aflaxman/2015_06_10a_pymc3_laplace_approx_proof_of_concept (1).ipynb

## 2015_06_10a_pymc3_laplace_approx_proof_of_concept (1).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": [
        "Sat Jun 13 20:40:45 PDT 2015\r\n"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Laplace approximation in PyMC3\n",
      "\n",
      "Following the approach in http://www.seanet.com/~bradbell/tmb.htm, use the example from http://www.seanet.com/~bradbell/marginal_example.pdf"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pymc3 as pm, theano.tensor as tt, theano.tensor.slinalg, scipy.optimize"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 28
    },
    {
     "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",
      "    q=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.eye(q)\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=100, p=2, q=None, seed=12345)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 29
    },
    {
     "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": [],
     "prompt_number": 30
    },
    {
     "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 2.34 s, sys: 4 ms, total: 2.35 s\n",
        "Wall time: 2.43 s\n"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "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": [],
     "prompt_number": 32
    },
    {
     "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": 33
    },
    {
     "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": 34,
       "text": [
        "271.52666734010722"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "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: 184.814175\n",
        "         Iterations: 0\n",
        "         Function evaluations: 167\n",
        "         Gradient evaluations: 31\n",
        "CPU times: user 1.51 s, sys: 2 \u00b5s, total: 1.51 s\n",
        "Wall time: 1.51 s\n"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "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": 36,
       "text": [
        "<matplotlib.text.Text at 0x7f36f8cf7550>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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kKSovr9SMGUerqKjI09gziekxAPpKlWhsk3RMmtea13k+gAzxeknJ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\n8SKVHJJJzwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f36f98d2410>"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "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": 37,
       "text": [
        "<matplotlib.text.Text at 0x7f36f8c56ed0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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I2wJPAvfFGH9OxUWPkiQpz82bN5chQ84lxreq2p544jeceupgZ1Ak1alaLf2K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\nSUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f36f8c90f90>"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "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": 38,
       "text": [
        "<matplotlib.axes._subplots.AxesSubplot at 0x7f36f8c3a490>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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pyV9MU266upw4nN++aYsXHZt2/vcfVrAdmZrL/mZxYpJL0t7j8f0+JK3HePLr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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f36f8bc5250>"
       ]
      }
     ],
     "prompt_number": 38
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}