Skip to content

Instantly share code, notes, and snippets.

Show Gist options
  • Star 7 You must be signed in to star a gist
  • Fork 1 You must be signed in to fork a gist
  • Save AustinRochford/fa24221f09df20071c06 to your computer and use it in GitHub Desktop.
Save AustinRochford/fa24221f09df20071c06 to your computer and use it in GitHub Desktop.
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"title: Fitting a Multivariate Normal Model in PyMC3 with an LKJ Prior\n",
"tags: Bayesian Statistics, PyMC3\n",
"---"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Outside of the [beta](https://en.wikipedia.org/wiki/Beta_distribution)-[binomial](https://en.wikipedia.org/wiki/Binomial_distribution) model, the multivariate normal model is likely the most studied Bayesian model in history. Unfortunately, as this [issue](https://github.com/pymc-devs/pymc3/issues/538) shows, `pymc3` cannot (yet) sample from the standard conjugate [normal-Wishart](https://en.wikipedia.org/wiki/Normal-Wishart_distribution) model. Fortunately, `pymc3` *does* support sampling from the [LKJ distribution](http://www.sciencedirect.com/science/article/pii/S0047259X09000876). This post will show how to fit a simple multivariate normal model using `pymc3` with an normal-LKJ prior.\n",
"\n",
"The normal-Wishart prior is conjugate for the multivariate normal model, so we can find the posterior distribution in closed form. Even with this closed form solution, sampling from a multivariate normal model in `pymc3` is important as a building block for more complex models that will be discussed in future posts.\n",
"\n",
"First, we generate some two-dimensional sample data."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Couldn't import dot_parser, loading of dot files will not be possible.\n"
]
}
],
"source": [
"from matplotlib.patches import Ellipse\n",
"from matplotlib import pyplot as plt\n",
"import numpy as np\n",
"import pymc3 as pm\n",
"import scipy as sp\n",
"import seaborn as sns\n",
"from theano import tensor as T"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"np.random.seed(3264602) # from random.org"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"N = 100\n",
"\n",
"mu_actual = sp.stats.uniform.rvs(-5, 10, size=2)\n",
"\n",
"cov_actual_sqrt = sp.stats.uniform.rvs(0, 2, size=(2, 2))\n",
"cov_actual = np.dot(cov_actual_sqrt.T, cov_actual_sqrt)\n",
"\n",
"x = sp.stats.multivariate_normal.rvs(mu_actual, cov_actual, size=N)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"var, U = np.linalg.eig(cov_actual)\n",
"angle = 180. / np.pi * np.arccos(np.abs(U[0, 0]))"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAecAAAFzCAYAAAAE+sEBAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\niEhmGM5EREQyw3AmIiKSmf8P1mRTInjtNNsAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f5405c6a850>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(8, 6))\n",
"\n",
"blue = sns.color_palette()[0]\n",
"\n",
"e = Ellipse(mu_actual, 2 * np.sqrt(5.991 * var[0]), 2 * np.sqrt(5.991 * var[1]), angle=-angle)\n",
"e.set_alpha(0.5)\n",
"e.set_facecolor('gray')\n",
"e.set_zorder(10);\n",
"ax.add_artist(e);\n",
"\n",
"ax.scatter(x[:, 0], x[:, 1], c='k', alpha=0.5, zorder=11);\n",
"\n",
"rect = plt.Rectangle((0, 0), 1, 1, fc='gray', alpha=0.5)\n",
"ax.legend([rect], ['95% true credible region'], loc=2);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The sampling distribution for our model is $x_i \\sim N(\\mu, \\Lambda)$, where $\\Lambda$ is the [precision matrix](https://en.wikipedia.org/wiki/Precision_(statistics)) of the distribution. The precision matrix is the inverse of the covariance matrix. The support of the LKJ distribution is the set of [correlation matrices](https://en.wikipedia.org/wiki/Correlation_and_dependence#Correlation_matrices), not covariance matrices. We will use the separation strategy from [Barnard et al.](http://www3.stat.sinica.edu.tw/statistica/oldpdf/A10n416.pdf) to combine an LKJ prior on the correlation matrix with a prior on the standard deviations of each dimension to produce a prior on the covariance matrix.\n",
"\n",
"Let $\\sigma$ be the vector of standard deviations of each component of our normal distribution, and $\\mathbf{C}$ be the correlation matrix. The relationship\n",
"\n",
"$$\\Sigma = \\operatorname{diag}(\\sigma)\\ \\mathbf{C} \\operatorname{diag}(\\sigma)$$\n",
"\n",
"shows that priors on $\\sigma$ and $\\mathbf{C}$ will induce a prior on $\\Sigma$. Following Barnard et al., we place a standard [lognormal](https://en.wikipedia.org/wiki/Log-normal_distribution) prior each the elements $\\sigma$, and an LKJ prior on the correlation matric $\\mathbf{C}$. The LKJ distribution requires a shape parameter $\\nu > 0$. If $\\mathbf{C} \\sim LKJ(\\nu)$, then $f(\\mathbf{C}) \\propto |\\mathbf{C}|^{\\nu - 1}$ (here $|\\cdot|$ is the determinant).\n",
"\n",
"We can now begin to build this model in `pymc3`."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"with pm.Model() as model:\n",
" sigma = pm.Lognormal('sigma', np.zeros(2), np.ones(2), shape=2)\n",
" \n",
" nu = pm.Uniform('nu', 0, 5)\n",
" C_triu = pm.LKJCorr('C_triu', nu, 2) "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"There is a slight complication in `pymc3`'s handling of the `LKJCorr` distribution; `pymc3` represents the support of this distribution as a one-dimensional vector of the upper triangular elements of the full covariance matrix. "
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false,
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"(1,)"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"C_triu.tag.test_value.shape"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In order to build a the full correlation matric $\\mathbf{C}$, we first build a $2 \\times 2$ tensor whose values are all `C_triu` and then set the diagonal entries to one. (Recall that a correlation matrix must be symmetric and positive definite with all diagonal entries equal to one.) We can then proceed to build the covariance matrix $\\Sigma$ and the precision matrix $\\Lambda$."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"with model:\n",
" C = pm.Deterministic('C', T.fill_diagonal(C_triu[np.zeros((2, 2), dtype=np.int64)], 1.))\n",
" \n",
" sigma_diag = pm.Deterministic('sigma_mat', T.nlinalg.diag(sigma))\n",
" cov = pm.Deterministic('cov', T.nlinalg.matrix_dot(sigma_diag, C, sigma_diag))\n",
" tau = pm.Deterministic('tau', T.nlinalg.matrix_inverse(cov))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"While defining `C` in terms of `C_triu` was simple in this case because our sampling distribution is two-dimensional, the example from this [StackOverflow question](http://stackoverflow.com/questions/29759789/modified-bpmf-in-pymc3-using-lkjcorr-priors-positivedefiniteerror-using-nuts) shows how to generalize this transformation to arbitrarily many dimensions.\n",
"\n",
"Finally, we define the prior on $\\mu$ and the sampling distribution."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"with model:\n",
" mu = pm.MvNormal('mu', 0, tau, shape=2)\n",
" \n",
" x_ = pm.MvNormal('x', mu, tau, observed=x)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We are now ready to fit this model using `pymc3`."
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"n_samples = 4000\n",
"n_burn = 2000\n",
"n_thin = 2"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" [-----------------100%-----------------] 4000 of 4000 complete in 5.8 sec"
]
}
],
"source": [
"with model:\n",
" step = pm.Metropolis()\n",
" trace_ = pm.sample(n_samples, step)"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"trace = trace_[n_burn::n_thin]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We see that the posterior estimate of $\\mu$ is reasonably accurate."
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAA1cAAACJCAYAAADAHsIyAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nP/bPSUo+OaVxAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f53f640d210>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pm.traceplot(trace, vars=['mu']);"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([-1.41086412, -4.6853101 ])"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"trace['mu'].mean(axis=0)"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([-1.41866859, -4.8018335 ])"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"mu_actual"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The estimates of the standard deviations are certainly biased."
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAA1cAAACJCAYAAADAHsIyAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nFMo48P8DejIbr7fmWSkAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f540611df90>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pm.traceplot(trace, vars=['sigma']);"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([ 0.75736536, 1.49451149])"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"trace['sigma'].mean(axis=0)"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([ 0.3522422 , 1.58192855])"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.sqrt(var)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"However, the 95% posterior credible region is visuall quite close to the true credible region, so we can be fairly satisfied with our model."
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"post_cov = trace['cov'].mean(axis=0)\n",
"\n",
"post_sigma, post_U = np.linalg.eig(post_cov)\n",
"post_angle = 180. / np.pi * np.arccos(np.abs(post_U[0, 0]))"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAecAAAFzCAYAAAAE+sEBAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nnImIiGSGyZmIiEhmmJyJiIhk5v8Do8KyO+VjSPEAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f53f5a52e90>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(8, 6))\n",
"\n",
"blue = sns.color_palette()[0]\n",
"\n",
"e = Ellipse(mu_actual, 2 * np.sqrt(5.991 * post_sigma[0]), 2 * np.sqrt(5.991 * post_sigma[1]), angle=-post_angle)\n",
"e.set_alpha(0.5)\n",
"e.set_facecolor(blue)\n",
"e.set_zorder(9);\n",
"ax.add_artist(e);\n",
"\n",
"e = Ellipse(mu_actual, 2 * np.sqrt(5.991 * var[0]), 2 * np.sqrt(5.991 * var[1]), angle=-angle)\n",
"e.set_alpha(0.5)\n",
"e.set_facecolor('gray')\n",
"e.set_zorder(10);\n",
"ax.add_artist(e);\n",
"\n",
"ax.scatter(x[:, 0], x[:, 1], c='k', alpha=0.5, zorder=11);\n",
"\n",
"rect = plt.Rectangle((0, 0), 1, 1, fc='gray', alpha=0.5)\n",
"post_rect = plt.Rectangle((0, 0), 1, 1, fc=blue, alpha=0.5)\n",
"ax.legend([rect, post_rect],\n",
" ['95% true credible region',\n",
" '95% posterior credible region'],\n",
" loc=2);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Again, this model is quite simple, but will be an important component of more complex models that I will blog about in the future.\n",
"\n",
"This post is available as an [IPython](http://ipython.org/) notebook [here](https://gist.github.com/AustinRochford/fa24221f09df20071c06)."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.6"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment