diff --git a/docs/source/examples.rst b/docs/source/examples.rst index 06859f216c..508b4365c9 100644 --- a/docs/source/examples.rst +++ b/docs/source/examples.rst @@ -6,6 +6,7 @@ Examples .. toctree:: notebooks/BEST.ipynb + notebooks/LKJ.ipynb notebooks/stochastic_volatility.ipynb notebooks/GLM-linear.ipynb notebooks/GLM-robust.ipynb diff --git a/docs/source/notebooks/LKJ.ipynb b/docs/source/notebooks/LKJ.ipynb new file mode 100644 index 0000000000..8dcd9fdd4b --- /dev/null +++ b/docs/source/notebooks/LKJ.ipynb @@ -0,0 +1,538 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Fitting a Multivariate Normal Model in PyMC3 with an LKJ Prior\n", + "\n", + "Author: [Austin Rochford](www.austinrochford.com)" + ] + }, + { + "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.\n", + "\n", + "First, we generate some two-dimensional sample data." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [], + "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 tt" + ] + }, + { + "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": 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imueI89tXc7vdGDLkGuTm5skdCkmMiZqSXjgcxpYtmxAK+ZGeniHJY8Z7aFqN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\n/lxTU4Np06ZJGmN3umvDqlWrsH79erz77rud3qb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+ "text/plain": [ + "" + ] + }, + "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": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Applied log-transform to sigma and added transformed sigma_log_ to model.\n", + "Applied interval-transform to nu and added transformed nu_interval_ to model.\n" + ] + } + ], + "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', tt.fill_diagonal(C_triu[np.zeros((2, 2), dtype=np.int64)], 1.))\n", + " \n", + " sigma_diag = pm.Deterministic('sigma_mat', tt.nlinalg.diag(sigma))\n", + " cov = pm.Deterministic('cov', tt.nlinalg.matrix_dot(sigma_diag, C, sigma_diag))" + ] + }, + { + "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, cov, shape=2)\n", + " \n", + " x_ = pm.MvNormal('x', mu, cov, 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": "stderr", + "output_type": "stream", + "text": [ + "WARNING (theano.tensor.blas): We did not found a dynamic library into the library_dir of the library we use for blas. If you use ATLAS, make sure to compile it with dynamics library.\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + " [-------100%-------] 4000 of 4000 in 4.1 sec. | SPS: 974.5 | ETA: 0.0" + ] + } + ], + "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": 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6s1iCIAiDhrN1jZ6jJQ+w56cytLVPbTwU1dbWdvr8jBkz+nzs+++/nzfffBOd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\nYOnSpTh48CCdO3Fee+01NDU1YdmyZXj44YfBcdxVPXcee+wx3HzzzVi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"metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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RoebcDZXDV8rn++P+fTg4cBjp7IKErMjoiHZpRWoKjT2bc2+5bBXCYDKYqeqn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\nTeTYzVrXMgGBWRVu6pp9gwyXlBNlMSVn690OM+5Uxy6BjEgXJB2ywhw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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "pm.traceplot(trace, varnames=['sigma']);" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 0.75396223, 1.49310645])" + ] + }, + "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 visually 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": 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aIYSYxlRV5Xj1aY6f6cRgn43VqSURj9NSfxytGqFkAnuhRe4K+HxULF465O1F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\nTNREREQqxkRNRESkYkzUREREKvb/AYXgv43sgWt3AAAAAElFTkSuQmCC\n", + "text/plain": [ + "" + ] + }, + "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);" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.1" + }, + "widgets": { + "state": {}, + "version": "1.1.2" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +}