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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# BBVI vs MLE for Variational inference\n",
"\n",
"We compare the estimations computed by Black Box Variational Inference (BBVI) and a more clasical Maximum Likelihood Estimator (MLE) for solving a logistic regression problem."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Imports and setup"
]
},
{
"cell_type": "code",
"execution_count": 59,
"metadata": {},
"outputs": [],
"source": [
"from autograd import grad\n",
"from autograd.extend import primitive, defvjp\n",
"from autograd.misc.optimizers import adam\n",
"import autograd.numpy as np\n",
"import autograd.numpy.random as npr\n",
"import autograd.scipy.stats.multivariate_normal as mvn\n",
"from autograd.test_util import check_grads\n",
"\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline\n",
"\n",
"@primitive\n",
"def to_tril(x):\n",
" d = int((np.sqrt(1 + 8*x.shape[0]) - 1) / 2)\n",
" L = np.zeros((d,d))\n",
" L[np.tril_indices(d)] = x\n",
" \n",
" return L\n",
"\n",
"def to_tril_vjp(ans, x):\n",
" d = ans.shape[0]\n",
" idx = np.tril_indices(d)\n",
" def vjp(g):\n",
" return g[idx]\n",
" \n",
" return vjp\n",
"\n",
"defvjp(to_tril, to_tril_vjp)\n",
"check_grads(to_tril, modes=['rev'])(npr.rand(3))\n",
"\n",
"@primitive\n",
"def set_diag(mat, x):\n",
" y = mat.copy()\n",
" y[np.diag_indices(mat.shape[0])] = x\n",
" return y\n",
"\n",
"def set_diag_vjp_1(ans, mat, x):\n",
" d = mat.shape[0]\n",
" z = np.zeros(d)\n",
" def vjp(g): return set_diag(g, z)\n",
" return vjp\n",
"\n",
"def set_diag_vjp_2(ans, mat, x):\n",
" idx = np.diag_indices(mat.shape[0])\n",
" def vjp(g): return g[idx]\n",
" return vjp\n",
"\n",
"defvjp(set_diag, set_diag_vjp_1, set_diag_vjp_2)\n",
"check_grads(set_diag, modes=['rev'])(npr.rand(3,3), npr.rand(3))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Setup\n",
"\n",
"Nothing surprising here, simply fake data and a binomial outcome model with model parameters $\\beta$. The error has a standard deviation of $0.1$."
]
},
{
"cell_type": "code",
"execution_count": 60,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"def logit_inv(eta):\n",
" return 1 / (1 + np.exp(-eta))\n",
"\n",
"def loglikelihood(w, s=0):\n",
" y_hat = logit_inv(np.dot(X, w))\n",
" return np.sum(np.log(y_hat[y==1])) + np.sum(np.log(1-y_hat[y==0]))\n",
"\n",
"n_obs = 1000\n",
"\n",
"betas = np.array([1, 4, -4])\n",
"D = betas.shape[0]\n",
"err = np.random.normal(size=n_obs, scale=0.1)\n",
"\n",
"# intercept-only model\n",
"X = np.random.multivariate_normal(np.zeros(D-1), np.eye(D-1), size=n_obs)\n",
"X = np.concatenate([np.ones(shape=(n_obs, 1)), X], axis=1)\n",
"\n",
"# logistic regression model\n",
"eta = X.dot(betas) + err\n",
"y = np.random.binomial(1, logit_inv(eta))\n",
"\n",
"plt.plot(X[:, 1], -(betas[0] + betas[1]*X[:, 1])/ betas[2], label=\"real decision boundary\")\n",
"plt.scatter(X[y==0, 1], X[y==0, 2], facecolors='none', edgecolors='r', label='y=0')\n",
"plt.scatter(X[y==1, 1], X[y==1, 2], marker='x', c='g', label='y=1')\n",
"plt.legend();"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## BBVI\n",
"\n",
"Based on existing implementation [1], estimating the posterior by maximizing the ELBO within a family of Gaussians with full-rank posterior. General useful information can be found in [2].\n",
"\n",
"We put a $N(0, 1)$ prior on the parameter $\\beta$.\n",
"\n",
"[1] https://www.cs.toronto.edu/~duvenaud/papers/blackbox.pdf\n",
"\n",
"[2] https://www.inf.ed.ac.uk/teaching/courses/mlpr/2018/notes/w9b_variational_details.html"
]
},
{
"cell_type": "code",
"execution_count": 70,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"log p(y|beta) = -226.290094\n",
"beta = [ 0.63090634 3.65817849 -3.65504584]\n",
"cov = \n",
"[[ 0.05476707 0.03082829 -0.03639252]\n",
" [ 0.03082829 0.16983083 -0.14133172]\n",
" [-0.03639252 -0.14133172 0.23042038]]\n",
"\n",
"CPU times: user 3.69 s, sys: 5.79 ms, total: 3.69 s\n",
"Wall time: 3.7 s\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"%%time\n",
"\n",
"# Setup the gradient of the objective function:\n",
"#\n",
"# J(m,V)=𝔼q[log q(w)]−𝔼q[log p(D|w)]−𝔼q[log p(w)]\n",
"#\n",
"# Based on the log likelihood: log p(D|w)\n",
"def make_grad_J(D, loglikelihood, prior_var, K=1):\n",
" \n",
" # Here we just compute: J(m,V)=𝔼q[log q(w)]−𝔼q[log p(D|w)]−𝔼q[log p(w)]\n",
" def J(params, t): \n",
" mean = params[:D]\n",
" L = x_to_L(params[D:])\n",
"\n",
" j = 0\n",
" \n",
" # neg entropy: 𝔼q[log q(w)] = -D/2 - log[ det(2pi * LL') ]/2\n",
" j += 0.5*D + np.sum(np.log(np.diag(L)))\n",
" \n",
" # cross entropy: 𝔼q[log p(w)]\n",
" # we assume a N(0, prior_var * Id)\n",
" # => 𝔼q[log p(w)] = Tr[LL']\n",
" j -= 0.5 * (np.linalg.norm(L, ord='fro')**2 + np.dot(mean, mean)) / prior_var\n",
" j -= 0.5 * D * np.log(prior_var)\n",
" \n",
" # log likelihood: 𝔼q[log p(D|w)]\n",
" # we use a MC approximation with 1 sample\n",
" for i in range(K):\n",
" u = npr.randn(D)\n",
" w = mean + np.dot(L, u)\n",
" j -= loglikelihood(w)/K\n",
" \n",
" return j\n",
" \n",
" grad_loglikelihood = grad(loglikelihood)\n",
" \n",
" return J, grad(J)\n",
"\n",
"\n",
"def x_to_L(x):\n",
" L = to_tril(x)\n",
" return set_diag(L, np.exp(np.diag(L)))\n",
"\n",
"num_iters = 2000\n",
"objs = np.zeros(shape=(num_iters, 2))\n",
"def callback(params, t, g):\n",
" objs[t,0] = batch_loglikelihood(params[:D])\n",
" objs[t,1] = J(params, t)\n",
"\n",
"D = betas.shape[0]\n",
"\n",
"init_mean = np.ones(D)\n",
"init_prec = np.ones(D*(D+1)/2)\n",
"init_params = np.concatenate([init_mean, init_prec])\n",
"\n",
"M = 0\n",
"batch_loglikelihood = lambda w: loglikelihood(w, s=M)*n_obs/max(1, M)\n",
"J, DJ = make_grad_J(D, batch_loglikelihood, 2, K=1)\n",
"\n",
"params = adam(DJ, init_params, step_size=0.01, num_iters=num_iters, callback=callback)\n",
"vi_betas = params[:D]\n",
"vi_L = x_to_L(params[D:])\n",
"\n",
"print(\"log p(y|beta) = %f\" % loglikelihood(params[:D]))\n",
"print(\"beta = %s\" % str(params[:D]))\n",
"print(\"cov = \\n%s\\n\" % str(vi_L.dot(vi_L.T)))\n",
"\n",
"plt.grid()\n",
"plt.xlabel(\"epoch\")\n",
"plt.plot(range(len(objs)), -objs[:,1], label=\"ELBO\", c=\"orange\")\n",
"plt.plot(range(len(objs)), objs[:,0], label=\"log p(y|w)\", c=\"blue\")\n",
"plt.legend()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## MLE\n",
"\n",
"Compute the MLE for both $\\beta$ and it's covariance. We first estimate $\\beta$ by maximizing the log likelihood and copmute the covariance estimate based on the estimated $\\beta$."
]
},
{
"cell_type": "code",
"execution_count": 62,
"metadata": {
"scrolled": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"log p(y|beta) = -225.772026\n",
"beta = [ 0.71176614 3.7851964 -3.75612606]\n",
"cov = \n",
"[[ 3.33601196e-04 -7.94546936e-06 5.09154122e-06]\n",
" [-7.94546936e-06 3.05052530e-04 -2.16260974e-05]\n",
" [ 5.09154122e-06 -2.16260974e-05 3.38165502e-04]]\n",
"\n",
"CPU times: user 1.53 s, sys: 9.84 ms, total: 1.54 s\n",
"Wall time: 1.51 s\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"%%time\n",
"\n",
"num_iters = 2000\n",
"objs = np.zeros(num_iters)\n",
"def callback(params, t, g): objs[t] = loglikelihood(params)\n",
"\n",
"D = betas.shape[0]\n",
"init_mean = np.ones(D)\n",
"\n",
"Dll = grad(lambda w, t: -loglikelihood(w))\n",
"\n",
"mle_betas = adam(Dll, init_mean, step_size=0.01, num_iters=num_iters, callback=callback)\n",
"mle_p = logit_inv(X.dot(mle_betas))\n",
"mle_D = np.diag(mle_p*(1-mle_p))\n",
"mle_cov = np.linalg.inv(X.T.dot(D).dot(X))\n",
"mle_L = np.linalg.cholesky(np.linalg.cholesky(mle_cov))\n",
"\n",
"print(\"log p(y|beta) = %f\" % objs[-1])\n",
"print(\"beta = %s\" % str(mle_betas))\n",
"print(\"cov = \\n%s\\n\" % str(mle_cov))\n",
"\n",
"plt.grid()\n",
"plt.xlabel(\"epoch\")\n",
"plt.ylabel(\"log p(y|w)\")\n",
"plt.plot(objs)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Comparison of results\n",
"\n",
"To compare out results, we first visually check the decision boundary computed for each estimator."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.scatter(X[y==0, 1], X[y==0, 2], facecolors='none', edgecolors='r', label='y=0')\n",
"plt.scatter(X[y==1, 1], X[y==1, 2], marker='x', c='g', label='y=1')\n",
"\n",
"plt.plot(X[:, 1], -(betas[0] + betas[1]*X[:, 1])/ betas[2], label=\"real decision boundary\")\n",
"plt.plot(X[:, 1], -(mle_betas[0] + mle_betas[1]*X[:, 1])/ mle_betas[2], label=\"mle decision boundary\")\n",
"plt.plot(X[:, 1], -(vi_betas[0] + vi_betas[1]*X[:, 1])/ vi_betas[2], label=\"vi decision boundary\")\n",
"\n",
"plt.legend();"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Since all decisions boundary seem to be equal, we consider instead the standardized error: $\\widehat{Cov}(\\hat \\beta)^{-1/2}(\n",
"\\widehat \\beta - \\beta)$.\n",
"\n",
"We expect that this quantity should be approximately $N(0, 1_d)$ for each estimator. To check this, we plot for each $\\beta_i$ the associated entry in the standardized error."
]
},
{
"cell_type": "code",
"execution_count": 65,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAABiCAYAAACrrJNiAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4zLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvIxREBQAAFfJJREFUeJztnXuQVPWVxz+nex49wCAD+EBeM0nIhjekBteNVrRi1ElMqVshm9FYG4LRUssK6FqL0VXQPFyTckUXdg1mfSRRo5K4sgk+YuIrKVGHBCNKQmDAYRhgHrwGhnn22T9+femeZh53hu6+PT3nU9XV9/Gbvqd/fed7zz2/8ztXVBXDMAwjtwgFbYBhGIaRekzcDcMwchATd8MwjBzExN0wDCMHMXE3DMPIQUzcDcMwchATd8MwjBzExN0wDCMH8SXuIlIhIn8VkW0icmsf7RaKiIpIeepMNAzDMAZKXn8NRCQMrAYuBGqBd0Vknap+mNSuGPgW8LafA48fP15LS0sHbLBhGMZwZuPGjY2qemp/7foVd+AsYJuqVgOIyM+By4APk9p9B/gBcIsfA0tLS6mqqvLT1DAMw4ghIh/5aecnLDMR2JWwXhvblniw+cBkVf2VbwsNI2hUoasLOjuhvb3vV2cnS19YwtIXlwRttREgS5e611DAj+cuPWw7Xm1MRELA/cCifj9I5FrgWoApU6b4s9AwBkqiaCeLd0cHRKNu2wDZtHODW9i6FfLyIByGggL3ys+Pb/Ne0tO/jjGU2bQpaAv840fca4HJCeuTgLqE9WJgFvCauJP5DGCdiFyqqt3iLqq6BlgDUF5ebuUojZOnszMu3m1t0NLillXdC5zIhsMQCrn3vDyIRAZ+rHDYvY8c6T47GoXWVnfMrq7ubUWgsBCKityxPPHP8/MvZxgnj58z7V1gmoiUAbuBSuBKb6eqHgLGe+si8hpwS7Kw+6Gjo4Pa2lpaW1sH+qc5TSQSYdKkSeTn5wdtSrBEo87zbmuDo0edqHZ2xj1kT7hHjEiv1yziXqFQ72Kt6mw7fBgOHIhvy8939o0Y4cS/oMA8fCMt9CvuqtopIjcCLwFh4BFV/UBE7gaqVHVdqoypra2luLiY0tJSxE54AFSVpqYmamtrKSsrC9qczBKNOi/82DFobnZeskdeXtwzzkZEnJAnX5CjUXdROnzYib2I8+yLi913KSw0sTdSgq97RFVdD6xP2nZnL23PH6wxra2tJuxJiAjjxo2joaEhaFPSj6rzzFtbnZgfPeq2hULOwx01KmgLT55QqHtIyPPwGxvjYj9ypPuukYj73oYxCLIuAGjCfiI53SeqTsyPHnXebEdH3OsdOTL3vdhkD1/VhZ2OHHHreXlwyimuL8yrNwZA1om7MQzwBiKPHIFDh9x6OOzEazADnbmENxBbWOjWu7pczL6pyXn9o0fHvfqQVQ8xesfEfRA89thjVFVVsWrVqqBNGTqoutj54cMu5KLqBL2oyESqL8JhN/gK7iLY3OzEXgTGjHGx+kjEPHrjBEzcjfSRGGI4cMCJUyayWXKVUCg+gKwaF3ovdDNqlIVujONkrbgvXZr6CQPz5sHKlX232blzJxUVFZx77rls2LCBuXPn8o1vfIPly5dTX1/PE0880a19Q0MD1113HTU1NQCsXLmSc845J7WGDzU6OuKC3tFhHno6EIkLfTQKBw+60E1+PpSUOKEf7qmzw5ysFfcg2bZtG88++yxr1qxhwYIFPPnkk/z+979n3bp1fP/73+fyyy8/3nbJkiXcdNNNnHvuudTU1HDxxRezZcuWAK0PiGjUhV0OHHCDo15WyHCPoWeCUCgeuvEyb+rr3SBsSYldWIcpWSvu/XnY6aSsrIzZs2cDMHPmTC644AJEhNmzZ7Nz585ubV955RU+/DBeQ+3w4cM0NzdTXFycSZODo63NhQcOHnSDfwUFLg5sBEPiLNi2NqitdXdOY8a4wVhLrRw2ZK24B0mhl6kAhEKh4+uhUIjOpJok0WiUt956i6JsnUyTDryJOPv3u3dvOr95h9mFl3WTGLYpKoJx48ybHwbYr3uSXHTRRd2yZjYNpcpCA6W93QlEdTXs3u1EY/RoFxIwochevLBNcbG7u6qthR073MW5oyNo64w0Yf+RJ8mDDz5IVVUVc+bMYcaMGTz00ENBm5RaVJ13XlvrRH3//vh0ebvFH3oUFsZ/O+9CXVfnxkvUavnlEhaWSaK0tJTNmzcfX3/sscd63Ldo0SIAxo8fz9NPP51JEzNDV5cbGG1sdB57QYHz0o3cIBx2A67gJpTV1LjfeNw4l2ljd2JDHhN3ozvt7fFKhqqW8TIc8H7jjg7Ys8cJf0mJu5hbOuWQxcTdcHhpjIcPuwFSG3Abfng1bqJRF35rbHQhnLFj7QI/BDFxH85Eoy700tTkbs0t9GKAu6h7IZtjx+Cjj1ys/tRTbXbxEMLEfTjS2ely0/fvd8uRiIm60TNeim97uxtUz8uD8eNdXN57MpWRlZi4Dyfa212+88GDbr2oKHsfdmFkF96zYru6YN8+NwO2pMTVtLG4fFZi4j4cSI6nD4c66UZ6CIed1x6NxksRjx7thN7i8lmFjZj1Q11dHQsXLgzajIGj6uLpO3e6NLfW1viEIxN242Tx4vKjRrl5EN555j09ywgc89z74cwzz2Tt2rVBm+Gfri5XkbGpyaW2eZNWDCMdeNUpi4ricfn8/Hhc3jKuAiNrxX3pi0vZtDe1U/nnnTGPlRW9VyRbtmwZU6dO5YYbbgBgxYoVFBcX8+ijj3ab2JSVdHS4pxp5+elFRXabbGQWLy7f2Ql79zphHzvW3THmZa3U5Cx2WU2gsrKy22zTZ555hgULFgRokQ9aW90/UnW1E/aiIstkMIIlLy/+KMCmJti+3Q3CtrUFbdmwwtflVEQqgAeAMPBjVf33pP03A98EOoEGYLGqfnQyhvXlYaeL+fPnU19fT11dHQ0NDZSUlDBlypSM29EvXr2XpiY3WOr9M1ks3cgmvLi8avzhLaNGOW++qMjO1zTTr7iLSBhYDVwI1ALvisg6Vf0wodmfgHJVbRGR64EfAF9Nh8HpZuHChaxdu5a9e/dSWVkZtDndSaz3YvF0Y6iQGJdva4vXsbG4fFrx47mfBWxT1WoAEfk5cBlwXNxV9dWE9huAq1JpZCaprKzkmmuuobGxkddff522bLiVjEadsFdXW70XY2jj1Zjv7LQ6NmnGzyVzIrArYb02tq03rgZe6GmHiFwrIlUiUtXQ0ODfygwyc+ZMmpubmThxIhMmTAjWmGjUZSC0t7tlL55ug1PGUCcvz911RiJupnR1tRs7am0N2rKcwY9K9BQY6zGRVUSuAsqB83rar6prgDUA5eXlWZsM+/777x9fTi4BnHZUnZB3drr3UKj7yzByicS4/NGjLuOrsNCFbOwhMCeFH3GvBSYnrE8C6pIbicjngduB81Q1C2IZQ4xoNC7q4OKUlvFiDBe8uDy4O9Xdu513X1LiPHwL2QwYP+L+LjBNRMqA3UAlcGViAxGZD/wIqFDV+pRbmauoupfnpYN5Kobh5ctHoy4jrKHBCbxX4sCybHzRr7iraqeI3Ai8hEuFfERVPxCRu4EqVV0H/BAYBTwrruNrVPXSNNo9tFF1A6RdXW5ZxETdMJJJDNkcO+ZqIxUWuqdFjRxpd7b94GtkTlXXA+uTtt2ZsPz5FNuVe3heuifqYKJuGH5ITKX0Zr8CjBnjsmwsc6xHLO0i3SQOkHoFlUzQDWNweBP2VN0zCQ4ccN782LHmzSdh4p4OzEs3jPSSOADb0RH35kePdjXmLTaf5bVlampg69bUvWpq+j3kAw88wKxZs5g5cyYrV8ZLIKxYsYKJEycyb9485s2bx/r1Lkr1hz/8gTlz5rBgwQK2bd0KnZ0crK/n4osvRjs74ymMCSdaR0cHt95+O9NmzGDW/Pmcdc45vPDiiwCUfvKTNDY2prgjDSOHyc933vzIkS6dsqYGduxwXn1HR9DWBUZ2e+6tre5HSxVHjvS5e/PmzTz88MO88847FBQUUFFRwSWXXMK0adMAuOmmm7jlllu6/c19993HL555hp3bt/Pfq1dz37338p177uG2ZcuQXm4R71ixgj1797L5T3+isLCQffv28fqbb6bmOxrGcCXRm+/qcmU66uud6I8Z4/YNo7BNdnvuGWbLli2cffbZjBgxgry8PM477zyee+65Ext6IZf2dvJDIY41N9Ny7Bj5BQVs37GD3XV1nPfZz/Z4jJaWFh5+5BH+8/77KSwsBOD000/nn4biA0EMI1sJh52oFxc77333bledcu9eV3RvGDxQxMQ9gVmzZvHGG2/Q1NRES0sL69evZ9euWOUFVVatWsWc2bNZvGgRB+rrQZVvL1vGtTfeyMpVq7jx+uu5fflyvrN8ea/H2LZ9O1MmT2a0PZDaMDKDV2DPC9vs2gXbtjnPvrU1Z4XexD2B6dOns2zZMi688EIqKiqYO2cOeeEwdHRw/eLFbP/gAza9/TYTJkzgX779bRBh3ty5bHjzTV59+WWqd+zgzAkTUFW++rWvcdWiRezbty/or2UYBsTDNsXF7v3QIfjoI+fR56DQm7gncfXixfyxqoo3fvtbxp5yCtPKyqCri9MnTCCcn08oL49rFi/mnXff7fZ3qsp377mHO267jbu+9z3uuuMOrrriCh5cvbpbu098/OPU7NpFc3NzJr+WYRiJhEJxoY9E4OBBJ/TV1U7ojx2Lzxofopi4Q7cYev2uXdDeTs2OHfzy+ee5orISQiH27NlzvPlzzz/PrJkzu33E4z/9KZd84QuUlJTQ0tJCKBQiFArR0tLSrd2IESO4etEivnXzzbS3twOwZ88efvbkk+n/noZhnEgo5IqUFRe7EM6hQy5048Xojx6NpzQPIbI7WyYS6TfDZcCfB/E8dK9Yl3eFFuHLV15JU1MT+fn5rH7gAUpKSgD419tuY9N77yEilE6dyo8SPPKWlhYe/9nPePnXvwbg5iVL+HJlJQUFBTz1k5+cYMZ377qLf1u+nBlz5xKJRBg5ciR333nnCe0Mw8gwnkcP3StVirgLQNcZsfkq2e8XiwYUYyovL9eqqqpu27Zs2cL06dPTc8BkMfe+t8iQmOywZetWpo8dG7QZw5rzf+Uyml770tqALTEyjiq0t3N+5ekAvPbU3vggbSSS0QmKIrJRVcv7a5fdnvvJkOidewW6PJImFRmGYfSJiAvZeHny+fmukNmBA249EokP1BYUZMVs9NwR995CLWBT/w3DSC3hcDx8A64GfWOj0x0vhOPF8AMS+6wTd1VF/HjVnpB7g6GJnnmOiXlQoTPDMHzi1aAHp0UdHZCYBh2JuNn2kUj3O4A0klXiHolEaGpqYty4cX0LfGdn/IlFkHNinoiq0nTgAJFhNG3aMIY0It3FHpzY798fd0hPO809fCSNZJW4T5o0idraWvp9eHbiQy6GAZFwmEmprLFjGEZmyc+PPyrw2LHuzmmayCpxz8/Pp6ysrP+G+/a5FCUr0m8YhtEjuRnLMAzDGOaYuBuGYeQgJu6GYRg5iC9xF5EKEfmriGwTkVt72F8oIk/H9r8tIqWpNtQwDMPwT7/iLiJhYDXwBWAGcIWIzEhqdjVwQFU/AdwP3JtqQw3DMAz/+MmWOQvYpqrVACLyc+Ay4MOENpcBK2LLa4FVIiKaztk33uQlw8gU3uls593wJRXnQIYmJfoR94nAroT1WuDve2ujqp0icggYB3R70rOIXAtcCzBlypRBmkx8Om8GckUNw2Neyafcgp13w5Z5n2pzCydzDoTD3Sc4pQk/4t7TTKHkS4+fNqjqGmANuKqQPo7dMyUlaZ/dZRjJrCx7NGgTjIBZefwUOCVIM3zhZ0C1FpicsD4JqOutjYjk4b75/lQYaBiGYQwcP577u8A0ESkDdgOVwJVJbdYBXwfeAhYCv+sv3r5x48ZGEfnIp53jSQrxZBFm2+Aw2wZPNttntg2Ogdg21U+jfsU9FkO/EXgJCAOPqOoHInI3UKWq64D/AX4qIttwHnulj8891Y+BACJS5ac4fRCYbYPDbBs82Wyf2TY40mGbr9oyqroeWJ+07c6E5VbgK6k0zDAMwxg8NkPVMAwjBxkq4r4maAP6wGwbHGbb4Mlm+8y2wZFy2wJ7QLZhGIaRPoaK524YhmEMABN3wzCMHCQrxV1EfigifxGRP4vIcyIyppd2fVarTJNtXxGRD0QkKiK9pi6JyE4ReV9ENolIVZbZFkS/jRWR34jI32LvPU4xFpGuWJ9tEpF1abYpa6ud+rBtkYg0JPTVNzNo2yMiUi8im3vZLyLyYMz2P4vIp7PItvNF5FBCv93ZU7s02TZZRF4VkS2x/9MlPbRJXd+pata9gIuAvNjyvcC9PbQJA9uBjwEFwHvAjAzYNh34O+A1oLyPdjuB8Rnut35tC7DffgDcGlu+taffNLbvSIb6qt9+AG4AHootVwJPZ5Fti4BVmTy/Eo79WeDTwOZe9n8ReAFXluRs4O0ssu184FcB9dsE4NOx5WJgaw+/a8r6Lis9d1V9WVW9yjwbcCUPkjlerVJV2wGvWmW6bduiqn9N93EGg0/bAum32DEejy0/DlyegWP2hZ9+SLR5LXCBSEaeyh7Ub+QLVX2DvsuLXAb8RB0bgDEiMiFLbAsMVd2jqn+MLTcDW3BFFxNJWd9lpbgnsRh3JUump2qVyR0VJAq8LCIbY9Uws4Wg+u10Vd0D7iQHTuulXUREqkRkg4ik8wLgpx+6VTsFvGqn6cbvb/Tl2K37WhGZ3MP+oMj2/81/EJH3ROQFEZkZhAGxEN984O2kXSnrO18zVNOBiLwCnNHDrttV9flYm9uBTuCJnj6ih20pyev0Y5sPzlHVOhE5DfiNiPwl5lUEbVsg/TaAj5kS67ePAb8TkfdVdXsq7EsiZdVO04Cf4/4f8JSqtonIdbg7jM+l3TJ/BNVvfvgjMFVVj4jIF4H/BaZl0gARGQX8AliqqoeTd/fwJ4Pqu8DEXVU/39d+Efk68CXgAo0Fo5LwU60yLbb5/Iy62Hu9iDyHu9U+aXFPgW2B9JuI7BORCaq6J3abWd/LZ3j9Vi0ir+G8m3SI+0CqndZKZqud9mubqjYlrD5Mdj39LG3n2MmSKKaqul5E/ktExqtqRgqKiUg+TtifUNVf9tAkZX2XlWEZEakAlgGXqmpLL82OV6sUkQLcgFdasyv8IiIjRaTYW8YNEPc4eh8AQfWbVzmU2PsJdxkiUiIihbHl8cA5dH/iVyrx0w+JNvuqdpop25LisJfi4rfZwjrgn2OZH2cDh7yQXNCIyBneuImInIXTwKa+/yplxxZckcUtqvofvTRLXd8FMWrsY1R5Gy7utCn28jIWzgTWJ40sb8V5drdnyLZ/xF1d24B9wEvJtuGyHN6LvT7IJtsC7LdxwG+Bv8Xex8a2lwM/ji1/Bng/1m/vA1en2aYT+gG4G+dUAESAZ2Pn4zvAxzLRVz5tuyd2br0HvAp8KoO2PQXsATpi59vVwHXAdbH9gnvu8vbY79hrVlkAtt2Y0G8bgM9k0LZzcSGWPydo2xfT1XdWfsAwDCMHycqwjGEYhnFymLgbhmHkICbuhmEYOYiJu2EYRg5i4m4YhpGDmLgbhmHkICbuhmEYOcj/A9RjE6RkgoaKAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"import scipy.stats as stats\n",
"\n",
"std_mle_beta = np.linalg.solve(mle_L, mle_betas - betas)\n",
"std_vi_beta = np.linalg.solve(vi_L, vi_betas - betas)\n",
"\n",
"for i in range(D):\n",
" plt.subplot(D,1,i+1)\n",
" \n",
" x = np.linspace(-2*1.96, 2*1.96, 100)\n",
" yy = stats.norm.pdf(x, 0, 1)\n",
" plt.plot([std_mle_beta[i],std_mle_beta[i]], [0, np.max(yy)], c='blue', label=\"mle\")\n",
" plt.plot([std_vi_beta[i],std_vi_beta[i]], [0, np.max(yy)], c='green', label=\"vi\")\n",
" \n",
" plt.fill_between(x,yy,0,where=(x>=-1.96)&(x<=1.96), color=(1,0,0,0.1), label=\"95% CI\")\n",
" plt.legend()\n",
" plt.show()"
]
}
],
"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": "2.7.15"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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