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@kforeman
Created March 11, 2015 21:04
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{
"metadata": {
"name": "",
"signature": "sha256:c4b96fc6cf951c4f9f77018991eb0df43bbfa0437920f6c69aa8d2ee5a06a2f2"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"PyMB Example"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Import Module"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import sys\n",
"sys.path.append('../..')\n",
"import PyMB\n",
"from PyMB import magic # enable %%PyMB cell magic\n",
"import numpy as np"
],
"language": "python",
"metadata": {},
"outputs": [
{
"javascript": [
"IPython.config.cell_magic_highlight['magic_clike'] = {'reg':[/^%%PyMB/]};"
],
"metadata": {},
"output_type": "display_data"
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Define the model"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$ Y \\sim \\mathcal{N}(\\hat{Y},\\sigma) $$\n",
"$$ \\hat{Y} = \\alpha + B x $$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Based on [https://github.com/kaskr/adcomp/blob/master/tmb_examples/linreg.cpp](https://github.com/kaskr/adcomp/blob/master/tmb_examples/linreg.cpp)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"See [the TMB tutorial](https://github.com/kaskr/adcomp/wiki/Tutorial#writing-the-c-function) for more information on writing custom models"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"%%PyMB LinearRegression\n",
"// DATA\n",
" DATA_VECTOR(Y);\n",
" DATA_VECTOR(x);\n",
"\n",
"// PARAMETERS\n",
" PARAMETER(alpha);\n",
" PARAMETER(Beta);\n",
" PARAMETER(logSigma);\n",
"\n",
"// MODEL\n",
" vector<Type> Y_hat = alpha + Beta*x;\n",
" REPORT(Y_hat);\n",
" Type nll = -sum(dnorm(Y, Y_hat, exp(logSigma), true));\n",
" return nll;"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Created model LinearRegression.\n",
"Using tmb_tmp/LinearRegression.cpp.\n",
"Compiled in 24.3s.\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Simulate data"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"LinearRegression.data = {\n",
" 'x': np.arange(10),\n",
" 'Y': np.random.normal(np.arange(10))\n",
"}"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Set initial parameter values"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"LinearRegression.init = {\n",
" 'alpha': 0.,\n",
" 'Beta': 0.,\n",
" 'logSigma': 0.\n",
"}"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Fit the model"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The model likelihood will be integrated wrt the random parameters. See [here](https://github.com/kaskr/adcomp/wiki/Tutorial#integrated-likelihood) for more information."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"LinearRegression.optimize(random=['alpha','Beta'])"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Matching hessian patterns... Done\n",
"\n",
"Model optimization complete in 0.1s.\n",
"\n",
"\n",
"--------------------------------------------------------------------------------\n",
"\n",
"\n",
"Simulated 100 draws in 0.2s.\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"alpha:\n",
"\tmean\t[ 0.31609895]\n",
"\tsd\t[ 0.73192141]\n",
"\tdraws\t[[-0.72558336 -0.71637844 ..., 1.25651001 -0.43803027]]\n",
"\tshape\t(1, 100)\n",
"Beta:\n",
"\tmean\t[ 0.88899844]\n",
"\tsd\t[ 0.13710144]\n",
"\tdraws\t[[ 1.09499943 1.00378394 ..., 0.55369137 0.89730876]]\n",
"\tshape\t(1, 100)\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Extract fitted values"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print(LinearRegression.report('Y_hat'))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"[ 0.31609895 1.20509738 2.09409582 2.98309425 3.87209269 4.76109113\n",
" 5.65008956 6.539088 7.42808643 8.31708487]\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Examine joint density"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"%matplotlib inline\n",
"import matplotlib.pyplot as plt\n",
"import seaborn as sns\n",
"import pandas as pd\n",
"df = pd.DataFrame({ k: v['draws'][0] for k,v in LinearRegression.parameters.iteritems() })\n",
"g = sns.PairGrid(df, diag_sharey=False)\n",
"g.map_lower(sns.kdeplot, cmap='Blues_d')\n",
"g.map_upper(plt.scatter)\n",
"g.map_diag(sns.kdeplot, lw=3)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stderr",
"text": [
"/usr/bin/anaconda/lib/python2.7/site-packages/matplotlib/axes/_axes.py:476: UserWarning: No labelled objects found. Use label='...' kwarg on individual plots.\n",
" warnings.warn(\"No labelled objects found. \"\n"
]
},
{
"metadata": {},
"output_type": "display_data",
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7ZBugksoWSvoyNV2TDgpnJo1a28iTkhViwGiBqEtrbQPalVKlWutuAK21TSnV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tXQ2MxTr3/SbgXRK+dNIneKnZKLtDEjB3PnVTOIc+/PKik/zmP/tTVwoUh/YInIGNOl8qpaHnlx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\nGF9ZIjLGGOOr/wdveVmJ9D4siwAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x7f8237203810>"
]
}
],
"prompt_number": 7
}
],
"metadata": {}
}
]
}
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