBPTuctGjjw3N98Z9++fapevaFVtO/I7z9DPXr0P+I4mzZt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PMyQZ16w/11wZ3uM64S/Icz8A0i4QUFw3xAsJkYOvRsd6zHuvORK6veK5L5KCVrpjrB3eBXuhv7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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7feded63c350>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(0)\n",
    "ax = fig.add_subplot(111, aspect='equal')\n",
    "ax.scatter(X, Y)\n",
    "ax.scatter(max_value, 3, 50, 'r')\n",
    "plt.xlim([-0.1, 6 * np.pi + 0.1])\n",
    "plt.ylim([-6.5,6.5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Look good!**\n",
    "\n",
    "# Discussion\n",
    "\n",
    "Finding the max of the conditional gmm is to be privileged. The weighted mean inevitably will give wrong answers. \n",
    "\n",
    "Finding the maximum is impossible analytically. Think of those cases when the maximum might not be unique (e.g. two Gaussians well separated of equal weights), it makes it really hard to find an analytical solution. I am sure talented mathematicians worked hard on this, if nothing is out there yet there must be a reason.\n",
    "\n",
    "Some have tried with gradient descent sort of things:\n",
    "\n",
    "-  Pulkkinen, Seppo, Marko Mikael Mäkelä, and Napsu Karmitsa. \"A continuation approach to mode-finding of multivariate Gaussian mixtures and kernel density estimates.\" Journal of Global Optimization 56.2 (2013): 459-487. https://www.researchgate.net/profile/Seppo_Pulkkinen/publication/255996172_A_continuation_approach_to_mode-finding_of_multivariate_Gaussian_mixtures_and_kernel_density_estimates/links/00b495215e455d90ed000000.pdf\n",
    "\n",
    "- Carreira-Perpiñán, Miguel Á. \"Mode-finding for mixtures of Gaussian distributions.\" IEEE Transactions on Pattern Analysis & Machine Intelligence11 (2000): 1318-1323. http://faculty.ucmerced.edu/mcarreira-perpinan/papers/cs-99-03.pdf\n",
    "De le même personne: http://www.cs.toronto.edu/~miguel/research/GMmodes.html\n",
    "Code matlab: http://www.cs.toronto.edu/~miguel/research/software/gm_modes.tar.gz\n",
    "\n",
    "- des slides: https://www.utu.fi/en/units/sci/units/math/Research/optimization/Documents/sovmat13012012.pdf\n",
    "\n",
    "\n",
    "But, as the function is generally very smooth, it should be easy to find the maximum using an optimization algorithm. CMA-ES should perfectly do the job, a quick study could be done on which initialization parameter to use.\n",
    "\n",
    "I propose the following for initializing CMA-ES: \"mean = centroid (pondéré) des Gaussiennes de la GMM à évaluer, sigma = covariance (pondéré) des centres par rapports au mean(centroid) + régularisation sur la diagonale\"\n",
    "\n",
    "Finally, in most scenario, it is way better to get stuck in a local maximum than sampling randomly or using the weighted mean. The next option is thus to take the mean of the Gaussian that has the largest weight.\n",
    "\n",
    "\n",
    "## Calinon's work  and ILO-GMM paper\n",
    "\n",
    "For Calinon's work and ILO-GMM paper, I believe the weighted mean works because of the properties of the problem, i.e. trajectories. You are never at two positions at the same time. Or, if time is not in the input space, the feature are made such that the model is unimodal (e.g. adding current speed (dx, dy)).\n",
    "\n",
    "It would be worth checking Calinon litterature to see if they tried the following XP: A user move an obect from position A to B in straight line. We place an obstacle on the way. The user now decide randomly to go one side or the other of the obstacle. \n",
    "\n",
    "This creates a bimodal dataset, very similar to what we encounter in inverse model for robotics. Taking the weighted mean would make you run into the obstacle.\n",
    "\n",
    "How would Calinon's work handle this? I guess they run very early into such problems and might have found a solution. It is worth investigating.\n",
    "\n",
    "\n",
    "# Conclusion\n",
    "\n",
    "It is important to consider the problem of redundancy/multilodalities/multimodes when designing our algorithms. Such problem is omnipresent in our robotic experiments when considering inverse models. \n",
    "\n",
    "NN (with k > 1) is not solving this problem. ILO-GMM, which models the multimodality, is promising but could be improved by adapting the number of Gaussians. For this we proposed to use a clustering algorithm.\n",
    "\n",
    "The clustering algorithm might fail when the data are not well separated but still non-linear. In such case, the clustering algorithm might tell us there is only one cluster, but modeling with one Gaussian won't be enough. To limit that problem we could:\n",
    "- start by enforcing a minimum in the number of Gaussian to use, e.g. 3.\n",
    "- use 3x the number of clusters as the number of components of the local GMM\n",
    "\n",
    "It would be nice to make a proper benchmark with a similar problem in a more concrete scenario, e.g. multi-segment arm.\n",
    "\n",
    "A future consideration should be the definition of locality, we consider each dimension as having the same local importance, that might not be the case in many practical problem. Can the robot/agent finds out by itself the weight to assign to each dimension for defining locality?"
   ]
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## ILOGMM.py

# coding: utf-8

# **The following serves as a simple introduction to ILO-GMM. It also illustrate, using carefully selected examples, problems we might encounter when learning forward and, especially, inverse models.**
#
# # Overview
#
# We compare different inference method for ILO-GMM:
# - Weighted mean of the Gaussian center by their relative importance
# - Max of the probability distribution
# - Mean of the most important (bigger weight) Gaussian
# - Sampling the probability distribution
#
# The data are sampled from a 1 period sinus with a small Gaussian noise.
#
# We investigate the forward and inverse model. We show that the inverse problem, which illustrates the redundancy/multimodal/multimodes problem, poses problem to some infering methods.
#
# We conclude that, for most practical robotic problems involving inverse models, the order of inference methods to use is as follow:
# - Max of the probability distribution
# - Mean of the most important (bigger weight) Gaussian
# - Sampling the probability distribution
# - Weighted mean of the Gaussian center by their relative importance
#
#
# We then consider the problem of redundancy using a 3 period sinus. This problem helps visualizing a limitation of ILO-GMM that is the fixed number of Gaussian. We explore briefly two options:
# - DPGMM: http://scikit-learn.org/stable/modules/generated/sklearn.mixture.DPGMM.html#sklearn.mixture.DPGMM
# - use of a clustering algortihm to identify the number of modes. DPGMM, wile showing promises in theroy, is not convincing experimentally on our simple example. The clustering shows more practical promises.
#
#
# # Before starting
#
# The code below requires the following python modules:
# - http://www.numpy.org/
# - http://scikit-learn.org/stable/index.html
# - https://github.com/AlexanderFabisch/gmr
# - http://matplotlib.org/
#
#
# # Simple 1 period Sinus
#
# ## Generate data

# In[1]:

import numpy as np
rng = np.random.RandomState(10)
X = np.linspace(0, 2 * np.pi, 500)[:, np.newaxis]
Y = np.sin(X).ravel() + rng.normal(0, 0.1, X.shape[0])
Y = Y[:, np.newaxis]


# ## Plot data

# In[2]:

import matplotlib.pyplot as plt
get_ipython().magic(u'matplotlib inline')


# In[3]:

fig = plt.figure(0)
ax = fig.add_subplot(111, aspect='equal')
ax.scatter(X, Y)
plt.xlim([-0.1,2 * np.pi + 0.1])
plt.ylim([-1.5,1.5])


# ## Build Tree to find NN

# In[4]:

from sklearn.neighbors import KDTree
X_tree = KDTree(X, leaf_size=2)
Y_tree = KDTree(Y, leaf_size=2)


# # Forward Model: example of unimodal/grouped data
#
# ## Find local data for x=1

# In[5]:

_, ind = X_tree.query(1, k=50)
local_X = X[ind]
local_Y = Y[ind]


# ## Plot local data at x=1

# In[6]:

fig = plt.figure(0)
ax = fig.add_subplot(111, aspect='equal')
ax.scatter(local_X, local_Y)
plt.xlim([-0.1,2 * np.pi + 0.1])
plt.ylim([-1.5,1.5])


# ## Fit local GMM with 3 components

# In[7]:

from sklearn.mixture import GMM


# In[8]:

local_gmm = GMM(n_components=3, covariance_type='full')
local_data = np.squeeze(np.concatenate((local_X, local_Y), axis=2))
local_gmm.fit(local_data)


# ## Plot local GMM
#
# Here I switch to https://github.com/AlexanderFabisch/gmr because there is a simple interface for conditional distribution and ellipse drawing
#
# However I fit the GMM using sklearn because I will later use the DPGMM from sklearn, so it is all consistent and it help see where to find the code to reimplement all this in a uniform python module.

# In[9]:

import gmr


# In[10]:

local_gmminf = gmr.gmm.GMM(3,
                           local_gmm.weights_,
                           local_gmm.means_,
                           local_gmm.covars_)


# In[11]:

ellipses = local_gmminf.to_ellipses(2)


# In[12]:

from matplotlib.patches import Ellipse

fig = plt.figure()
ax = fig.add_subplot(111, aspect='equal')

for ellipse in ellipses:
    e = Ellipse(xy=ellipse[0], angle=ellipse[1][0]*180/np.pi, width=ellipse[1][1], height=ellipse[1][2])
    ax.add_artist(e)
    e.set_clip_box(ax.bbox)
    e.set_alpha(0.5)
    e.set_facecolor(rng.rand(3))

plt.xlim([-0.1,2 * np.pi + 0.1])
plt.ylim([-1.5,1.5])


# ## We compute and plot the conditional for x=1

# In[13]:

conditional_gmm = local_gmminf.condition([0], [1])


# In[14]:

YY = np.linspace(-1.5, 1.5, 500)[:, np.newaxis]
proba = conditional_gmm.to_probability_density(YY)
plt.plot(proba, YY)


# ### Method 1: Find the Max

# In[15]:

max_proba = np.max(proba)
max_id = np.where(proba == max_proba)[0]
max_value = YY[max_id][0,0]


# In[16]:

plt.plot(proba, YY)
plt.plot([0, max_proba], [max_value, max_value], 'r')


# In[17]:

fig = plt.figure(0)
ax = fig.add_subplot(111, aspect='equal')
ax.scatter(X, Y)
ax.scatter(1, max_value, 50, 'r')
plt.xlim([-0.1,2 * np.pi + 0.1])
plt.ylim([-1.5,1.5])


# ### Method 2: Sample from distribution

# In[18]:

sampled_values = conditional_gmm.sample(10)


# In[19]:

fig = plt.figure(0)
ax = fig.add_subplot(111, aspect='equal')
ax.scatter(X, Y)
ax.scatter(np.ones(sampled_values.shape), sampled_values, 50, 'r')
plt.xlim([-0.1,2 * np.pi + 0.1])
plt.ylim([-1.5,1.5])


# ### Method 3: Weighted mean

# In[20]:

weighted_mean = conditional_gmm.priors.dot(conditional_gmm.means)


# In[21]:

plt.plot(proba, YY)
plt.plot([0, max_proba], [weighted_mean, weighted_mean], 'r')


# **Note that it is not the max.**

# In[22]:

fig = plt.figure(0)
ax = fig.add_subplot(111, aspect='equal')
ax.scatter(X, Y)
ax.scatter(1, weighted_mean, 50, 'r')
plt.xlim([-0.1,2 * np.pi + 0.1])
plt.ylim([-1.5,1.5])


# ### Method 4: Mean of most important Gaussian

# In[23]:

max_weight = np.max(conditional_gmm.priors)
max_ind = np.where(conditional_gmm.priors == max_weight)[0][0]

fig = plt.figure(0)
ax = fig.add_subplot(111, aspect='equal')
ax.scatter(X, Y)
ax.scatter(1, conditional_gmm.means[max_ind], 50, 'r')
plt.xlim([-0.1,2 * np.pi + 0.1])
plt.ylim([-1.5,1.5])


# ### Ranking
#
# - Max
# - Mean of most weighted Gaussian
# - Weighted Mean
# - Sample

# # Inverse Model: example of redundancy/multimodality/multimodes
#
# ## Find local data for y=0.5

# In[24]:

_, ind = Y_tree.query(0.5, k=50)
local_X = X[ind]
local_Y = Y[ind]


# ## Plot local data at y=0.5

# In[25]:

fig = plt.figure(0)
ax = fig.add_subplot(111, aspect='equal')
ax.scatter(local_X, local_Y)
plt.xlim([-0.1,2 * np.pi + 0.1])
plt.ylim([-1.5,1.5])


# **This is the problem of redundancy**

# ## Fit local GMM with 3 components

# In[26]:

local_gmm = GMM(n_components=3, covariance_type='full')
local_data = np.squeeze(np.concatenate((local_X, local_Y), axis=2))
local_gmm.fit(local_data)


# ## Plot local GMM

# In[27]:

local_gmminf = gmr.gmm.GMM(3,
                           local_gmm.weights_,
                           local_gmm.means_,
                           local_gmm.covars_)


# In[28]:

ellipses = local_gmminf.to_ellipses(2)


# In[29]:

from matplotlib.patches import Ellipse

fig = plt.figure()
ax = fig.add_subplot(111, aspect='equal')

for ellipse in ellipses:
    e = Ellipse(xy=ellipse[0], angle=ellipse[1][0]*180/np.pi, width=ellipse[1][1], height=ellipse[1][2])
    ax.add_artist(e)
    e.set_clip_box(ax.bbox)
    e.set_alpha(0.5)
    e.set_facecolor(rng.rand(3))

plt.xlim([-0.1,2 * np.pi + 0.1])
plt.ylim([-1.5,1.5])


# **Note that the GMM model well the bi-modality of the data**

# ## We compute and plot the conditional for y=0.5

# In[30]:

conditional_gmm = local_gmminf.condition([1], [0.5])


# In[31]:

proba = conditional_gmm.to_probability_density(X)
plt.plot(X, proba)


# **Note that the GMM model well the bi-modality of the data**

# ### Method 1: Find the Max

# In[32]:

max_proba = np.max(proba)
max_id = np.where(proba == max_proba)[0]
max_value = X[max_id][0,0]


# In[33]:

plt.plot(X, proba)
plt.plot([max_value, max_value], [0, max_proba] , 'r')


# In[34]:

fig = plt.figure(0)
ax = fig.add_subplot(111, aspect='equal')
ax.scatter(X, Y)
ax.scatter(max_value, 0.5, 50, 'r')
plt.xlim([-0.1,2 * np.pi + 0.1])
plt.ylim([-1.5,1.5])


# ### Method 2: Sample from distribution

# In[35]:

sampled_values = conditional_gmm.sample(10)


# In[36]:

fig = plt.figure(0)
ax = fig.add_subplot(111, aspect='equal')
ax.scatter(X, Y)
ax.scatter(sampled_values, 0.5 * np.ones(sampled_values.shape), 50, 'r')
plt.xlim([-0.1,2 * np.pi + 0.1])
plt.ylim([-1.5,1.5])


# ### Method 3: Weighted mean

# In[37]:

weighted_mean = conditional_gmm.priors.dot(conditional_gmm.means)


# In[38]:

plt.plot(X, proba)
plt.plot([weighted_mean, weighted_mean],[0, max_proba], 'r')


# ** This is not desired **

# In[39]:

fig = plt.figure(0)
ax = fig.add_subplot(111, aspect='equal')
ax.scatter(X, Y)
ax.scatter(weighted_mean, 0.5, 50, 'r')
plt.xlim([-0.1,2 * np.pi + 0.1])
plt.ylim([-1.5,1.5])


# ** This is not desired **

# ### Method 4: Mean of most important Gaussian

# In[40]:

max_weight = np.max(conditional_gmm.priors)
max_ind = np.where(conditional_gmm.priors == max_weight)[0][0]

fig = plt.figure(0)
ax = fig.add_subplot(111, aspect='equal')
ax.scatter(X, Y)
ax.scatter(conditional_gmm.means[max_ind], 0.5, 50, 'r')
plt.xlim([-0.1,2 * np.pi + 0.1])
plt.ylim([-1.5,1.5])


# ### Ranking
#
# - Max
# - Mean of most weighted Gaussian
# - Sample
# - Weighted Mean

# # Bigger redundancy: the need to adapt the number of gaussian

# ## Generate more redundant data

# In[41]:

rng = np.random.RandomState(10)
X = np.linspace(0, 6 * np.pi, 1000)[:, np.newaxis]
Y = 6*np.sin(X).ravel() + rng.normal(0, 0.5, X.shape[0])
Y = Y[:, np.newaxis]


# ## Plot data

# In[42]:

fig = plt.figure(0)
ax = fig.add_subplot(111, aspect='equal')
ax.scatter(X, Y)
plt.xlim([-0.1, 6 * np.pi + 0.1])
plt.ylim([-6.5,6.5])


# ## Build Tree to find NN

# In[43]:

from sklearn.neighbors import KDTree
X_tree = KDTree(X, leaf_size=2)
Y_tree = KDTree(Y, leaf_size=2)


# # Inverse Model
#
# ## Find local data for y=3

# In[44]:

_, ind = Y_tree.query(3, k=100)
local_X = X[ind]
local_Y = Y[ind]


# ## Plot local data at y=3

# In[45]:

fig = plt.figure(0)
ax = fig.add_subplot(111, aspect='equal')
ax.scatter(local_X, local_Y)
plt.xlim([-0.1, 6 * np.pi + 0.1])
plt.ylim([-6.5,6.5])


# ## Fit local GMM with 3 components

# In[46]:

local_gmm = GMM(n_components=3, covariance_type='full')
local_data = np.squeeze(np.concatenate((local_X, local_Y), axis=2))
local_gmm.fit(local_data)


# ## Plot local GMM

# In[47]:

local_gmminf = gmr.gmm.GMM(3,
                           local_gmm.weights_,
                           local_gmm.means_,
                           local_gmm.covars_)


# In[48]:

ellipses = local_gmminf.to_ellipses(2)


# In[49]:

from matplotlib.patches import Ellipse

fig = plt.figure()
ax = fig.add_subplot(111, aspect='equal')
ax.scatter(local_X, local_Y)


for ellipse in ellipses:
    e = Ellipse(xy=ellipse[0], angle=ellipse[1][0]*180/np.pi, width=ellipse[1][1], height=ellipse[1][2])
    ax.add_artist(e)
    e.set_clip_box(ax.bbox)
    e.set_alpha(0.5)
    e.set_facecolor(rng.rand(3))

plt.xlim([-0.1, 6 * np.pi + 0.1])
plt.ylim([-6.5,6.5])


# **There is not enough gaussian to model this properly**
#
# Such problem are arise quite often in our simple example, e.g. multidimensional arm
#
# **Note that the same problem might arise with a simple NN model if we take the weighted mean of more than 1 neigborh**

# ## We compute and plot the conditional for y=3

# In[50]:

conditional_gmm = local_gmminf.condition([1], [3])


# In[51]:

proba = conditional_gmm.to_probability_density(X)
plt.plot(X, proba)


# ## Find the Max

# In[52]:

max_proba = np.max(proba)
max_id = np.where(proba == max_proba)[0]
max_value = X[max_id][0,0]


# In[53]:

plt.plot(X, proba)
plt.plot([max_value, max_value], [0, max_proba] , 'r')


# In[54]:

fig = plt.figure(0)
ax = fig.add_subplot(111, aspect='equal')
ax.scatter(X, Y)
ax.scatter(max_value, 3, 50, 'r')
plt.xlim([-0.1, 6 * np.pi + 0.1])
plt.ylim([-6.5,6.5])


# ** This is not desired **

# # Would DPGMM solve the problem?
#
# Short answer: I did'nt succeed, on paper it is what we look for but in pratice it did not work on this simple example.
#
# I tried as above, simply replace GMM by DPGMM. It looked to me some prior was pulling Gaussians towards [0,0] but I am not sure at all..
#
# So I tried scaling the data, but this didn't help.
#
# ## Fit local DPGMM

# In[55]:

from sklearn.mixture import DPGMM
local_gmm = DPGMM(n_components=10,
                  covariance_type='full',
                  alpha=1,
                  tol=1e-3,
                  params='wmc',
                  init_params='wmc')
local_data = np.squeeze(np.concatenate((local_X, local_Y), axis=2))
local_gmm.fit(local_data)


# **Play a bit with the parameter to get a sense of what is a happening: http://scikit-learn.org/stable/modules/generated/sklearn.mixture.DPGMM.html#sklearn.mixture.DPGMM**
#
# ## Plot local GMM

# In[56]:

local_gmminf = gmr.gmm.GMM(local_gmm.weights_.shape[0],
                           local_gmm.weights_,
                           local_gmm.means_,
                           local_gmm._get_covars())


# In[57]:

ellipses = local_gmminf.to_ellipses(2)


# In[58]:

from matplotlib.patches import Ellipse

fig = plt.figure()
ax = fig.add_subplot(111) ##, aspect='equal')
ax.scatter(local_X, local_Y)


for ellipse in ellipses:
    e = Ellipse(xy=ellipse[0], angle=ellipse[1][0]*180/np.pi, width=ellipse[1][1], height=ellipse[1][2])
    ax.add_artist(e)
    e.set_clip_box(ax.bbox)
    e.set_alpha(0.5)
    e.set_facecolor(rng.rand(3))

plt.xlim([-0.1, 6 * np.pi + 0.1])
plt.ylim([-6.5,6.5])


# **Note that the Gaussian you see at [0,0] are the ones that are not in use, there is a way to know this. See here: http://scikit-learn.org/stable/auto_examples/mixture/plot_gmm_sin.html#example-mixture-plot-gmm-sin-py**

# ## Let's try to estimate the number of clusters with a clustering algorithm
#
# See: http://scikit-learn.org/stable/modules/clustering.html
#
# I picked: http://scikit-learn.org/stable/modules/generated/sklearn.cluster.AffinityPropagation.html#sklearn.cluster.AffinityPropagation
#

# In[59]:

from sklearn.cluster import AffinityPropagation

af = AffinityPropagation(damping=0.6)
af.fit(local_data)
n_clusters = len(af.cluster_centers_)
print("We found {} clusters".format(n_clusters))


# ## Plot the clusters

# In[60]:

fig = plt.figure()
ax = fig.add_subplot(111) ##, aspect='equal')
ax.scatter(local_X, local_Y, 5)

for cs in af.cluster_centers_:
    ax.scatter(cs[0], cs[1], 100, rng.rand(3))

plt.xlim([-0.1, 6 * np.pi + 0.1])
plt.ylim([-6.5,6.5])


# ## Let's use this number ot fit the GMM

# In[61]:

local_gmm = GMM(n_components=n_clusters, covariance_type='full')
local_gmm.fit(local_data)


# In[62]:

local_gmminf = gmr.gmm.GMM(n_clusters,
                           local_gmm.weights_,
                           local_gmm.means_,
                           local_gmm.covars_)


# In[63]:

ellipses = local_gmminf.to_ellipses(2)


# In[64]:


from matplotlib.patches import Ellipse

fig = plt.figure()
ax = fig.add_subplot(111, aspect='equal')
ax.scatter(local_X, local_Y)


for ellipse in ellipses:
    e = Ellipse(xy=ellipse[0], angle=ellipse[1][0]*180/np.pi, width=ellipse[1][1], height=ellipse[1][2])
    ax.add_artist(e)
    e.set_clip_box(ax.bbox)
    e.set_alpha(0.5)
    e.set_facecolor(rng.rand(3))

plt.xlim([-0.1, 6 * np.pi + 0.1])
plt.ylim([-6.5,6.5])


# ## Compute the conditional for y=3

# In[65]:

conditional_gmm = local_gmminf.condition([1], [3])


# In[66]:

proba = conditional_gmm.to_probability_density(X)
plt.plot(X, proba)


# ## Find the max

# In[67]:

max_proba = np.max(proba)
max_id = np.where(proba == max_proba)[0]
max_value = X[max_id][0,0]


# In[68]:

plt.plot(X, proba)
plt.plot([max_value, max_value], [0, max_proba] , 'r')


# In[69]:

fig = plt.figure(0)
ax = fig.add_subplot(111, aspect='equal')
ax.scatter(X, Y)
ax.scatter(max_value, 3, 50, 'r')
plt.xlim([-0.1, 6 * np.pi + 0.1])
plt.ylim([-6.5,6.5])


# **Look good!**
#
# # Discussion
#
# Finding the max of the conditional gmm is to be privileged. The weighted mean inevitably will give wrong answers.
#
# Finding the maximum is impossible analytically. Think of those cases when the maximum might not be unique (e.g. two Gaussians well separated of equal weights), it makes it really hard to find an analytical solution. I am sure talented mathematicians worked hard on this, if nothing is out there yet there must be a reason.
#
# Some have tried with gradient descent sort of things:
#
# -  Pulkkinen, Seppo, Marko Mikael Mäkelä, and Napsu Karmitsa. "A continuation approach to mode-finding of multivariate Gaussian mixtures and kernel density estimates." Journal of Global Optimization 56.2 (2013): 459-487. https://www.researchgate.net/profile/Seppo_Pulkkinen/publication/255996172_A_continuation_approach_to_mode-finding_of_multivariate_Gaussian_mixtures_and_kernel_density_estimates/links/00b495215e455d90ed000000.pdf
#
# - Carreira-Perpiñán, Miguel Á. "Mode-finding for mixtures of Gaussian distributions." IEEE Transactions on Pattern Analysis & Machine Intelligence11 (2000): 1318-1323. http://faculty.ucmerced.edu/mcarreira-perpinan/papers/cs-99-03.pdf
# De le même personne: http://www.cs.toronto.edu/~miguel/research/GMmodes.html
# Code matlab: http://www.cs.toronto.edu/~miguel/research/software/gm_modes.tar.gz
#
# - des slides: https://www.utu.fi/en/units/sci/units/math/Research/optimization/Documents/sovmat13012012.pdf
#
#
# But, as the function is generally very smooth, it should be easy to find the maximum using an optimization algorithm. CMA-ES should perfectly do the job, a quick study could be done on which initialization parameter to use.
#
# I propose the following for initializing CMA-ES: "mean = centroid (pondéré) des Gaussiennes de la GMM à évaluer, sigma = covariance (pondéré) des centres par rapports au mean(centroid) + régularisation sur la diagonale"
#
# Finally, in most scenario, it is way better to get stuck in a local maximum than sampling randomly or using the weighted mean. The next option is thus to take the mean of the Gaussian that has the largest weight.
#
#
# ## Calinon's work  and ILO-GMM paper
#
# For Calinon's work and ILO-GMM paper, I believe the weighted mean works because of the properties of the problem, i.e. trajectories. You are never at two positions at the same time. Or, if time is not in the input space, the feature are made such that the model is unimodal (e.g. adding current speed (dx, dy)).
#
# It would be worth checking Calinon litterature to see if they tried the following XP: A user move an obect from position A to B in straight line. We place an obstacle on the way. The user now decide randomly to go one side or the other of the obstacle.
#
# This creates a bimodal dataset, very similar to what we encounter in inverse model for robotics. Taking the weighted mean would make you run into the obstacle.
#
# How would Calinon's work handle this? I guess they run very early into such problems and might have found a solution. It is worth investigating.
#
#
# # Conclusion
#
# It is important to consider the problem of redundancy/multilodalities/multimodes when designing our algorithms. Such problem is omnipresent in our robotic experiments when considering inverse models.
#
# NN (with k > 1) is not solving this problem. ILO-GMM, which models the multimodality, is promising but could be improved by adapting the number of Gaussians. For this we proposed to use a clustering algorithm.
#
# The clustering algorithm might fail when the data are not well separated but still non-linear. In such case, the clustering algorithm might tell us there is only one cluster, but modeling with one Gaussian won't be enough. To limit that problem we could:
# - start by enforcing a minimum in the number of Gaussian to use, e.g. 3.
# - use 3x the number of clusters as the number of components of the local GMM
#
# It would be nice to make a proper benchmark with a similar problem in a more concrete scenario, e.g. multi-segment arm.
#
# A future consideration should be the definition of locality, we consider each dimension as having the same local importance, that might not be the case in many practical problem. Can the robot/agent finds out by itself the weight to assign to each dimension for defining locality?

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<p><strong>The following serves as a simple introduction to ILO-GMM. It also illustrate, using carefully selected examples, problems we might encounter when learning forward and, especially, inverse models.</strong></p>
<h1 id="Overview">Overview<a class="anchor-link" href="#Overview">&#182;</a></h1><p>We compare different inference method for ILO-GMM:</p>
<ul>
<li>Weighted mean of the Gaussian center by their relative importance</li>
<li>Max of the probability distribution</li>
<li>Mean of the most important (bigger weight) Gaussian</li>
<li>Sampling the probability distribution</li>
</ul>
<p>The data are sampled from a 1 period sinus with a small Gaussian noise.</p>
<p>We investigate the forward and inverse model. We show that the inverse problem, which illustrates the redundancy/multimodal/multimodes problem, poses problem to some infering methods.</p>
<p>We conclude that, for most practical robotic problems involving inverse models, the order of inference methods to use is as follow:</p>
<ul>
<li>Max of the probability distribution</li>
<li>Mean of the most important (bigger weight) Gaussian</li>
<li>Sampling the probability distribution</li>
<li>Weighted mean of the Gaussian center by their relative importance</li>
</ul>
<p>We then consider the problem of redundancy using a 3 period sinus. This problem helps visualizing a limitation of ILO-GMM that is the fixed number of Gaussian. We explore briefly two options:</p>
<ul>
<li>DPGMM: <a href="http://scikit-learn.org/stable/modules/generated/sklearn.mixture.DPGMM.html#sklearn.mixture.DPGMM">http://scikit-learn.org/stable/modules/generated/sklearn.mixture.DPGMM.html#sklearn.mixture.DPGMM</a></li>
<li>use of a clustering algortihm to identify the number of modes. DPGMM, wile showing promises in theroy, is not convincing experimentally on our simple example. The clustering shows more practical promises.</li>
</ul>
<h1 id="Before-starting">Before starting<a class="anchor-link" href="#Before-starting">&#182;</a></h1><p>The code below requires the following python modules:</p>
<ul>
<li><a href="http://www.numpy.org/">http://www.numpy.org/</a></li>
<li><a href="http://scikit-learn.org/stable/index.html">http://scikit-learn.org/stable/index.html</a></li>
<li><a href="https://github.com/AlexanderFabisch/gmr">https://github.com/AlexanderFabisch/gmr</a></li>
<li><a href="http://matplotlib.org/">http://matplotlib.org/</a></li>
</ul>
<h1 id="Simple-1-period-Sinus">Simple 1 period Sinus<a class="anchor-link" href="#Simple-1-period-Sinus">&#182;</a></h1><h2 id="Generate-data">Generate data<a class="anchor-link" href="#Generate-data">&#182;</a></h2>
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<div class=" highlight hl-ipython2"><pre><span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="n">rng</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">RandomState</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">,</span> <span class="mi">500</span><span class="p">)[:,</span> <span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">]</span>
<span class="n">Y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">X</span><span class="p">)</span><span class="o">.</span><span class="n">ravel</span><span class="p">()</span> <span class="o">+</span> <span class="n">rng</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">,</span> <span class="n">X</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
<span class="n">Y</span> <span class="o">=</span> <span class="n">Y</span><span class="p">[:,</span> <span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">]</span>
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<h2 id="Plot-data">Plot data<a class="anchor-link" href="#Plot-data">&#182;</a></h2>
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<div class=" highlight hl-ipython2"><pre><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span>
<span class="o">%</span><span class="k">matplotlib</span> inline
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<div class=" highlight hl-ipython2"><pre><span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">111</span><span class="p">,</span> <span class="n">aspect</span><span class="o">=</span><span class="s">&#39;equal&#39;</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">Y</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlim</span><span class="p">([</span><span class="o">-</span><span class="mf">0.1</span><span class="p">,</span><span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">+</span> <span class="mf">0.1</span><span class="p">])</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylim</span><span class="p">([</span><span class="o">-</span><span class="mf">1.5</span><span class="p">,</span><span class="mf">1.5</span><span class="p">])</span>
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<pre>(-1.5, 1.5)</pre>
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	# coding: utf-8

	# The following serves as a simple introduction to ILO-GMM. It also illustrate, using carefully selected examples, problems we might encounter when learning forward and, especially, inverse models.
	#
	# # Overview
	#
	# We compare different inference method for ILO-GMM:
	# - Weighted mean of the Gaussian center by their relative importance
	# - Max of the probability distribution
	# - Mean of the most important (bigger weight) Gaussian
	# - Sampling the probability distribution
	#
	# The data are sampled from a 1 period sinus with a small Gaussian noise.
	#
	# We investigate the forward and inverse model. We show that the inverse problem, which illustrates the redundancy/multimodal/multimodes problem, poses problem to some infering methods.
	#
	# We conclude that, for most practical robotic problems involving inverse models, the order of inference methods to use is as follow:
	# - Max of the probability distribution
	# - Mean of the most important (bigger weight) Gaussian
	# - Sampling the probability distribution
	# - Weighted mean of the Gaussian center by their relative importance
	#
	#
	# We then consider the problem of redundancy using a 3 period sinus. This problem helps visualizing a limitation of ILO-GMM that is the fixed number of Gaussian. We explore briefly two options:
	# - DPGMM: http://scikit-learn.org/stable/modules/generated/sklearn.mixture.DPGMM.html#sklearn.mixture.DPGMM
	# - use of a clustering algortihm to identify the number of modes. DPGMM, wile showing promises in theroy, is not convincing experimentally on our simple example. The clustering shows more practical promises.
	#
	#
	# # Before starting
	#
	# The code below requires the following python modules:
	# - http://www.numpy.org/
	# - http://scikit-learn.org/stable/index.html
	# - https://github.com/AlexanderFabisch/gmr
	# - http://matplotlib.org/
	#
	#
	# # Simple 1 period Sinus
	#
	# ## Generate data

	# In[1]:

	import numpy as np
	rng = np.random.RandomState(10)
	X = np.linspace(0, 2 * np.pi, 500)[:, np.newaxis]
	Y = np.sin(X).ravel() + rng.normal(0, 0.1, X.shape[0])
	Y = Y[:, np.newaxis]


	# ## Plot data

	# In[2]:

	import matplotlib.pyplot as plt
	get_ipython().magic(u'matplotlib inline')


	# In[3]:

	fig = plt.figure(0)
	ax = fig.add_subplot(111, aspect='equal')
	ax.scatter(X, Y)
	plt.xlim([-0.1,2 * np.pi + 0.1])
	plt.ylim([-1.5,1.5])


	# ## Build Tree to find NN

	# In[4]:

	from sklearn.neighbors import KDTree
	X_tree = KDTree(X, leaf_size=2)
	Y_tree = KDTree(Y, leaf_size=2)


	# # Forward Model: example of unimodal/grouped data
	#
	# ## Find local data for x=1

	# In[5]:

	_, ind = X_tree.query(1, k=50)
	local_X = X[ind]
	local_Y = Y[ind]


	# ## Plot local data at x=1

	# In[6]:

	fig = plt.figure(0)
	ax = fig.add_subplot(111, aspect='equal')
	ax.scatter(local_X, local_Y)
	plt.xlim([-0.1,2 * np.pi + 0.1])
	plt.ylim([-1.5,1.5])


	# ## Fit local GMM with 3 components

	# In[7]:

	from sklearn.mixture import GMM


	# In[8]:

	local_gmm = GMM(n_components=3, covariance_type='full')
	local_data = np.squeeze(np.concatenate((local_X, local_Y), axis=2))
	local_gmm.fit(local_data)


	# ## Plot local GMM
	#
	# Here I switch to https://github.com/AlexanderFabisch/gmr because there is a simple interface for conditional distribution and ellipse drawing
	#
	# However I fit the GMM using sklearn because I will later use the DPGMM from sklearn, so it is all consistent and it help see where to find the code to reimplement all this in a uniform python module.

	# In[9]:

	import gmr


	# In[10]:

	local_gmminf = gmr.gmm.GMM(3,
	local_gmm.weights_,
	local_gmm.means_,
	local_gmm.covars_)


	# In[11]:

	ellipses = local_gmminf.to_ellipses(2)


	# In[12]:

	from matplotlib.patches import Ellipse

	fig = plt.figure()
	ax = fig.add_subplot(111, aspect='equal')

	for ellipse in ellipses:
	e = Ellipse(xy=ellipse[0], angle=ellipse[1][0]*180/np.pi, width=ellipse[1][1], height=ellipse[1][2])
	ax.add_artist(e)
	e.set_clip_box(ax.bbox)
	e.set_alpha(0.5)
	e.set_facecolor(rng.rand(3))

	plt.xlim([-0.1,2 * np.pi + 0.1])
	plt.ylim([-1.5,1.5])


	# ## We compute and plot the conditional for x=1

	# In[13]:

	conditional_gmm = local_gmminf.condition([0], [1])


	# In[14]:

	YY = np.linspace(-1.5, 1.5, 500)[:, np.newaxis]
	proba = conditional_gmm.to_probability_density(YY)
	plt.plot(proba, YY)


	# ### Method 1: Find the Max

	# In[15]:

	max_proba = np.max(proba)
	max_id = np.where(proba == max_proba)[0]
	max_value = YY[max_id][0,0]


	# In[16]:

	plt.plot(proba, YY)
	plt.plot([0, max_proba], [max_value, max_value], 'r')


	# In[17]:

	fig = plt.figure(0)
	ax = fig.add_subplot(111, aspect='equal')
	ax.scatter(X, Y)
	ax.scatter(1, max_value, 50, 'r')
	plt.xlim([-0.1,2 * np.pi + 0.1])
	plt.ylim([-1.5,1.5])


	# ### Method 2: Sample from distribution

	# In[18]:

	sampled_values = conditional_gmm.sample(10)


	# In[19]:

	fig = plt.figure(0)
	ax = fig.add_subplot(111, aspect='equal')
	ax.scatter(X, Y)
	ax.scatter(np.ones(sampled_values.shape), sampled_values, 50, 'r')
	plt.xlim([-0.1,2 * np.pi + 0.1])
	plt.ylim([-1.5,1.5])


	# ### Method 3: Weighted mean

	# In[20]:

	weighted_mean = conditional_gmm.priors.dot(conditional_gmm.means)


	# In[21]:

	plt.plot(proba, YY)
	plt.plot([0, max_proba], [weighted_mean, weighted_mean], 'r')


	# Note that it is not the max.

	# In[22]:

	fig = plt.figure(0)
	ax = fig.add_subplot(111, aspect='equal')
	ax.scatter(X, Y)
	ax.scatter(1, weighted_mean, 50, 'r')
	plt.xlim([-0.1,2 * np.pi + 0.1])
	plt.ylim([-1.5,1.5])


	# ### Method 4: Mean of most important Gaussian

	# In[23]:

	max_weight = np.max(conditional_gmm.priors)
	max_ind = np.where(conditional_gmm.priors == max_weight)[0][0]

	fig = plt.figure(0)
	ax = fig.add_subplot(111, aspect='equal')
	ax.scatter(X, Y)
	ax.scatter(1, conditional_gmm.means[max_ind], 50, 'r')
	plt.xlim([-0.1,2 * np.pi + 0.1])
	plt.ylim([-1.5,1.5])


	# ### Ranking
	#
	# - Max
	# - Mean of most weighted Gaussian
	# - Weighted Mean
	# - Sample

	# # Inverse Model: example of redundancy/multimodality/multimodes
	#
	# ## Find local data for y=0.5

	# In[24]:

	_, ind = Y_tree.query(0.5, k=50)
	local_X = X[ind]
	local_Y = Y[ind]


	# ## Plot local data at y=0.5

	# In[25]:

	fig = plt.figure(0)
	ax = fig.add_subplot(111, aspect='equal')
	ax.scatter(local_X, local_Y)
	plt.xlim([-0.1,2 * np.pi + 0.1])
	plt.ylim([-1.5,1.5])


	# This is the problem of redundancy

	# ## Fit local GMM with 3 components

	# In[26]:

	local_gmm = GMM(n_components=3, covariance_type='full')
	local_data = np.squeeze(np.concatenate((local_X, local_Y), axis=2))
	local_gmm.fit(local_data)


	# ## Plot local GMM

	# In[27]:

	local_gmminf = gmr.gmm.GMM(3,
	local_gmm.weights_,
	local_gmm.means_,
	local_gmm.covars_)


	# In[28]:

	ellipses = local_gmminf.to_ellipses(2)


	# In[29]:

	from matplotlib.patches import Ellipse

	fig = plt.figure()
	ax = fig.add_subplot(111, aspect='equal')

	for ellipse in ellipses:
	e = Ellipse(xy=ellipse[0], angle=ellipse[1][0]*180/np.pi, width=ellipse[1][1], height=ellipse[1][2])
	ax.add_artist(e)
	e.set_clip_box(ax.bbox)
	e.set_alpha(0.5)
	e.set_facecolor(rng.rand(3))

	plt.xlim([-0.1,2 * np.pi + 0.1])
	plt.ylim([-1.5,1.5])


	# Note that the GMM model well the bi-modality of the data

	# ## We compute and plot the conditional for y=0.5

	# In[30]:

	conditional_gmm = local_gmminf.condition([1], [0.5])


	# In[31]:

	proba = conditional_gmm.to_probability_density(X)
	plt.plot(X, proba)


	# Note that the GMM model well the bi-modality of the data

	# ### Method 1: Find the Max

	# In[32]:

	max_proba = np.max(proba)
	max_id = np.where(proba == max_proba)[0]
	max_value = X[max_id][0,0]


	# In[33]:

	plt.plot(X, proba)
	plt.plot([max_value, max_value], [0, max_proba] , 'r')


	# In[34]:

	fig = plt.figure(0)
	ax = fig.add_subplot(111, aspect='equal')
	ax.scatter(X, Y)
	ax.scatter(max_value, 0.5, 50, 'r')
	plt.xlim([-0.1,2 * np.pi + 0.1])
	plt.ylim([-1.5,1.5])


	# ### Method 2: Sample from distribution

	# In[35]:

	sampled_values = conditional_gmm.sample(10)


	# In[36]:

	fig = plt.figure(0)
	ax = fig.add_subplot(111, aspect='equal')
	ax.scatter(X, Y)
	ax.scatter(sampled_values, 0.5 * np.ones(sampled_values.shape), 50, 'r')
	plt.xlim([-0.1,2 * np.pi + 0.1])
	plt.ylim([-1.5,1.5])


	# ### Method 3: Weighted mean

	# In[37]:

	weighted_mean = conditional_gmm.priors.dot(conditional_gmm.means)


	# In[38]:

	plt.plot(X, proba)
	plt.plot([weighted_mean, weighted_mean],[0, max_proba], 'r')


	# This is not desired

	# In[39]:

	fig = plt.figure(0)
	ax = fig.add_subplot(111, aspect='equal')
	ax.scatter(X, Y)
	ax.scatter(weighted_mean, 0.5, 50, 'r')
	plt.xlim([-0.1,2 * np.pi + 0.1])
	plt.ylim([-1.5,1.5])


	# This is not desired

	# ### Method 4: Mean of most important Gaussian

	# In[40]:

	max_weight = np.max(conditional_gmm.priors)
	max_ind = np.where(conditional_gmm.priors == max_weight)[0][0]

	fig = plt.figure(0)
	ax = fig.add_subplot(111, aspect='equal')
	ax.scatter(X, Y)
	ax.scatter(conditional_gmm.means[max_ind], 0.5, 50, 'r')
	plt.xlim([-0.1,2 * np.pi + 0.1])
	plt.ylim([-1.5,1.5])


	# ### Ranking
	#
	# - Max
	# - Mean of most weighted Gaussian
	# - Sample
	# - Weighted Mean

	# # Bigger redundancy: the need to adapt the number of gaussian

	# ## Generate more redundant data

	# In[41]:

	rng = np.random.RandomState(10)
	X = np.linspace(0, 6 * np.pi, 1000)[:, np.newaxis]
	Y = 6*np.sin(X).ravel() + rng.normal(0, 0.5, X.shape[0])
	Y = Y[:, np.newaxis]


	# ## Plot data

	# In[42]:

	fig = plt.figure(0)
	ax = fig.add_subplot(111, aspect='equal')
	ax.scatter(X, Y)
	plt.xlim([-0.1, 6 * np.pi + 0.1])
	plt.ylim([-6.5,6.5])


	# ## Build Tree to find NN

	# In[43]:

	from sklearn.neighbors import KDTree
	X_tree = KDTree(X, leaf_size=2)
	Y_tree = KDTree(Y, leaf_size=2)


	# # Inverse Model
	#
	# ## Find local data for y=3

	# In[44]:

	_, ind = Y_tree.query(3, k=100)
	local_X = X[ind]
	local_Y = Y[ind]


	# ## Plot local data at y=3

	# In[45]:

	fig = plt.figure(0)
	ax = fig.add_subplot(111, aspect='equal')
	ax.scatter(local_X, local_Y)
	plt.xlim([-0.1, 6 * np.pi + 0.1])
	plt.ylim([-6.5,6.5])


	# ## Fit local GMM with 3 components

	# In[46]:

	local_gmm = GMM(n_components=3, covariance_type='full')
	local_data = np.squeeze(np.concatenate((local_X, local_Y), axis=2))
	local_gmm.fit(local_data)


	# ## Plot local GMM

	# In[47]:

	local_gmminf = gmr.gmm.GMM(3,
	local_gmm.weights_,
	local_gmm.means_,
	local_gmm.covars_)


	# In[48]:

	ellipses = local_gmminf.to_ellipses(2)


	# In[49]:

	from matplotlib.patches import Ellipse

	fig = plt.figure()
	ax = fig.add_subplot(111, aspect='equal')
	ax.scatter(local_X, local_Y)


	for ellipse in ellipses:
	e = Ellipse(xy=ellipse[0], angle=ellipse[1][0]*180/np.pi, width=ellipse[1][1], height=ellipse[1][2])
	ax.add_artist(e)
	e.set_clip_box(ax.bbox)
	e.set_alpha(0.5)
	e.set_facecolor(rng.rand(3))

	plt.xlim([-0.1, 6 * np.pi + 0.1])
	plt.ylim([-6.5,6.5])


	# There is not enough gaussian to model this properly
	#
	# Such problem are arise quite often in our simple example, e.g. multidimensional arm
	#
	# Note that the same problem might arise with a simple NN model if we take the weighted mean of more than 1 neigborh

	# ## We compute and plot the conditional for y=3

	# In[50]:

	conditional_gmm = local_gmminf.condition([1], [3])


	# In[51]:

	proba = conditional_gmm.to_probability_density(X)
	plt.plot(X, proba)


	# ## Find the Max

	# In[52]:

	max_proba = np.max(proba)
	max_id = np.where(proba == max_proba)[0]
	max_value = X[max_id][0,0]


	# In[53]:

	plt.plot(X, proba)
	plt.plot([max_value, max_value], [0, max_proba] , 'r')


	# In[54]:

	fig = plt.figure(0)
	ax = fig.add_subplot(111, aspect='equal')
	ax.scatter(X, Y)
	ax.scatter(max_value, 3, 50, 'r')
	plt.xlim([-0.1, 6 * np.pi + 0.1])
	plt.ylim([-6.5,6.5])


	# This is not desired

	# # Would DPGMM solve the problem?
	#
	# Short answer: I did'nt succeed, on paper it is what we look for but in pratice it did not work on this simple example.
	#
	# I tried as above, simply replace GMM by DPGMM. It looked to me some prior was pulling Gaussians towards [0,0] but I am not sure at all..
	#
	# So I tried scaling the data, but this didn't help.
	#
	# ## Fit local DPGMM

	# In[55]:

	from sklearn.mixture import DPGMM
	local_gmm = DPGMM(n_components=10,
	covariance_type='full',
	alpha=1,
	tol=1e-3,
	params='wmc',
	init_params='wmc')
	local_data = np.squeeze(np.concatenate((local_X, local_Y), axis=2))
	local_gmm.fit(local_data)


	# Play a bit with the parameter to get a sense of what is a happening: http://scikit-learn.org/stable/modules/generated/sklearn.mixture.DPGMM.html#sklearn.mixture.DPGMM
	#
	# ## Plot local GMM

	# In[56]:

	local_gmminf = gmr.gmm.GMM(local_gmm.weights_.shape[0],
	local_gmm.weights_,
	local_gmm.means_,
	local_gmm._get_covars())


	# In[57]:

	ellipses = local_gmminf.to_ellipses(2)


	# In[58]:

	from matplotlib.patches import Ellipse

	fig = plt.figure()
	ax = fig.add_subplot(111) ##, aspect='equal')
	ax.scatter(local_X, local_Y)


	for ellipse in ellipses:
	e = Ellipse(xy=ellipse[0], angle=ellipse[1][0]*180/np.pi, width=ellipse[1][1], height=ellipse[1][2])
	ax.add_artist(e)
	e.set_clip_box(ax.bbox)
	e.set_alpha(0.5)
	e.set_facecolor(rng.rand(3))

	plt.xlim([-0.1, 6 * np.pi + 0.1])
	plt.ylim([-6.5,6.5])


	# Note that the Gaussian you see at [0,0] are the ones that are not in use, there is a way to know this. See here: http://scikit-learn.org/stable/auto_examples/mixture/plot_gmm_sin.html#example-mixture-plot-gmm-sin-py

	# ## Let's try to estimate the number of clusters with a clustering algorithm
	#
	# See: http://scikit-learn.org/stable/modules/clustering.html
	#
	# I picked: http://scikit-learn.org/stable/modules/generated/sklearn.cluster.AffinityPropagation.html#sklearn.cluster.AffinityPropagation
	#

	# In[59]:

	from sklearn.cluster import AffinityPropagation

	af = AffinityPropagation(damping=0.6)
	af.fit(local_data)
	n_clusters = len(af.cluster_centers_)
	print("We found {} clusters".format(n_clusters))


	# ## Plot the clusters

	# In[60]:

	fig = plt.figure()
	ax = fig.add_subplot(111) ##, aspect='equal')
	ax.scatter(local_X, local_Y, 5)

	for cs in af.cluster_centers_:
	ax.scatter(cs[0], cs[1], 100, rng.rand(3))

	plt.xlim([-0.1, 6 * np.pi + 0.1])
	plt.ylim([-6.5,6.5])


	# ## Let's use this number ot fit the GMM

	# In[61]:

	local_gmm = GMM(n_components=n_clusters, covariance_type='full')
	local_gmm.fit(local_data)


	# In[62]:

	local_gmminf = gmr.gmm.GMM(n_clusters,
	local_gmm.weights_,
	local_gmm.means_,
	local_gmm.covars_)


	# In[63]:

	ellipses = local_gmminf.to_ellipses(2)


	# In[64]:


	from matplotlib.patches import Ellipse

	fig = plt.figure()
	ax = fig.add_subplot(111, aspect='equal')
	ax.scatter(local_X, local_Y)


	for ellipse in ellipses:
	e = Ellipse(xy=ellipse[0], angle=ellipse[1][0]*180/np.pi, width=ellipse[1][1], height=ellipse[1][2])
	ax.add_artist(e)
	e.set_clip_box(ax.bbox)
	e.set_alpha(0.5)
	e.set_facecolor(rng.rand(3))

	plt.xlim([-0.1, 6 * np.pi + 0.1])
	plt.ylim([-6.5,6.5])


	# ## Compute the conditional for y=3

	# In[65]:

	conditional_gmm = local_gmminf.condition([1], [3])


	# In[66]:

	proba = conditional_gmm.to_probability_density(X)
	plt.plot(X, proba)


	# ## Find the max

	# In[67]:

	max_proba = np.max(proba)
	max_id = np.where(proba == max_proba)[0]
	max_value = X[max_id][0,0]


	# In[68]:

	plt.plot(X, proba)
	plt.plot([max_value, max_value], [0, max_proba] , 'r')


	# In[69]:

	fig = plt.figure(0)
	ax = fig.add_subplot(111, aspect='equal')
	ax.scatter(X, Y)
	ax.scatter(max_value, 3, 50, 'r')
	plt.xlim([-0.1, 6 * np.pi + 0.1])
	plt.ylim([-6.5,6.5])


	# Look good!
	#
	# # Discussion
	#
	# Finding the max of the conditional gmm is to be privileged. The weighted mean inevitably will give wrong answers.
	#
	# Finding the maximum is impossible analytically. Think of those cases when the maximum might not be unique (e.g. two Gaussians well separated of equal weights), it makes it really hard to find an analytical solution. I am sure talented mathematicians worked hard on this, if nothing is out there yet there must be a reason.
	#
	# Some have tried with gradient descent sort of things:
	#
	# - Pulkkinen, Seppo, Marko Mikael Mäkelä, and Napsu Karmitsa. "A continuation approach to mode-finding of multivariate Gaussian mixtures and kernel density estimates." Journal of Global Optimization 56.2 (2013): 459-487. https://www.researchgate.net/profile/Seppo_Pulkkinen/publication/255996172_A_continuation_approach_to_mode-finding_of_multivariate_Gaussian_mixtures_and_kernel_density_estimates/links/00b495215e455d90ed000000.pdf
	#
	# - Carreira-Perpiñán, Miguel Á. "Mode-finding for mixtures of Gaussian distributions." IEEE Transactions on Pattern Analysis & Machine Intelligence11 (2000): 1318-1323. http://faculty.ucmerced.edu/mcarreira-perpinan/papers/cs-99-03.pdf
	# De le même personne: http://www.cs.toronto.edu/~miguel/research/GMmodes.html
	# Code matlab: http://www.cs.toronto.edu/~miguel/research/software/gm_modes.tar.gz
	#
	# - des slides: https://www.utu.fi/en/units/sci/units/math/Research/optimization/Documents/sovmat13012012.pdf
	#
	#
	# But, as the function is generally very smooth, it should be easy to find the maximum using an optimization algorithm. CMA-ES should perfectly do the job, a quick study could be done on which initialization parameter to use.
	#
	# I propose the following for initializing CMA-ES: "mean = centroid (pondéré) des Gaussiennes de la GMM à évaluer, sigma = covariance (pondéré) des centres par rapports au mean(centroid) + régularisation sur la diagonale"
	#
	# Finally, in most scenario, it is way better to get stuck in a local maximum than sampling randomly or using the weighted mean. The next option is thus to take the mean of the Gaussian that has the largest weight.
	#
	#
	# ## Calinon's work and ILO-GMM paper
	#
	# For Calinon's work and ILO-GMM paper, I believe the weighted mean works because of the properties of the problem, i.e. trajectories. You are never at two positions at the same time. Or, if time is not in the input space, the feature are made such that the model is unimodal (e.g. adding current speed (dx, dy)).
	#
	# It would be worth checking Calinon litterature to see if they tried the following XP: A user move an obect from position A to B in straight line. We place an obstacle on the way. The user now decide randomly to go one side or the other of the obstacle.
	#
	# This creates a bimodal dataset, very similar to what we encounter in inverse model for robotics. Taking the weighted mean would make you run into the obstacle.
	#
	# How would Calinon's work handle this? I guess they run very early into such problems and might have found a solution. It is worth investigating.
	#
	#
	# # Conclusion
	#
	# It is important to consider the problem of redundancy/multilodalities/multimodes when designing our algorithms. Such problem is omnipresent in our robotic experiments when considering inverse models.
	#
	# NN (with k > 1) is not solving this problem. ILO-GMM, which models the multimodality, is promising but could be improved by adapting the number of Gaussians. For this we proposed to use a clustering algorithm.
	#
	# The clustering algorithm might fail when the data are not well separated but still non-linear. In such case, the clustering algorithm might tell us there is only one cluster, but modeling with one Gaussian won't be enough. To limit that problem we could:
	# - start by enforcing a minimum in the number of Gaussian to use, e.g. 3.
	# - use 3x the number of clusters as the number of components of the local GMM
	#
	# It would be nice to make a proper benchmark with a similar problem in a more concrete scenario, e.g. multi-segment arm.
	#
	# A future consideration should be the definition of locality, we consider each dimension as having the same local importance, that might not be the case in many practical problem. Can the robot/agent finds out by itself the weight to assign to each dimension for defining locality?