aflaxman/2015_06_10a_pymc3_laplace_approx_proof_of_concept.ipynb

## 2015_06_10a_pymc3_laplace_approx_proof_of_concept.ipynb
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  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "!date\n",
      "import numpy as np, pandas as pd, matplotlib.pyplot as plt, seaborn as sns\n",
      "%matplotlib inline\n",
      "sns.set_context('poster')\n",
      "sns.set_style('darkgrid')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Thu Jun 11 10:52:33 PDT 2015\r\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Laplace approximation in PyMC3\n",
      "\n",
      "Following the approach in http://www.seanet.com/~bradbell/tmb.htm"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pymc3 as pm, theano.tensor as tt, theano.tensor.slinalg, scipy.optimize"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Couldn't import dot_parser, loading of dot files will not be possible.\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def sim_data(n, p, q, seed):\n",
      "    \"\"\"Simulate data to fit with Laplace approximation\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    n : int, rows of data\n",
      "    p : int, number of fixed effect coeffs\n",
      "    q : int, number of random effect coeffs\n",
      "    \n",
      "    Results\n",
      "    -------\n",
      "    returns dict  PyMC3 model\n",
      "    \"\"\"\n",
      "\n",
      "    # sim data for random effect model\n",
      "    np.random.seed(seed)  # set random seed for reproducibility\n",
      "\n",
      "    # ground truth for model parameters\n",
      "    beta_true = np.linspace(-1,1,p)\n",
      "\n",
      "    u_true = np.linspace(-1,1,q)\n",
      "    sigma_true = .1\n",
      "\n",
      "    # covariates\n",
      "    X = np.random.normal(size=(n,p))\n",
      "    Z = np.random.uniform(0, 1, size=(n,q))\n",
      "    Z = 1. * (Z < .1)\n",
      "\n",
      "    # observed data\n",
      "    y = np.dot(X, beta_true) + np.dot(Z, u_true) + np.random.normal(0., sigma_true, size=n)\n",
      "\n",
      "    return locals()\n",
      "data = sim_data(n=1000, p=5, q=500, seed=12345)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def make_model(data):\n",
      "    \"\"\"Create a random effects model from simulated data\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    data : dict, as returned by sim_data function\n",
      "    \n",
      "    Results\n",
      "    -------\n",
      "    returns PyMC3 model for data\n",
      "    \"\"\"\n",
      "    \n",
      "    m = pm.Model()\n",
      "    with m:\n",
      "        beta  = pm.Normal('beta', mu=0., sd=1., shape=data['p'])\n",
      "        u     = pm.Normal('u', mu=0., sd=1., shape=data['q'])\n",
      "        sigma = pm.HalfNormal('sigma', sd=1.)\n",
      "\n",
      "        y_obs = pm.Normal('y_obs', mu=tt.dot(data['X'], beta) + tt.dot(data['Z'], u), sd=sigma, observed=data['y'])\n",
      "        \n",
      "    return m\n",
      "\n",
      "m = make_model(data)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "WARNING (theano.gof.compilelock): Overriding existing lock by dead process '32184' (I am process '24906')\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "WARNING:theano.gof.compilelock:Overriding existing lock by dead process '32184' (I am process '24906')\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Cannot compute test value: input 0 (<TensorType(float32, matrix)>) of Op Dot22(<TensorType(float32, matrix)>, <TensorType(float32, matrix)>) missing default value\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# find MAP\n",
      "with m:\n",
      "    %time map_pt = pm.find_MAP()\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "CPU times: user 34.3 s, sys: 268 ms, total: 34.5 s\n",
        "Wall time: 34.7 s\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# find Laplace approximation, by approximating integral of random effects with determinant of Hessian\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "H_uu = pm.hessian(m.logpt, [m.u])\n",
      "\n",
      "# use Cholesky factorization to calculate determinant\n",
      "L_H_uu = theano.tensor.slinalg.Cholesky()(H_uu)\n",
      "\n",
      "# calculate log determinant of H_uu by summing log of diagonal of Cholesky factorization\n",
      "log_det_H_uu = tt.sum(tt.log(tt.diag(L_H_uu)))\n",
      "\n",
      "# make that into a theano function\n",
      "f_log_det_H_uu = m.fn(log_det_H_uu)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "/homes/abie/anaconda/envs/testenv/lib/python2.7/site-packages/theano/scan_module/scan_perform_ext.py:133: RuntimeWarning: numpy.ndarray size changed, may indicate binary incompatibility\n",
        "  from scan_perform.scan_perform import *\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def argmax_u(m, start):\n",
      "    \"\"\"Find u that maximizes model posterior for fixed beta, sigma\n",
      "    \n",
      "    Parameter\n",
      "    ---------\n",
      "    start : dict, with keys for all (transformed) model, e.g.\n",
      "      start={'u':np.zeros(q), 'beta':beta_val, 'sigma_log':np.log(sigma_val)}\n",
      "      \n",
      "    Results\n",
      "    -------\n",
      "    return u_hat as an array\n",
      "    \"\"\"\n",
      "    \n",
      "    with m:\n",
      "        pt = pm.find_MAP(start=start, vars=[m.u])\n",
      "    return pt['u']\n",
      "\n",
      "u_hat = argmax_u(m, {'u':np.zeros(data['q']), 'beta':.5*np.ones(data['p']), 'sigma_log':np.log(.1)})"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "u_hat = np.zeros(data['q'])\n",
      "\n",
      "def approx_marginal_neg_log_posterior(theta):\n",
      "    \"\"\"Laplace approximation of the marginal negative log posterior of m\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    theta : array of shape (p+1,), with first p for beta, and final entry for sigma\n",
      "    \n",
      "    Results\n",
      "    -------\n",
      "    returns approx -logp as a float\n",
      "    \"\"\"\n",
      "    global u_hat\n",
      "    global m\n",
      "    beta = theta[:-1]\n",
      "    \n",
      "    sigma = theta[-1]\n",
      "    # prevent optimizer from going astray\n",
      "    if sigma <= 1e-6:\n",
      "        sigma = 1e-6\n",
      "    sigma_log = np.log(sigma)\n",
      "    \n",
      "    pt = {'u': u_hat, 'beta': beta, 'sigma_log':sigma_log}\n",
      "    u_hat = argmax_u(m, pt)\n",
      "    pt['u'] = u_hat\n",
      "    det_H_logp = f_log_det_H_uu(pt)\n",
      "    \n",
      "    return .5*det_H_logp - m.logp(pt)\n",
      "    \n",
      "\n",
      "approx_marginal_neg_log_posterior(.5*np.ones(data['p']+1))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "4704.9488202994035"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%time theta = scipy.optimize.fmin_bfgs(approx_marginal_neg_log_posterior, .1*np.ones(data['p']+1))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Warning: Desired error not necessarily achieved due to precision loss.\n",
        "         Current function value: 496.161295\n",
        "         Iterations: 66\n",
        "         Function evaluations: 862\n",
        "         Gradient evaluations: 106\n",
        "CPU times: user 26min 17s, sys: 11.2 s, total: 26min 28s\n",
        "Wall time: 26min 29s\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Compare the results"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(map_pt['u'], u_hat, 'o')\n",
      "plt.plot([-1,1], [-1,1], 'k--')\n",
      "\n",
      "plt.xlabel('Random Effect Coeffs from MAP')\n",
      "plt.ylabel('Random Effect Coeffs from LA')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "<matplotlib.text.Text at 0x7fc67d90b250>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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jqS1qVkiJMVaHEJYDqff+kyRJ7drE+2cxe0nm0wBKuvSiU5debFj7LgVFHdhr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\nt5o5h9duxxrDZ10x070OfDuPY+fGGD/Ncmw3km4Ls1odoVqqNXXb4Ac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       "text": [
        "<matplotlib.figure.Figure at 0x7fc67df54f10>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(map_pt['beta'], theta[:-1], 'o')\n",
      "plt.plot([-1,1], [-1,1], 'k--')\n",
      "plt.xlabel('Fixed Effect Coeffs from MAP')\n",
      "plt.ylabel('Fixed Effect Coeffs from LA')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "<matplotlib.text.Text at 0x7fc67d782250>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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LZEalACirpX8V0Hzb4kiSpFzTqVNnysvLAdh55w5MnDiJI444MuFUknJdJjMq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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fc67d87ee10>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pd.Series({'Spread of RE from MAP': np.exp(map_pt['sigma_log']),\n",
      "          'Spread of RE from LA': theta[-1]}).plot(kind='barh')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "<matplotlib.axes._subplots.AxesSubplot at 0x7fc67d723210>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Q22+uHa613lJKeeWw7Clp57beJW2W3a/l1gFp0derrbXeUEo5LslbSikH1Vqn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\nYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fc67d87e410>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    }
   ],
   "metadata": {}
  }
 ]
}