Created
March 3, 2017 12:07
-
-
Save pwl/2f3c3e240b477eac9a37b06791b2a659 to your computer and use it in GitHub Desktop.
Probabilistic PCA with ARD
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
{ | |
"cells": [ | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"# Bayesian PCA\n", | |
"Includes bias and noise." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 2, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"[[ 1.]\n", | |
" [-1.]]\n" | |
] | |
} | |
], | |
"source": [ | |
"from __future__ import absolute_import\n", | |
"from __future__ import division\n", | |
"from __future__ import print_function\n", | |
"\n", | |
"import edward as ed\n", | |
"import numpy as np\n", | |
"import tensorflow as tf\n", | |
"import matplotlib.pyplot as plt\n", | |
"\n", | |
"from edward.models import Normal\n", | |
"\n", | |
"\n", | |
"# note that in the function below D should be greater then K\n", | |
"def build_toy_dataset(N, D, K, sigma=1):\n", | |
" x_train = np.zeros([D, N])\n", | |
" w = np.zeros([D,K])\n", | |
" for k in range(K):\n", | |
" w[k,k]=1.0/(k+1)\n", | |
" w[k+1,k]=-1.0/(k+1)\n", | |
" print(w)\n", | |
" z = np.random.normal(0.0, 1.0, size=(K, N))\n", | |
" mean = np.dot(w, z)\n", | |
" shift=np.zeros([D])\n", | |
" shift[1]=10\n", | |
" for d in range(D):\n", | |
" for n in range(N):\n", | |
" x_train[d, n] = np.random.normal(mean[d, n], sigma)+shift[d]\n", | |
"# print(\"True principal axes:\")\n", | |
"# print(w)\n", | |
"# print(\"Shift:\")\n", | |
"# print(shift)\n", | |
" return x_train.astype(np.float32,copy=False)\n", | |
"\n", | |
"\n", | |
"#ed.set_seed(142)\n", | |
"\n", | |
"N = 1000 # number of data points\n", | |
"D = 2 # data dimensionality\n", | |
"K = 1 # latent dimensionality\n", | |
"\n", | |
"# DATA\n", | |
"\n", | |
"x_train = build_toy_dataset(N, D, K, sigma = 0.1)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"# The working original version of PPCA\n", | |
"It assumes that\n", | |
"\\begin{align}\n", | |
"w_{ij}&\\sim N(0,1)\\\\\n", | |
"z_j&\\sim N(0,1)\\\\\n", | |
"x_i&\\sim N((w\\cdot z)_i,1)\\\\\n", | |
"\\end{align}" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 3, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [], | |
"source": [ | |
"# MODEL\n", | |
"\n", | |
"K=1\n", | |
"\n", | |
"w = Normal(mu=tf.zeros([D, K]), sigma=tf.ones([D, K]))\n", | |
"z = Normal(mu=tf.zeros([K, N]), sigma=tf.ones([K, N]))\n", | |
"x = Normal(mu=tf.matmul(w, z), sigma=tf.ones([D, N]))\n", | |
"\n", | |
"# INFERENCE\n", | |
"qw = Normal(mu=tf.Variable(tf.random_normal([D, K])),\n", | |
" sigma=tf.nn.softplus(tf.Variable(tf.random_normal([D, K]))))\n", | |
"qz = Normal(mu=tf.Variable(tf.random_normal([K, N])),\n", | |
" sigma=tf.nn.softplus(tf.Variable(tf.random_normal([K, N]))))" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Run the inference algorithm" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 4, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"Iteration 1 [ 0%]: Loss = 54470.285\n", | |
"Iteration 100 [ 10%]: Loss = 6317.818\n", | |
"Iteration 200 [ 20%]: Loss = 5631.526\n", | |
"Iteration 300 [ 30%]: Loss = 5436.849\n", | |
"Iteration 400 [ 40%]: Loss = 5351.975\n", | |
"Iteration 500 [ 50%]: Loss = 5324.237\n", | |
"Iteration 600 [ 60%]: Loss = 5292.580\n", | |
"Iteration 700 [ 70%]: Loss = 5280.140\n", | |
"Iteration 800 [ 80%]: Loss = 5284.117\n", | |
"Iteration 900 [ 90%]: Loss = 5253.170\n", | |
"Iteration 1000 [100%]: Loss = 5265.507\n", | |
"Inferred principal axes (columns):\n", | |
"[[-0.05535497]\n", | |
" [ 8.54162025]]\n", | |
"[[ 0.00078462]\n", | |
" [ 0.00077497]]\n" | |
] | |
} | |
], | |
"source": [ | |
"inference = ed.KLqp({w: qw, z: qz}, data={x: x_train})\n", | |
"inference.run(n_iter=1000, n_print=100, n_samples=10)\n", | |
"\n", | |
"print(\"Inferred principal axes (columns):\")\n", | |
"print(qw.mean().eval())\n", | |
"print(qw.variance().eval())" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Although it looks like we are pretty close to the data, the predicted principal directions are completely off now. This is because the product $W\\cdot z$ tries to recreate $W\\cdot z+\\mu$ with $\\mu=(0,10)$ by shifting $z$ away from the center. This leaves no degrees of freedom in $W$ to recreate the original axis." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 5, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAXQAAAD8CAYAAABn919SAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x7efed4575978>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"qx = ed.copy(x,{z:qz, w:qw})\n", | |
"plt.scatter(*qx.sample().eval(),c='r',alpha=0.2)\n", | |
"plt.scatter(*x_train,c='b',alpha=0.2)\n", | |
"plt.xlim(-4,4)\n", | |
"plt.ylim(-4+10,4+10)\n", | |
"plt.show()" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"The variables in the latent space are shifted away from the origin." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 6, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAX8AAAD8CAYAAACfF6SlAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nw1+SGmT4S1KDDH9JatD/Ar87z4NU7kxxAAAAAElFTkSuQmCC\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x7eff405b4ac8>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"qz_sam=qz.sample().eval()\n", | |
"plt.hist(qz_sam[0])\n", | |
"plt.xlim(-2,2)\n", | |
"plt.show()" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## Adding the mean\n", | |
"\n", | |
"We add the mean $\\mu$ to capture the shift of the data set (the original example assumes data is centered at zero). The new priors are\n", | |
"\\begin{align}\n", | |
"w_{ij}&\\sim N(0,1)\\\\\n", | |
"z_j&\\sim N(0,1)\\\\\n", | |
"\\mu_i &\\sim N(0,1)\\\\\n", | |
"x_i&\\sim N((w\\cdot z)_i+\\mu_i,1)\\\\\n", | |
"\\end{align}\n", | |
"\n", | |
"### Initial conditions\n", | |
"\n", | |
"We also add initial conditions for the approximation of the mean $q_\\mu$ as $(q_\\mu)_0\\sim N(\\bar x,1)$, where $\\bar x$ is the mean of the data. This improves the convergence significantly and prevents the latent variable compensation effect visible in the previous example (PCA without the mean)." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 44, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [], | |
"source": [ | |
"# MODEL\n", | |
"\n", | |
"K=1\n", | |
"\n", | |
"w = Normal(mu=tf.zeros([D, K]), sigma=tf.ones([D, K]))\n", | |
"z = Normal(mu=tf.zeros([K, N]), sigma=tf.ones([K, N]))\n", | |
"mu= Normal(mu=tf.zeros([D]), sigma=tf.ones([D]))\n", | |
"x = Normal(mu=tf.matmul(w, z)+tf.transpose(tf.reshape(tf.tile(mu,[N]),[N,D])),\n", | |
" sigma=tf.ones([D, N]))\n", | |
"\n", | |
"# INFERENCE\n", | |
"qw = Normal(mu=tf.Variable(tf.random_normal([D, K])),\n", | |
" sigma=tf.nn.softplus(tf.Variable(tf.random_normal([D, K]))))\n", | |
"qz = Normal(mu=tf.Variable(tf.random_normal([K, N])),\n", | |
" sigma=tf.nn.softplus(tf.Variable(tf.random_normal([K, N]))))\n", | |
"\n", | |
"# initial conditions for qmu, improves convergence\n", | |
"data_mean = np.mean(x_train,axis=1).astype(np.float32,copy=False)\n", | |
"\n", | |
"qmu= Normal(mu=tf.Variable(data_mean+tf.random_normal([D])),\n", | |
" sigma=tf.nn.softplus(tf.Variable(tf.random_normal([D]))))" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 45, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"Iteration 1 [ 0%]: Loss = 66609.680\n", | |
"Iteration 100 [ 10%]: Loss = 27355.543\n", | |
"Iteration 200 [ 20%]: Loss = 27223.678\n", | |
"Iteration 300 [ 30%]: Loss = 27205.492\n", | |
"Iteration 400 [ 40%]: Loss = 27197.633\n", | |
"Iteration 500 [ 50%]: Loss = 27210.598\n", | |
"Iteration 600 [ 60%]: Loss = 27191.035\n", | |
"Iteration 700 [ 70%]: Loss = 27207.539\n", | |
"Iteration 800 [ 80%]: Loss = 27162.736\n", | |
"Iteration 900 [ 90%]: Loss = 27172.986\n", | |
"Iteration 1000 [100%]: Loss = 27167.166\n", | |
"Inferred principal axes (columns):\n", | |
"[[ 0.72713369]\n", | |
" [-0.7239145 ]]\n", | |
"[[ 0.00014755]\n", | |
" [ 0.0008513 ]]\n", | |
"Inferred center:\n", | |
"[ 9.53229144e-03 9.98693562e+00]\n", | |
"[ 0.00010397 0.00056424]\n" | |
] | |
} | |
], | |
"source": [ | |
"inference = ed.KLqp({w: qw, z: qz, mu: qmu}, data={x: x_train})\n", | |
"inference.run(n_iter=1000, n_print=100, n_samples=10)\n", | |
"\n", | |
"print(\"Inferred principal axes (columns):\")\n", | |
"print(qw.mean().eval())\n", | |
"print(qw.variance().eval())\n", | |
"print(\"Inferred center:\")\n", | |
"print(qmu.mean().eval())\n", | |
"print(qmu.variance().eval())" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 46, | |
"metadata": { | |
"collapsed": false, | |
"scrolled": true | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAgAAAAFkCAYAAABW9YMrAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x7f7dc5e31f60>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"qx = ed.copy(x,{z:qz, w:qw, mu:qmu})\n", | |
"plt.scatter(*qx.sample().eval(),c='r',alpha=0.2)\n", | |
"plt.scatter(*x_train,c='b',alpha=0.2)\n", | |
"plt.xlim(-4,4)\n", | |
"plt.ylim(-4+10,4+10)\n", | |
"plt.show()" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Now the variables in the latent space are centered!" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 47, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAhkAAAFkCAYAAACNTikJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAAPYQAAD2EBqD+naQAAHoxJREFUeJzt3X+QXeV93/H3x2CJQCvJmCKFOMSOiZV129hoCaAmyLRy\nQ2ym2C2dlLVVbJjWsYMZqhk3TDpOTM00HjsNIhhIGeM4doFtGVzXrg3IBtvUxrLUSjhObIFjB7qx\nsQRrhKSBCIz09I9zNrm6Wf24u/fZu3f1fs3cWe0533vu8+yz2v3sc85zbkopSJIk9duLBt0ASZK0\nMBkyJElSFYYMSZJUhSFDkiRVYciQJElVGDIkSVIVhgxJklSFIUOSJFVhyJAkSVUYMiRJUhU9hYwk\n70zyJ0l2t4+vJfnVrpr3J3k8ybNJvpDkjK79i5PclGQyyd4kdyU5tavmJUlub19jV5Jbk5w0825K\nkqS51utMxl8CVwOrgFHgi8Cnk4wAJLkaeDfwDuBs4BlgY5JFHce4HrgQuBhYA5wGfLLrde4ARoC1\nbe0a4JYe2ypJkgYos32DtCQ/At5TSvlYkseB3yulbGj3LQF2Am8rpdzZfv4kcEkp5VNtzUpgO3Bu\nKWVLG1i+BYyWUh5qay4APge8rJSyY1YNliRJc2LG12QkeVGSS4ATga8leQWwArh/qqaUsgfYDKxu\nN50FHN9V8wgw0VFzLrBrKmC07gMKcM5M2ytJkubW8b0+Ick/ADYBJwB7gX9eSnkkyWqaILCz6yk7\nacIHwHLg+TZ8HKpmBfBE585Syv4kT3XUTNeulwIXAI8B+3rsliRJx7ITgJcDG0spP+rXQXsOGcDD\nwGuApcC/BD6RZE2/GjQLFwC3D7oRkiQNsbfSXBfZFz2HjFLKC8BftJ8+lORs4CrgQ0BoZis6ZzOW\nA1OnPnYAi5Is6ZrNWN7um6rpXm1yHHByR810HgO47bbbGBkZ6bFXw2X9+vVs2LBh0M2ozn4uPMdK\nX+3nwnIs9HP79u2sW7cO2t+l/TKTmYxuLwIWl1IeTbKDZkXIN+GvL/w8B7iprd0KvNDWdF74eTrN\nKRjaj8uSnNlxXcZamgCz+TDt2AcwMjLCqlWr+tCt+Wvp0qULvo9gPxeiY6Wv9nNhOVb62err5QY9\nhYwkvwvcQ3Oh5t+lmVZ5HfArbcn1wHuTfJcmDV0LfB/4NDQXgib5KHBdkl0013TcADxYStnS1jyc\nZCPwkSTvAhYBHwbGXVkiSdLw6HUm41Tg48BPArtpZix+pZTyRYBSyoeSnEhzT4tlwFeAN5RSnu84\nxnpgP3AXsBi4F7ii63XeAtxIs6rkQFt7VY9tlSRJA9RTyCil/JujqLkGuOYw+58Drmwfh6p5GljX\nS9skSdL84nuXDKGxsbFBN2FO2M+F51jpq/1cWI6VftYw6zt+zhdJVgFbt27deixdoCNJ0qxt27aN\n0dFRaO62va1fx3UmQ5IkVWHIkCRJVRgyJElSFYYMSZJUhSFDkiRVYciQJElVGDIkSVIVhgxJklSF\nIUOSJFVhyJAkSVUYMiRJUhWGDEmSVIUhQ5IkVWHIkCRJVRgyJElSFYYMSZJUhSFDkiRVYciQJElV\nGDIkSVIVhgxJklSFIUOSJFVhyJAkSVUYMiRJUhWGDEmSVIUhQ5IkVWHIkCRJVRgyJElSFYYMSZJU\nhSFDkiRVYciQJElVGDIkSVIVhgxJklSFIUOSJFVhyJAkSVUcP+gGSDq2TExMMDk5OehmDKVTTjmF\n008/fdDNkI6aIUPSnJmYmGDlyhH27Xt20E0ZSieccCKPPLLdoKGhYciQNGcmJyfbgHEbMDLo5gyZ\n7ezbt47JyUlDhoaGIUPSAIwAqwbdCEmVeeGnJEmqoqeQkeS3kmxJsifJziSfSvKqrpqPJTnQ9bi7\nq2ZxkpuSTCbZm+SuJKd21bwkye1JdifZleTWJCfNvKuSJGku9TqTcR7wYeAc4PXAi4HPJ/mJrrp7\ngOXAivYx1rX/euBC4GJgDXAa8Mmumjto5lTXtrVrgFt6bK8kSRqQnq7JKKW8sfPzJG8HngBGga92\n7HqulPLkdMdIsgS4HLiklPJAu+0yYHuSs0spW5KMABcAo6WUh9qaK4HPJXlPKWVHL+2WJElzb7bX\nZCwDCvBU1/bz29MpDye5OcnJHftGacLN/VMbSimPABPA6nbTucCuqYDRuq99rXNm2WZJkjQHZry6\nJEloTnt8tZTy7Y5d99Cc+ngUeCXwAeDuJKtLKYXm9MnzpZQ9XYfc2e6j/fhE585Syv4kT3XUSJKk\neWw2S1hvBl4N/FLnxlLKnR2ffivJnwLfA84HvjSL1zsq69evZ+nSpQdtGxsbY2ys+7IQSZKOPePj\n44yPjx+0bffu3VVea0YhI8mNwBuB80opPzxcbSnl0SSTwBk0IWMHsCjJkq7ZjOXtPtqP3atNjgNO\n7qiZ1oYNG1i1yvX3kiRNZ7o/vLdt28bo6GjfX6vnazLagPEm4B+XUiaOov5lwEuBqTCyFXiBZtXI\nVM1K4HRgU7tpE7AsyZkdh1oLBNjca5slSdLc62kmI8nNNMtRLwKeSbK83bW7lLKvvY/F+2iuydhB\nM3vxQeA7wEaAUsqeJB8FrkuyC9gL3AA8WErZ0tY8nGQj8JEk7wIW0SydHXdliSRJw6HX0yXvpFnh\n8eWu7ZcBnwD2A78AXEqz8uRxmnDxO6WUH3fUr29r7wIWA/cCV3Qd8y3AjTSrSg60tVf12F5JkjQg\nvd4n47CnV0op+4BfPYrjPAdc2T4OVfM0sK6X9kmSpPnDN0iTZmBiYoLJyclBN2PobN++fdBNkDSH\nDBlSjyYmJli5cqR9y3JJ0qEYMqQeTU5OtgHjNpq319HRuxv47UE3QtIcMWRIMzYCeE+W3ni6RDqW\nzPa9SyRJkqZlyJAkSVUYMiRJUhWGDEmSVIUhQ5IkVWHIkCRJVRgyJElSFYYMSZJUhSFDkiRVYciQ\nJElVGDIkSVIVhgxJklSFIUOSJFVhyJAkSVUYMiRJUhWGDEmSVIUhQ5IkVWHIkCRJVRgyJElSFYYM\nSZJUhSFDkiRVYciQJElVGDIkSVIVhgxJklSFIUOSJFVhyJAkSVUYMiRJUhWGDEmSVIUhQ5IkVWHI\nkCRJVRgyJElSFYYMSZJUhSFDkiRVYciQJElVGDIkSVIVhgxJklRFTyEjyW8l2ZJkT5KdST6V5FXT\n1L0/yeNJnk3yhSRndO1fnOSmJJNJ9ia5K8mpXTUvSXJ7kt1JdiW5NclJM+umJEmaa73OZJwHfBg4\nB3g98GLg80l+YqogydXAu4F3AGcDzwAbkyzqOM71wIXAxcAa4DTgk12vdQcwAqxta9cAt/TYXkmS\nNCDH91JcSnlj5+dJ3g48AYwCX203XwVcW0r5bFtzKbATeDNwZ5IlwOXAJaWUB9qay4DtSc4upWxJ\nMgJcAIyWUh5qa64EPpfkPaWUHTPqrSRJmjOzvSZjGVCApwCSvAJYAdw/VVBK2QNsBla3m86iCTed\nNY8AEx015wK7pgJG6772tc6ZZZslSdIcmHHISBKa0x5fLaV8u928giYI7Owq39nuA1gOPN+Gj0PV\nrKCZIflrpZT9NGFmBZIkad7r6XRJl5uBVwO/1Ke2SJKkBWRGISPJjcAbgfNKKT/s2LUDCM1sReds\nxnLgoY6aRUmWdM1mLG/3TdV0rzY5Dji5o2Za69evZ+nSpQdtGxsbY2xs7Ch6JknSwjY+Ps74+PhB\n23bv3l3ltXoOGW3AeBPwulLKROe+UsqjSXbQrAj5Zlu/hOY6ipvasq3AC23Np9qalcDpwKa2ZhOw\nLMmZHddlrKUJMJsP174NGzawatWqXrslSdIxYbo/vLdt28bo6GjfX6unkJHkZmAMuAh4Jsnydtfu\nUsq+9t/XA+9N8l3gMeBa4PvAp6G5EDTJR4HrkuwC9gI3AA+WUra0NQ8n2Qh8JMm7gEU0S2fHXVki\nSdJw6HUm4500F3Z+uWv7ZcAnAEopH0pyIs09LZYBXwHeUEp5vqN+PbAfuAtYDNwLXNF1zLcAN9Ks\nKjnQ1l7VY3slSdKA9HqfjKNajVJKuQa45jD7nwOubB+HqnkaWNdL+yRJ0vzhe5dIkqQqDBmSJKkK\nQ4YkSarCkCFJkqowZEiSpCoMGZIkqQpDhiRJqsKQIUmSqjBkSJKkKgwZkiSpCkOGJEmqwpAhSZKq\nMGRIkqQqDBmSJKkKQ4YkSarCkCFJkqowZEiSpCoMGZIkqQpDhiRJqsKQIUmSqjBkSJKkKgwZkiSp\nCkOGJEmqwpAhSZKqMGRIkqQqDBmSJKkKQ4YkSarCkCFJkqo4ftAN0OBMTEwwOTk56GYMne3btw+6\nCZI0FAwZx6iJiQlWrhxh375nB90USdICZcg4Rk1OTrYB4zZgZNDNGTJ3A7896EZI0rxnyDjmjQCr\nBt2IIePpEkk6Gl74KUmSqjBkSJKkKgwZkiSpCq/JkKQh4hLqmTnllFM4/fTTB92MY44hQ5KGwg+B\nF7Fu3bpBN2QonXDCiTzyyHaDxhwzZEjSUHgaOIDLzmdiO/v2rWNyctKQMccMGZI0VFx2ruHhhZ+S\nJKkKQ4YkSaqi55CR5Lwkn0nygyQHklzUtf9j7fbOx91dNYuT3JRkMsneJHclObWr5iVJbk+yO8mu\nJLcmOWlm3ZQkSXNtJjMZJwHfAH4DKIeouQdYDqxoH2Nd+68HLgQuBtYApwGf7Kq5g+bk49q2dg1w\nywzaK0mSBqDnCz9LKfcC9wIkySHKniulPDndjiRLgMuBS0opD7TbLgO2Jzm7lLIlyQhwATBaSnmo\nrbkS+FyS95RSdvTabkmSNLdqXZNxfpKdSR5OcnOSkzv2jdKEm/unNpRSHgEmgNXtpnOBXVMBo3Uf\nzczJOZXaLEmS+qjGEtZ7aE59PAq8EvgAcHeS1aWUQnP65PlSyp6u5+1s99F+fKJzZyllf5KnOmok\nSdI81veQUUq5s+PTbyX5U+B7wPnAl/r9et3Wr1/P0qVLD9o2NjbG2Fj3ZSGSJB17xsfHGR8fP2jb\n7t27q7xW9ZtxlVIeTTIJnEETMnYAi5Is6ZrNWN7uo/3YvdrkOODkjpppbdiwgVWrvFGNJEnTme4P\n723btjE6Otr316p+n4wkLwNeSnPjfYCtwAs0q0amalYCpwOb2k2bgGVJzuw41FogwObabZYkSbPX\n80xGe6+KM2h+4QP8bJLXAE+1j/fRXJOxo637IPAdYCNAKWVPko8C1yXZBewFbgAeLKVsaWseTrIR\n+EiSdwGLgA8D464skSRpOMzkdMlZNKc9Svv4/Xb7x2nunfELwKXAMuBxmnDxO6WUH3ccYz2wH7gL\nWEyzJPaKrtd5C3AjzaqSA23tVTNoryRJGoCZ3CfjAQ5/muVXj+IYzwFXto9D1TwN+J7GkiQNKd+7\nRJIkVWHIkCRJVRgyJElSFYYMSZJUhSFDkiRVYciQJElVGDIkSVIVhgxJklSFIUOSJFVhyJAkSVUY\nMiRJUhWGDEmSVIUhQ5IkVWHIkCRJVRgyJElSFYYMSZJUhSFDkiRVYciQJElVGDIkSVIVhgxJklSF\nIUOSJFVhyJAkSVUYMiRJUhWGDEmSVIUhQ5IkVWHIkCRJVRgyJElSFYYMSZJUhSFDkiRVYciQJElV\nGDIkSVIVhgxJklSFIUOSJFVhyJAkSVUYMiRJUhWGDEmSVIUhQ5IkVWHIkCRJVRgyJElSFYYMSZJU\nhSFDkiRV0XPISHJeks8k+UGSA0kumqbm/UkeT/Jski8kOaNr/+IkNyWZTLI3yV1JTu2qeUmS25Ps\nTrIrya1JTuq9i5IkaRBmMpNxEvAN4DeA0r0zydXAu4F3AGcDzwAbkyzqKLseuBC4GFgDnAZ8sutQ\ndwAjwNq2dg1wywzaK0mSBuD4Xp9QSrkXuBcgSaYpuQq4tpTy2bbmUmAn8GbgziRLgMuBS0opD7Q1\nlwHbk5xdStmSZAS4ABgtpTzU1lwJfC7Je0opO3pttyRJmlt9vSYjySuAFcD9U9tKKXuAzcDqdtNZ\nNOGms+YRYKKj5lxg11TAaN1HM3NyTj/bLEmS6uj3hZ8raILAzq7tO9t9AMuB59vwcaiaFcATnTtL\nKfuBpzpqJEnSPNbz6ZL5bv369SxduvSgbWNjY4yNjQ2oRZIkzR/j4+OMj48ftG337t1VXqvfIWMH\nEJrZis7ZjOXAQx01i5Is6ZrNWN7um6rpXm1yHHByR820NmzYwKpVq2bcAUmSFrLp/vDetm0bo6Oj\nfX+tvp4uKaU8ShMC1k5tay/0PAf4WrtpK/BCV81K4HRgU7tpE7AsyZkdh19LE2A297PNkiSpjp5n\nMtp7VZxB8wsf4GeTvAZ4qpTylzTLU9+b5LvAY8C1wPeBT0NzIWiSjwLXJdkF7AVuAB4spWxpax5O\nshH4SJJ3AYuADwPjriyRJGk4zOR0yVnAl2gu8CzA77fbPw5cXkr5UJITae5psQz4CvCGUsrzHcdY\nD+wH7gIW0yyJvaLrdd4C3EizquRAW3vVDNorSZIGYCb3yXiAI5xmKaVcA1xzmP3PAVe2j0PVPA2s\n67V9kiRpfvC9SyRJUhWGDEmSVIUhQ5IkVWHIkCRJVRgyJElSFYYMSZJUhSFDkiRVYciQJElVGDIk\nSVIVhgxJklSFIUOSJFVhyJAkSVUYMiRJUhWGDEmSVIUhQ5IkVWHIkCRJVRgyJElSFYYMSZJUhSFD\nkiRVYciQJElVGDIkSVIVhgxJklSFIUOSJFVhyJAkSVUYMiRJUhWGDEmSVIUhQ5IkVWHIkCRJVRw/\n6Ab02/bt2wfdhKHg10mSVNuCCxnr1q0bdBMkSRILMGTAbcDIoBsxBO4GfnvQjZAkLWALMGSMAKsG\n3Ygh4OkSSVJdXvgpSZKqWIAzGZIk/W1e8H5otb42hgxJ0gL3Q+BFLgwYAEOGJGmBexo4gAsDDmc7\n0P8QZsiQJB0jXBgw17zwU5IkVWHIkCRJVRgyJElSFX0PGUnel+RA1+PbXTXvT/J4kmeTfCHJGV37\nFye5Kclkkr1J7kpyar/bKkmS6qk1k/FnwHJgRfv45akdSa4G3g28AzgbeAbYmGRRx/OvBy4ELgbW\nAKcBn6zUVkmSVEGt1SUvlFKePMS+q4BrSymfBUhyKbATeDNwZ5IlwOXAJaWUB9qay4DtSc4upWyp\n1GZJktRHtWYyfi7JD5J8L8ltSX4aIMkraGY27p8qLKXsATYDq9tNZ9GEn86aR4CJjhpJkjTP1QgZ\nXwfeDlwAvBN4BfC/k5xEEzAKzcxFp53tPmhOszzfho9D1UiSpHmu76dLSikbOz79syRbgP8H/Brw\ncL9fT5IkzU/V7/hZStmd5DvAGcCXgdDMVnTOZiwHHmr/vQNYlGRJ12zG8nbfEawHlnZtG2sfkiQd\n68bbR6fdVV6peshI8ndoAsbHSymPJtkBrAW+2e5fApwD3NQ+ZSvwQlvzqbZmJXA6sOnIr7gBbxsr\nSdKhTPeH9zZgtO+v1PeQkeT3gP9Fc4rkp4D/CPwY+G9tyfXAe5N8F3gMuBb4PvBpaC4ETfJR4Lok\nu4C9wA3Ag64skSRpeNSYyXgZcAfwUuBJ4KvAuaWUHwGUUj6U5ETgFmAZ8BXgDaWU5zuOsR7YD9wF\nLAbuBa6o0FZJklRJjQs/j3jxQynlGuCaw+x/DriyfUiSpCHke5dIkqQqDBmSJKkKQ4YkSarCkCFJ\nkqowZEiSpCoMGZIkqQpDhiRJqsKQIUmSqjBkSJKkKgwZkiSpCkOGJEmqwpAhSZKqMGRIkqQqDBmS\nJKkKQ4YkSarCkCFJkqowZEiSpCoMGZIkqQpDhiRJqsKQIUmSqjBkSJKkKgwZkiSpCkOGJEmqwpAh\nSZKqMGRIkqQqDBmSJKkKQ4YkSarCkCFJkqowZEiSpCoMGZIkqQpDhiRJqsKQIUmSqjBkSJKkKgwZ\nkiSpCkOGJEmqwpAhSZKqMGRIkqQqDBmSJKkKQ4YkSarCkCFJkqowZAyl8UE3YI7Yz4Xna4NuwBw5\nVsbUfurw5n3ISHJFkkeT/FWSryf5xUG3afCOlW94+7nwbBp0A+bIsTKm9lOHN69DRpJ/Bfw+8D7g\nTOBPgI1JThlowyRJ0hHN65ABrAduKaV8opTyMPBO4Fng8sE2S5IkHcm8DRlJXgyMAvdPbSulFOA+\nYPWg2iVJko7O8YNuwGGcAhwH7OzavhNYOU39Cc2Hu4HtNds1D3wfuH2Wx3iw/Tifv1796GcN/f7a\nzdd+1vBU+3E+f9/1Q40xnY//Z4fle3e2X7th6edsPDr1jxP6edQ0kwPzT5KfBH4ArC6lbO7Y/kFg\nTSlldVf9W1j43wWSJNX01lLKHf062HyeyZgE9gPLu7YvB3ZMU78ReCvwGLCvasskSVpYTgBeTvO7\ntG/m7UwGQJKvA5tLKVe1nweYAG4opfzeQBsnSZIOaz7PZABcB/xxkq3AFprVJicCfzzIRkmSpCOb\n1yGjlHJne0+M99OcJvkGcEEp5cnBtkySJB3JvD5dIkmShte8vU+GJEkaboYMSZJUxdCGjCQ/k+TW\nJH+R5Nkkf57kmvZOoUd67vuTPN4+7wtJzpiLNs9Ukv+Q5MEkzyR56sjPgCQfS3Kg63F37bbOxkz6\n2T5v2MbzJUluT7I7ya72+/ikIzxn3o9nr29mmOT8JFuT7EvynSRvm6u2zkYv/UzyumnGbX+SU+ey\nzb1Kcl6SzyT5Qdvmi47iOUM3nr32c4jH87eSbEmyJ8nOJJ9K8qqjeN6sx3RoQwbw80CAfwu8mmbl\nyTuB/3S4JyW5Gng38A7gbOAZmjddW1S1tbPzYuBO4A97fN49NBfMrmgfY31uV7/13M8hHc87gBFg\nLXAhsAa45SieN2/Hs9c3M0zycuCzNG8b8BrgD4Bbk/zTuWjvTM3wTRsL8HP8zbj9ZCnlidptnaWT\naC60/w2a9h/WsI4nPfazNYzjeR7wYeAc4PU0P2s/n+QnDvWEvo1pKWXBPID3AN89Qs3jwPqOz5cA\nfwX82qDbfxT9exvw1FHWfgz4H4Nu8xz0c6jGkyYcHwDO7Nh2AfACsGJYxxP4OvAHHZ+H5l7Mv3mI\n+g8C3+zaNg7cPei+9Lmfr6O5qeCSQbd9Fn0+AFx0hJqhHM8Z9HPox7Ptxyltf3+59pgO80zGdJbx\nN2+O8LckeQVN8ux807U9wGYW5puund9OjT2c5OYkJw+6Qf00pOO5GthVSnmoY9t9NH8dnXOE587L\n8czM3szw3HZ/p42HqR+4GfYTmiDyjfaU3ueT/KO6LR2IoRvPWVgI47mM5mfO4U5L92VMF0zIaM/D\nvxv4L4cpW0HzhZ3uTddWVGraoNwDXAr8E+A3aRL43Uky0Fb11zCO5wrgoKnVUsp+mv/sh2vzfB7P\nw72Z4aH6tOIQ9UuSLO5v8/pmJv38IfDrwMXAvwD+EvhyktfWauSADON4zsTQj2f7M+N64KullG8f\nprQvYzrvbsaV5APA1YcpKcBIKeU7Hc/5KZofwv+9lPJHlZvYFzPpZy9KKXd2fPqtJH8KfA84H/jS\nTI45E7X7OV8cbT9nevz5Mp7qTft93fm9/fUkr6S5hmzeXxipgy2Q8byZ5jrGX5qLF5t3IQP4zzTn\nnw/nL6b+keQ04Is0qezXj/C8HTRTXcs5OKEtBx6a9hn19NTP2SqlPJpkEjiDuf2lVLOfwzieO4CD\nrkRPchxwMtO/8d+0Bjie0+n1zQxpt09Xv6eU8lx/m9c3M+nndLYwRz/g59Awjme/DM14JrkReCNw\nXinlh0co78uYzruQUUr5EfCjo6ltZzC+CPwf4PKjOPajSXbQXNX/zfYYS2jOhd800zbPRC/97Ick\nLwNeSjPdN2dq9nMYxzPJJmBZkjM7rstYSxOWNh/t6w1qPKdTSvlxmvcXWgt8Bv56SnYtcMMhnrYJ\neEPXtl9pt89LM+zndF7LPBi3Phu68eyjoRjPNmC8CXhdKWXiKJ7SnzEd9FWus7g69jTgz4HPt/9e\nPvXoqnsYeFPH579J88vgnwH/EPif7XEWDbpPh+nrT9MsIfodYHf779cAJ03XT5plWR+i+WX7MzQ/\nBP8vsB148aD7069+DvF43t2Oxy/S/AX0CPBfD/V9OwzjCfwa8CzNdSM/T7Mk90fA32v3fwD4eEf9\ny4G9NFewr6RZQvg88PpB96XP/bwKuAh4JfD3ac6F/xg4f9B9OUI/T2r/772WZhXCv2s//+kFNp69\n9nNYx/NmYBfNUtblHY8TOmp+t8aYDrzzs/iivY1m6rLzcQDY31W3H7i0a9s1NEsfn6W5WvaMQffn\nCH392DR93Q+sma6fwAnAvTTTXftopun/cOoH4Xx99NrPIR7PZcBtNEFqF/AR4MSumqEbz/aH0GM0\nS4g3AWd1je0Xu+rXAFvb+j8H/vWg+9DvfgL/vu3bM8CTNCtT1sx1m2fQx9dN/TztevzRQhrPXvs5\nxOM5XR8P+llaa0x9gzRJklTFglnCKkmS5hdDhiRJqsKQIUmSqjBkSJKkKgwZkiSpCkOGJEmqwpAh\nSZKqMGRIkqQqDBmSJKkKQ4YkSarCkCFJkqr4/7CkEJ1aYymUAAAAAElFTkSuQmCC\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x7f7dc5cc6048>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"qz_sam=qz.sample().eval()\n", | |
"plt.hist(qz_sam[0])\n", | |
"plt.xlim(-2,2)\n", | |
"plt.show()" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## Adding the noise variance (LogNormal posterior)\n", | |
"\n", | |
"Now we add the variance $\\sigma$ to get the width of the distribution around the line. The new priors are\n", | |
"\\begin{align}\n", | |
"w_{ij}&\\sim N(0,1)\\\\\n", | |
"z_j&\\sim N(0,1)\\\\\n", | |
"\\mu_i &\\sim N(0,1)\\\\\n", | |
"\\sigma &\\sim Gamma(1,1)\\\\\n", | |
"x_i&\\sim N((w\\cdot z)_i+\\mu_i,\\sigma)\\\\\n", | |
"\\end{align}" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 48, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"Iteration 1 [ 0%]: Loss = 991087.125\n", | |
"Iteration 1000 [ 10%]: Loss = 11453.900\n", | |
"Iteration 2000 [ 20%]: Loss = 9491.107\n", | |
"Iteration 3000 [ 30%]: Loss = 10180.900\n", | |
"Iteration 4000 [ 40%]: Loss = 9239.549\n", | |
"Iteration 5000 [ 50%]: Loss = 9392.727\n", | |
"Iteration 6000 [ 60%]: Loss = 9284.889\n", | |
"Iteration 7000 [ 70%]: Loss = 9288.990\n", | |
"Iteration 8000 [ 80%]: Loss = 9316.354\n", | |
"Iteration 9000 [ 90%]: Loss = 9214.365\n", | |
"Iteration 10000 [100%]: Loss = 9523.346\n", | |
"Inferred principal axes (columns):\n", | |
"[[-1.01378536]\n", | |
" [ 1.01291251]]\n", | |
"[[ 3.22195010e-05]\n", | |
" [ 6.35342712e-06]]\n", | |
"Inferred center:\n", | |
"[ 0.01017162 9.98824501]\n", | |
"[ 1.07507576e-05 1.01069354e-05]\n" | |
] | |
} | |
], | |
"source": [ | |
"# MODEL\n", | |
"\n", | |
"K=1\n", | |
"\n", | |
"ds = tf.contrib.distributions\n", | |
"\n", | |
"sigma = ed.models.Gamma(1.0,1.0)\n", | |
"\n", | |
"w = Normal(mu=tf.zeros([D, K]), sigma=tf.ones([D, K]))\n", | |
"z = Normal(mu=tf.zeros([K, N]), sigma=tf.ones([K, N]))\n", | |
"mu= Normal(mu=tf.zeros([D]), sigma=tf.ones([D]))\n", | |
"x = Normal(mu=tf.matmul(w, z)+\n", | |
" tf.transpose(tf.reshape(tf.tile(mu,[N]),[N,D])), sigma=sigma*tf.ones([D, N]))\n", | |
"\n", | |
"# INFERENCE\n", | |
"qw = Normal(mu=tf.Variable(tf.random_normal([D, K])),\n", | |
" sigma=tf.nn.softplus(tf.Variable(tf.random_normal([D, K]))))\n", | |
"qz = Normal(mu=tf.Variable(tf.random_normal([K, N])),\n", | |
" sigma=tf.nn.softplus(tf.Variable(tf.random_normal([K, N]))))\n", | |
"\n", | |
"# initial conditions for qmu, improves convergence\n", | |
"data_mean = np.mean(x_train,axis=1).astype(np.float32,copy=False)\n", | |
"\n", | |
"qmu= Normal(mu=tf.Variable(data_mean+tf.random_normal([D])),\n", | |
" sigma=tf.nn.softplus(tf.Variable(tf.random_normal([D]))))\n", | |
"\n", | |
"qsigma = ed.models.TransformedDistribution(\n", | |
" distribution=ed.models.NormalWithSoftplusSigma(mu=tf.Variable(0.0),\n", | |
" sigma=tf.Variable(1.0)),\n", | |
" bijector=ds.bijector.Exp(),\n", | |
" name=\"LogNormalTransformedDistribution\")\n", | |
"\n", | |
"inference = ed.KLqp({w: qw, z: qz, mu: qmu, sigma: qsigma}, data={x: x_train})\n", | |
"inference.run(n_iter=10000, n_samples=10)\n", | |
"\n", | |
"print(\"Inferred principal axes (columns):\")\n", | |
"print(qw.mean().eval())\n", | |
"print(qw.variance().eval())\n", | |
"print(\"Inferred center:\")\n", | |
"print(qmu.mean().eval())\n", | |
"print(qmu.variance().eval())" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Note that the loss function is much smaller now but we needed more iterations to converge." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 49, | |
"metadata": { | |
"collapsed": false, | |
"scrolled": true | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAgAAAAFkCAYAAABW9YMrAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x7f7dc1909ef0>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"qx = ed.copy(x,{z:qz, w:qw, mu:qmu, sigma:qsigma})\n", | |
"plt.scatter(*qx.sample().eval(),c='r',alpha=0.2)\n", | |
"plt.scatter(*x_train,c='b',alpha=0.2)\n", | |
"plt.xlim(-4,4)\n", | |
"plt.ylim(-4+10,4+10)\n", | |
"plt.show()" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"The distribution of $\\sigma$ should be close to $0.1$ that we started with." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 50, | |
"metadata": { | |
"collapsed": false, | |
"scrolled": true | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAhAAAAFkCAYAAABxWwLDAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAAPYQAAD2EBqD+naQAAGdJJREFUeJzt3X+QXeV93/H3V8gSFbWWaYklcCx+DMlabjqQXQJhXEgd\nuaYkNcUKalis4PhHqYuVoZtMjT0REwW1jU3GLHZLEtq4DbHjTTCZDDb1IBPiuBhsGLRgx/FahiDl\nWrAoufxYgcRqbfbpH+dsZ3e7EnrunnPP7vJ+zZwZ3ec895zveWZ17+c+99xzIqWEJElSjhVNFyBJ\nkpYeA4QkScpmgJAkSdkMEJIkKZsBQpIkZTNASJKkbAYISZKUzQAhSZKyGSAkSVI2A4QkScqWHSAi\n4qKI+EJEPBURUxFx2Yx1KyPi4xHxrYh4qexze0ScOmcbqyPi1ohoR8SLEXFnRLyhigOSJEn162QG\n4iTgMeBaYO6NNNYA5wK/Cfwk8C6gF7hrTr9bgJ8HfgG4GDgN+NMOapEkSQ2IhdxMKyKmgMtTSl84\nRp/zgIeA01NK+yNiLfD3wJUppT8r+/QCo8BPp5Qe7rggSZLUFd04B+JkipmKF8rH/cBK4L7pDiml\nPUALuLAL9UiSpAVaWefGI2I18DHgcymll8rm9cBkSungnO4HynXzbecfA5cA+4CJeqqVJGlZOhE4\nA9iVUnq2qo3WFiAiYiXweYrZh2sXuLlLgD9acFGSJL12vRv4XFUbqyVAzAgPbwJ+dsbsA8AzwKqI\nWDtnFmJduW4++wA++9nPsnHjxhoq1nwGBwcZGhpquozXFMe8+xzz7nPMu2t0dJStW7dC+V5alcoD\nxIzwcBbwtpTS83O67AZ+CGwCZp5EuQH4+lE2OwGwceNG+vr6qi5ZR9HT0+N4d5lj3n2Oefc55o2p\n9BSA7AAREScBZwNRNp0VEecAzwFjFD/HPBf4V8DrImJd2e+5lNIPUkoHI+LTwM0R8TzwIvAp4AF/\ngSFJ0tLQyQzEecBXKM5tSMAnyvbbKa7/8M6y/bGyPcrHbwP+T9k2CLwC3AmsBu4BPtRBLZIkqQHZ\nASKl9FWO/fPPV/1paErpCPAr5SJJkpYY74WhoxoYGGi6hNccx7z7HPPuc8yXhwVdibJbIqIP2L17\n925PvJEkKcPIyAj9/f0A/Smlkaq26wyEJEnKZoCQJEnZDBCSJCmbAUKSJGWr9WZaKrRaLdrtNqec\ncgobNmxouhxJkhbMAFGzVqtFb+9GJiYOc+KJa9izZ9QQIUla8vwKo2btdpuJicPAdiYmDtNut5su\nSZKkBTNAdM3pTRcgSVJlDBCSJCmbAUKSJGUzQEiSpGwGCEmSlM0AIUmSshkgJElSNgOEJEnKZoCQ\nJEnZDBCSJCmbAaJmY2NjTZcgSVLlDBA1arVabN58RdNlSJJUOQNEjdrtNpOTE02XIUlS5QwQkiQp\nmwFCkiRlM0B0mSdVSpKWAwNE1zwLrGDz5i20Wq2mi5EkaUEMEF3zEjDF5OTLtNvtpouRJGlBDBA1\nabVajI6ONl2GJEm1WNl0ActRq9Wit3cjExOHmy5FkqRaOANRg3a7XYaH9zddiiRJtTBA1OrUpguQ\nJKkWBghJkpTNACFJkrIZICRJUjYDhCRJymaAkCRJ2QwQkiQpmwFCkiRlM0BIkqRsBghJkpTNACFJ\nkrJlB4iIuCgivhART0XEVERcNk+fGyPi6Yg4HBH3RsTZc9avjohbI6IdES9GxJ0R8YaFHIgkSeqe\nTmYgTgIeA64F0tyVEXE9sA24BjgfOATsiohVM7rdAvw88AvAxcBpwJ92UIskSWpA9u28U0r3APcA\nRETM0+U6YGdK6e6yz9XAAeBy4I6IWAu8D7gypfTVss97gdGIOD+l9HBHRyJJkrqm0nMgIuJMYD1w\n33RbSukg8BBwYdl0HkVwmdlnD9Ca0UeSJC1iVZ9EuZ7ia40Dc9oPlOsA1gGTZbA4Wh9JkrSIZX+F\n0aTBwUF6enpmtQ0MDDAwMNBQRZIkLR7Dw8MMDw/PahsfH69lX1UHiGeAoJhlmDkLsQ54dEafVRGx\nds4sxLpy3VENDQ3R19dXYbmSJC0f832oHhkZob+/v/J9VfoVRkppL0UI2DTdVp40eQHwYNm0G/jh\nnD69wAbg61XWI0mS6pE9AxERJwFnU8w0AJwVEecAz6WUvk/xE83tEfEEsA/YCewH7oLipMqI+DRw\nc0Q8D7wIfAp4wF9gSJK0NHTyFcZ5wFcoTpZMwCfK9tuB96WUboqINcBtwMnA/cClKaXJGdsYBF4B\n7gRWU/ws9EMdHYEkSeq6Tq4D8VVe5auPlNIOYMcx1h8BfqVcJEnSEuO9MCRJUjYDhCRJymaAkCRJ\n2QwQkiQpmwFCkiRlM0BIkqRsBogGjI6O0mq1mi5DkqSOGSC6bgVbt26lt3ejIUKStGQZILpuCtjO\nxMRh2u1208VIktQRA0QjTm+6AEmSFsQAIUmSshkgJElSNgOEJEnKZoCQJEnZDBCSJCmbAUKSJGUz\nQEiSpGwGCEmSlM0AIUmSshkgajA2NtZ0CZIk1coAUbFWq8XmzVc0XYYkSbUyQFSs3W4zOTnRdBmS\nJNXKACFJkrIZICRJUjYDhCRJymaAkCRJ2QwQkiQpmwFCkiRlM0BIkqRsBghJkpTNACFJkrIZICRJ\nUjYDhCRJymaAkCRJ2QwQkiQpmwFCkiRlM0BIkqRsBghJkpTNACFJkrIZICRJUrbKA0RErIiInRHx\nZEQcjognImL7PP1ujIinyz73RsTZVdciSZLqUccMxEeAfwdcC7wZ+DDw4YjYNt0hIq4HtgHXAOcD\nh4BdEbGqhnokSVLFVtawzQuBu1JK95SPWxFxFUVQmHYdsDOldDdARFwNHAAuB+6ooSZJklShOmYg\nHgQ2RcSPAUTEOcBbgS+Vj88E1gP3TT8hpXQQeIgifEiSpEWujhmIjwFrge9GxCsUIeXXU0p/XK5f\nDySKGYeZDpTrJEnSIldHgPhF4CrgSuA7wLnAJyPi6ZTSZ2rYnyRJ6rI6AsRNwG+llD5fPv7riDgD\n+CjwGeAZIIB1zJ6FWAc8eqwNDw4O0tPTM6ttYGCAgYGBSgqXJGkpGx4eZnh4eFbb+Ph4LfuqI0Cs\nAV6Z0zZFeb5FSmlvRDwDbAK+BRARa4ELgFuPteGhoSH6+voqL1iSpOVgvg/VIyMj9Pf3V76vOgLE\nF4HtEbEf+GugDxgEfn9Gn1vKPk8A+4CdwH7grhrqkSRJFasjQGyjCAS3Am8AngZ+t2wDIKV0U0Ss\nAW4DTgbuBy5NKU3WUI8kSapY5QEipXQI+NVyOVa/HcCOqvcvSZLq570wJElSNgOEJEnKZoCQJEnZ\nDBCSJCmbAUKSJGUzQEiSpGwGCEmSlM0AIUmSshkgJElSNgOEJEnKZoCQJEnZDBCSJCmbAaJBY2Nj\nTZcgSVJHDBCNeBZYwebNW2i1Wk0XI0lSNgNEI14CppicfJl2u910MZIkZTNASJKkbAYISZKUzQAh\nSZKyGSAkSVI2A4QkScpmgJAkSdkMEJIkKZsBQpIkZTNASJKkbAYISZKUzQBRoVarxejoaNNlSJJU\nu5VNF7BctFotens3MjFxuOlSJEmqnTMQFWm322V4eH/TpUiSVDsDROVObboASZJqZ4CQJEnZDBCS\nJCmbAUKSJGUzQEiSpGwGCEmSlM0AIUmSshkgJElSNgOEJEnKZoCQJEnZDBCSJCmbAUKSJGUzQEiS\npGy1BIiIOC0iPhMR7Yg4HBHfjIi+OX1ujIiny/X3RsTZddQiSZKqV3mAiIiTgQeAI8AlwEbg14Dn\nZ/S5HtgGXAOcDxwCdkXEqqrrkSRJ1VtZwzY/ArRSSh+Y0fa3c/pcB+xMKd0NEBFXAweAy4E7aqhJ\nkiRVqI6vMN4JPBIRd0TEgYgYiYj/FyYi4kxgPXDfdFtK6SDwEHBhDfVIkqSK1REgzgL+PbAHeAfw\nu8CnIuKXyvXrgUQx4zDTgXKdJEla5Or4CmMF8HBK6Yby8Tcj4ieADwKfWciGBwcH6enpmdU2MDDA\nwMDAQjYrSdKyMDw8zPDw8Ky28fHxWvZVR4AYA0bntI0Cm8t/PwMEsI7ZsxDrgEePteGhoSH6+vqO\n1UWSpNes+T5Uj4yM0N/fX/m+6vgK4wGgd05bL+WJlCmlvRQhYtP0yohYC1wAPFhDPZIkqWJ1zEAM\nAQ9ExEcpflFxAfAB4N/O6HMLsD0ingD2ATuB/cBdNdQjSZIqVnmASCk9EhHvAj4G3ADsBa5LKf3x\njD43RcQa4DbgZOB+4NKU0mTV9UiSpOrVMQNBSulLwJdepc8OYEcd+5ckSfXyXhiSJCmbAUKSJGUz\nQEiSpGwGCEmSlM0AIUmSshkgJElSNgOEJEnKZoCQJEnZDBCSJCmbAUKSJGUzQEiSpGwGCEmSlM0A\n0bDR0VFarVbTZUiSlMUA0agVbN26ld7ejYYISdKSYoBo1BSwnYmJw7Tb7aaLkSTpuBkgGnd60wVI\nkpTNACFJkrIZICRJUjYDhCRJymaAkCRJ2QwQkiQpmwFCkiRlM0BUZGxsrOkSJEnqGgNEBVqtFps3\nX9F0GZIkdY0BogLtdpvJyYmmy5AkqWsMEJIkKZsBQpIkZTNASJKkbAYISZKUzQAhSZKyGSAkSVI2\nA4QkScpmgJAkSdkMEJIkKZsBQpIkZTNASJKkbAYISZKUzQAhSZKyGSAkSVI2A4QkScpmgFgkxsbG\nmi5BkqTjVnuAiIiPRMRURNw8p/3GiHg6Ig5HxL0RcXbdtSxOzwIr2Lx5C61Wq+liJEk6LrUGiIj4\nKeAa4Jtz2q8HtpXrzgcOAbsiYlWd9SxOLwFTTE6+TLvdbroYSZKOS20BIiL+IfBZ4APAC3NWXwfs\nTCndnVL6NnA1cBpweV31SJKk6tQ5A3Er8MWU0l/MbIyIM4H1wH3TbSmlg8BDwIU11iNJkiqyso6N\nRsSVwLnAefOsXg8k4MCc9gPlOkmStMhVHiAi4keBW4C3p5R+UOW2BwcH6enpmdU2MDDAwMBAlbuR\nJGlJGh4eZnh4eFbb+Ph4LfuqYwaiH/gRYCQiomw7Abg4IrYBbwYCWMfsWYh1wKPH2vDQ0BB9fX3V\nVyxJ0jIw34fqkZER+vv7K99XHedA/DnwTym+wjinXB6hOKHynJTSk8AzwKbpJ0TEWuAC4MEa6pEk\nSRWrfAYipXQI+M7Mtog4BDybUhotm24BtkfEE8A+YCewH7ir6nokSVL1ajmJch5p1oOUboqINcBt\nwMnA/cClKaXJLtUjSZIWoCsBIqX0s/O07QB2dGP/kiSpWt4LQ5IkZTNASJKkbAYISZKUzQAhSZKy\nGSAkSVI2A4QkScpmgJAkSdkMEJIkKZsBQpIkZTNASJKkbAYISZKUzQAhSZKyGSAkSVI2A4QkScpm\ngJAkSdkMEJIkKZsBQpIkZTNASJKkbAYISZKUzQAhSZKyGSAkSVI2A4QkScpmgJAkSdkMEJIkKZsB\nYoFarRajo6NNlyFJUletbLqApazVatHbu5GJicNNlyJJUlc5A7EA7Xa7DA/vb7oUSZK6ygBRiVOb\nLkCSpK4yQEiSpGwGCEmSlM0AIUmSshkgJElSNgOEJEnKZoCQJEnZDBCSJCmbAUKSJGUzQEiSpGwG\nCEmSlM0AIUmSshkgJElStsoDRER8NCIejoiDEXEgIv4sIn58nn43RsTTEXE4Iu6NiLOrrkWSJNWj\njhmIi4D/ClwAvB14HfDliPgH0x0i4npgG3ANcD5wCNgVEatqqEeSJFVsZdUbTCn93MzHEfHLwN8B\n/cDXyubrgJ0ppbvLPlcDB4DLgTuqrkmSJFWrG+dAnAwk4DmAiDgTWA/cN90hpXQQeAi4sAv1SJKk\nBao1QEREALcAX0spfadsXk8RKA7M6X6gXCdJkha5umcgfgd4C3BlzftZFkZHR2m1Wk2XIUnSq6r8\nHIhpEfHfgJ8DLkopjc1Y9QwQwDpmz0KsAx491jYHBwfp6emZ1TYwMMDAwEAlNTdrBVu3buXEE9ew\nZ88oGzZsaLogSdISMzw8zPDw8Ky28fHxWvZVS4Aow8O/Bn4mpTTrI3VKaW9EPANsAr5V9l9L8auN\nW4+13aGhIfr6+uooeRGYArYzMfGfaLfbBghJUrb5PlSPjIzQ399f+b4qDxAR8TvAAHAZcCgi1pWr\nxlNKE+W/bwG2R8QTwD5gJ7AfuKvqepaW05suQJKk41LHDMQHKU6S/Ms57e8F/hAgpXRTRKwBbqP4\nlcb9wKUppcka6pEkSRWr4zoQx3ViZkppB7Cj6v1LkqT6eS8MSZKUzQAhSZKyGSAkSVI2A4QkScpm\ngJAkSdkMEJIkKZsBQpIkZTNASJKkbAYISZKUzQAhSZKyGSAkSVI2A4QkScpmgJAkSdkMEJIkKZsB\nQpIkZTNASJKkbAYISZKUzQAhSZKyGSAkSVI2A4QkScpmgFiAsbGxJbVdSZKqYoDoUKvVYvPmKyre\n6rPACjZv3kKr1ap425IkVccA0aF2u83k5ETFW30JmGJy8mXa7XbF25YkqToGCEmSlM0AIUmSshkg\nJElSNgOEJEnKZoCQJEnZDBCSJCmbAUKSJGVb2XQBmt/o6ChHjhzhjW98Ixs2bGi6HEmSZjFALEor\n2Lp1K3ACq1ev4nvf+64hQpK0qPgVRgcef/xxvv/979e4hyng/cArHDniVSklSYuPMxCZ7rzzTrZs\n2dKFPZ3ahX1IktQZZyAyPfnkk5xwwuuJeF3TpUiS1BgDRAeK8HBCV/fZarW8Q6ckadEwQCwBY2Nj\n9PZupLd3oyFCkrQoGCCWgBdeeIGJicNMTBz2hEpJ0qJggJAkSdkMEJIkKZsBQkc1PDzcdAmvOY55\n9znm3eeYLw+NBoiI+FBE7I2IlyPiGxHxU03Wo9n8T959jnn3Oebd55gvD40FiIj4ReATwG8APwl8\nE9gVEac0VZMkSTo+Tc5ADAK3pZT+MKX0XeCDwGHgfQ3WtCjt3bu36RIkSZqlkQARxZWY+oH7pttS\nSgn4c+DCJmpavFZwww03NF2EJEmzNHUvjFMoLuV4YE77AaB3nv4nQnGL66Y99dRTTE1NkNIPZ7T+\nVY3/ngL+GfA1oLtjMD4+zsjISNf2J8e8CY559znm3TXjfePEKrcbxQf/7oqIU4GngAtTSg/NaP84\ncHFK6cI5/a8C/qi7VUqStKy8O6X0uao21tQMRBt4BVg3p30d8Mw8/XcB7wb2ARO1ViZJ0vJyInAG\nxXtpZRqZgQCIiG8AD6WUrisfB9ACPpVS+u1GipIkScelqRkIgJuBP4iI3cDDFL/KWAP8QYM1SZKk\n49BYgEgp3VFe8+FGiq8uHgMuSSn9fVM1SZKk49PYVxiSJGnp8l4YkiQpmwFCkiRlWzQBIvfGWhHx\nzyNid0RMRMT3IuI93ap1ucgZ84h4V0R8OSL+LiLGI+LBiHhHN+tdDjq9gVxEvDUifhARXn0nUwev\nLasi4j9HxL7y9eXJiPjlLpW7LHQw5u+OiMci4lBEPB0Rn46If9Stepe6iLgoIr4QEU9FxFREXHYc\nz1nwe+iiCBC5N9aKiDOAuykuhX0O8Eng9yPiX3Sj3uWgg5uZXQx8GbgU6AO+AnwxIs7pQrnLQqc3\nkIuIHuB2iku9K0OHY/554G3Ae4EfBwaAPTWXumx08Hr+Voq/7/8BvAW4Ajgf+O9dKXh5OInihwjX\nAq96YmNl76EppcYX4BvAJ2c8DmA/8OGj9P848K05bcPAl5o+lqWy5I75UbbxbWB708eyVJZOx7z8\n2/5NihfkkaaPYyktHby2/EvgOeDkpmtfqksHY/5rwONz2rYBraaPZSkuFPc/uOxV+lTyHtr4DESH\nN9b6af7/T2O7jtFfM1RxM7Pywl+vp3ix1avodMwj4r3AmRQBQhk6HPN3Ao8A10fE/ojYExG/HRGV\n3kNguepwzL8OvCkiLi23sQ7YAvzveqt9TavkPbTxAMGxb6y1/ijPWX+U/msjYnW15S1LnYz5XP+R\nYtrsjgrrWs6yxzwifgz4LxTXr5+qt7xlqZO/87OAi4B/AlwOXEcxpX5rTTUuN9ljnlJ6ENgK/ElE\nTAJjwPMUsxCqRyXvoYshQGiJKW9udgOwJaXUbrqe5SgiVlDcQO43Ukp/M93cYEmvFSsopoCvSik9\nklK6B/hV4D1+OKlHRLyF4jv4HRTnV11CMet2W4Nl6Tg0eSnrabk31qJsn6//wZTSkWrLW5Y6GXMA\nIuJKipObrkgpfaWe8pal3DF/PXAecG5ETH/6XUHx7dEk8I6U0l/WVOty0cnf+RjwVErppRltoxTh\n7UeBv5n3WZrWyZh/BHggpXRz+fjbEXEtcH9E/HpKae4nZS1cJe+hjc9ApJR+AOwGNk23ld+vbwIe\nPMrTvj6zf+kdZbteRYdjTkQMAJ8Griw/mek4dTDmB4GfAM6lOEv6HOD3gO+W/36o5pKXvA7/zh8A\nTouINTPaeilmJfbXVOqy0eGYrwF+OKdtiuLXBM661aOa99Cmzxgtz/78N8Bh4GrgzRRTV88CP1Ku\n/y3g9hn9zwBepDiTtJfipyuTwNubPpalsnQw5leVY/xBiqQ6vaxt+liWypI75vM8319h1DzmFOf1\n/C3wJ8BGip8v7wF+r+ljWSpLB2P+HuBI+dpyJvBWihssPtj0sSyVpfy7PYfiA8cU8B/Kx286yphX\n8h7a+IHPOKBrgX3AyxQp6LwZ6/4X8Bdz+l9MkXRfBh4HfqnpY1hqS86YU1z34ZV5lv/Z9HEspSX3\n73zOcw0QXRhzims/7AJeKsPETcDqpo9jKS0djPmHgL8qx3w/xXUhTm36OJbKAvxMGRzmfX2u6z3U\nm2lJkqRsjZ8DIUmSlh4DhCRJymaAkCRJ2QwQkiQpmwFCkiRlM0BIkqRsBghJkpTNACFJkrIZICRJ\nUjYDhCRJymaAkCRJ2f4vN+lJgPaJgRUAAAAASUVORK5CYII=\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x7f7dc5cc6d30>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"plt.hist(qsigma.sample(1000).eval(),bins=20)\n", | |
"plt.xlim(0,1)\n", | |
"plt.show()" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## Adding the automatic relevance determination.\n", | |
"\n", | |
"So far we used the knowledge on the dimensionality of the latent space by setting $K=1$. We can determine the number of latent dimensions by setting a higher $K$ (in this case $K=2$) and adding another prior $\\alpha=(\\alpha_1,\\dots,\\alpha_K)$ for the scale of each dimension.\n", | |
"\\begin{align}\n", | |
"\\alpha_j&\\sim Gamma(1,1)\\\\\n", | |
"w_{ij}&\\sim N(0,\\alpha_j)\\\\\n", | |
"z_j&\\sim N(0,1)\\\\\n", | |
"\\mu_i &\\sim N(0,1)\\\\\n", | |
"\\sigma &\\sim Gamma(1,1)\\\\\n", | |
"x_i&\\sim N((w\\cdot z)_i+\\mu_i,\\sigma)\\\\\n", | |
"\\end{align}\n", | |
"\n", | |
"We expect the posterior for either $\\alpha_1$ or $\\alpha_2$, say $\\alpha_2$, to drop down to zero, signaling that there are is only one significant dimension left, $\\alpha_1\\ne0$." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 51, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"Iteration 1 [ 0%]: Loss = 338026.875\n", | |
"Iteration 1000 [ 10%]: Loss = 9805.922\n", | |
"Iteration 2000 [ 20%]: Loss = 9334.182\n", | |
"Iteration 3000 [ 30%]: Loss = 9217.198\n", | |
"Iteration 4000 [ 40%]: Loss = 9190.154\n", | |
"Iteration 5000 [ 50%]: Loss = 9118.033\n", | |
"Iteration 6000 [ 60%]: Loss = 9195.638\n", | |
"Iteration 7000 [ 70%]: Loss = 9133.659\n", | |
"Iteration 8000 [ 80%]: Loss = 9120.769\n", | |
"Iteration 9000 [ 90%]: Loss = 9111.705\n", | |
"Iteration 10000 [100%]: Loss = 9141.464\n", | |
"Inferred principal axes (columns):\n", | |
"[[ -1.01255262e+00 2.54292445e-05]\n", | |
" [ 1.01165628e+00 5.29239833e-06]]\n", | |
"[[ 1.40580789e-06 4.67178052e-06]\n", | |
" [ 1.37689140e-05 2.54442912e-05]]\n", | |
"Inferred center:\n", | |
"[ 0.01011961 9.98821449]\n", | |
"[ 7.89400383e-06 2.02747538e-06]\n" | |
] | |
} | |
], | |
"source": [ | |
"# MODEL\n", | |
"\n", | |
"K=2\n", | |
"\n", | |
"ds = tf.contrib.distributions\n", | |
"\n", | |
"sigma = ed.models.Gamma(1.0,1.0)\n", | |
"\n", | |
"\n", | |
"alpha = ed.models.Gamma(tf.ones([K]),tf.ones([K]))\n", | |
"w = Normal(mu=tf.zeros([D, K]), sigma=tf.reshape(tf.tile(alpha,[D]),[D,K]))\n", | |
"z = Normal(mu=tf.zeros([K, N]), sigma=tf.ones([K, N]))\n", | |
"mu= Normal(mu=tf.zeros([D]), sigma=tf.ones([D]))\n", | |
"x = Normal(mu=tf.matmul(w, z)+\n", | |
" tf.transpose(tf.reshape(tf.tile(mu,[N]),[N,D])), sigma=sigma*tf.ones([D, N]))\n", | |
"\n", | |
"# INFERENCE\n", | |
"qalpha = ed.models.TransformedDistribution(\n", | |
" distribution=ed.models.NormalWithSoftplusSigma(mu=tf.Variable(tf.zeros([K])),\n", | |
" sigma=tf.Variable(tf.ones([K]))),\n", | |
" bijector=ds.bijector.Exp(),\n", | |
" name=\"qalpha\")\n", | |
"\n", | |
"qw = Normal(mu=tf.Variable(tf.random_normal([D, K])),\n", | |
" sigma=tf.nn.softplus(tf.Variable(tf.random_normal([D, K]))))\n", | |
"qz = Normal(mu=tf.Variable(tf.random_normal([K, N])),\n", | |
" sigma=tf.nn.softplus(tf.Variable(tf.random_normal([K, N]))))\n", | |
"\n", | |
"# initial conditions for qmu, improves convergence\n", | |
"data_mean = np.mean(x_train,axis=1).astype(np.float32,copy=False)\n", | |
"\n", | |
"qmu= Normal(mu=tf.Variable(data_mean+tf.random_normal([D])),\n", | |
" sigma=tf.nn.softplus(tf.Variable(tf.random_normal([D]))))\n", | |
"\n", | |
"qsigma = ed.models.TransformedDistribution(\n", | |
" distribution=ed.models.NormalWithSoftplusSigma(mu=tf.Variable(0.0),\n", | |
" sigma=tf.Variable(1.0)),\n", | |
" bijector=ds.bijector.Exp(),\n", | |
" name=\"qsigma\")\n", | |
"\n", | |
"inference = ed.KLqp({alpha: qalpha, w: qw, z: qz, mu: qmu, sigma: qsigma}, data={x: x_train})\n", | |
"inference.run(n_iter=10000, n_samples=10)\n", | |
"\n", | |
"print(\"Inferred principal axes (columns):\")\n", | |
"print(qw.mean().eval())\n", | |
"print(qw.variance().eval())\n", | |
"print(\"Inferred center:\")\n", | |
"print(qmu.mean().eval())\n", | |
"print(qmu.variance().eval())" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"With this step the loss function should be comparable to the previous example but we removed one of the parameters of the model (the number of latent dimensions)." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 52, | |
"metadata": { | |
"collapsed": false, | |
"scrolled": true | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAgAAAAFkCAYAAABW9YMrAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x7f7dbba8d9e8>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"qx = ed.copy(x,{alpha: qalpha, z:qz, w:qw, mu:qmu, sigma:qsigma})\n", | |
"plt.scatter(*qx.sample().eval(),c='r',alpha=0.2)\n", | |
"plt.scatter(*x_train,c='b',alpha=0.2)\n", | |
"plt.xlim(-4,4)\n", | |
"plt.ylim(-4+10,4+10)\n", | |
"plt.show()" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"The distribution of $\\sigma$ should be close to $0.1$ that we started with." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 53, | |
"metadata": { | |
"collapsed": false, | |
"scrolled": true | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAhAAAAFkCAYAAABxWwLDAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ntMfBay4AAAAASUVORK5CYII=\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x7f7dbbb2d2b0>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"plt.hist(qsigma.sample(1000).eval(),bins=20)\n", | |
"plt.xlim(0,1)\n", | |
"plt.show()" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"As expected, one of the $\\alpha_j$ collapses to $0$, while the other stays close to $1$." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 54, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAhIAAAFkCAYAAAB1rtL+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAAPYQAAD2EBqD+naQAAGQNJREFUeJzt3X+QndV93/H3B2OJ4FSiDSCZuoxxiRVlnMGRiDDjokyK\nxhTj2qR0GtambqAuxQZmZ9NMsF08VtFMmuIJUrFxhmmYJhi8GSrGg+1SZIwTym8VRMjYlslQg9Yy\nsCCsCI2okEGnfzzP2ncvktAe7d17d/f9mrnD3nPO89zvXq+1nz3nPPdJKQVJkqQaR/W7AEmSNHsZ\nJCRJUjWDhCRJqmaQkCRJ1QwSkiSpmkFCkiRVM0hIkqRqBglJklTNICFJkqoZJCRJUrUpB4kkZyX5\nepIfJ9mf5MMHGHNNkmeTvJLk7iSndvUvTHJDkh1JdifZmOTErjF/P8mtSXYl2ZnkT5O8berfoiRJ\n6pWaGYm3AX8NfAp4w406klwFXAFcCqwC9gCbkizoGLYBOA+4AFgNnATc3nWqrwLLgbPbsauBGyvq\nlSRJPZIjuWlXkv3A+aWUr3e0PQt8oZSyvn2+CBgH/k0p5bb2+YvAhaWUr7VjlgFbgfeVUjYnWQ58\nD1hZSnm8HXMO8D+Bd5RSnq8uWpIkTZtp3SOR5BRgKXDPRFsp5WXgEeDMtul04OiuMU8CYx1j3gfs\nnAgRrW/TzICcMZ01S5KkekdP8/mW0vyyH+9qH2/7AJYA+9qAcbAxS4EXOjtLKa8n+UnHmEmS/BJw\nDvAMsLeyfkmS5qNjgHcCm0opL03lwOkOEv10DnBrv4uQJGkW+xjNHsXDNt1B4nkgNLMOnbMSS4DH\nO8YsSLKoa1ZiSds3Mab7Ko63AP+gY0y3ZwBuueUWli9fPqnjueee40Mf+hD8JpPnM3YC3zrwMTo8\nIyMjrF+/vt9lzCu+5zPP93zm+Z7PrK1bt3LRRRdB+7t0KqY1SJRSnk7yPM2VFn8DP9tseQZwQzvs\nMeC1dkznZsuTgYfaMQ8BxyX59Y59EmfThJRHDvLyewGWL1/OihUrJnVs27at+eJk4B93dDzX/OdA\nx+jwLF682Pduhvmezzzf85nne943U94aMOUg0X6Ww6k0v9QB3pXkNOAnpZQf0VzaeXWSp2iSzTpg\nO3AHNJsvk9wEXJdkJ7AbuB54oJSyuR3zgySbgP+W5JPAAuCLwKhXbEiSNDhqZiROB/6SZlNlAf64\nbf9z4JJSyrVJjqX5zIfjgPuAc0sp+zrOMQK8DmwEFgJ3AZd3vc5HgS/RXK2xvx07XFGvJEnqkSkH\niVLKvbzJZaOllLXA2kP0vwpc2T4ONubvgIumWp8kSZo53mtDR2RoaKjfJcw7vuczz/d85vmezx4G\nCR0R/88+83zPZ57v+czzPZ89DBKSJKmaQUKSJFUzSEiSpGoGCUmSVM0gIUmSqhkkJElSNYOEJEmq\nZpCQJEnVDBKSJKmaQUKSJFUzSEiSpGoGCUmSVM0gIUmSqhkkJElSNYOEJEmqZpCQJEnVDBKSJKma\nQUKSJFUzSEiSpGoGCUmSVM0gIUmSqhkkJElSNYOEJEmqZpCQJEnVDBKSJKmaQUKSJFUzSEiSpGoG\nCUmSVM0gIUmSqhkkJElSNYOEJEmqZpCQJEnVDBKSJKmaQUKSJFUzSEiSpGoGCUmSVM0gIUmSqhkk\nJElSNYOEJEmqZpCQJEnVDBKSJKmaQUKSJFUzSEiSpGoGCUmSVM0gIUmSqhkkJElSNYOEJEmqZpCQ\nJEnVDBKSJKnatAeJJEclWZfkh0leSfJUkqsPMO6aJM+2Y+5OcmpX/8IkNyTZkWR3ko1JTpzueiVJ\nUr1ezEh8Gvj3wKeAXwH+APiDJFdMDEhyFXAFcCmwCtgDbEqyoOM8G4DzgAuA1cBJwO09qFeSJFU6\nugfnPBO4o5RyV/t8LMlHaQLDhGFgXSnlmwBJPg6MA+cDtyVZBFwCXFhKubcdczGwNcmqUsrmHtQt\nSZKmqBczEg8CZyf5ZYAkpwHvB+5sn58CLAXumTiglPIy8AhNCAE4nSbkdI55EhjrGCNJkvqsFzMS\nfwQsAn6Q5HWasPIfSyl/0fYvBQrNDESn8bYPYAmwrw0YBxsjSZL6rBdB4neAjwIXAt8H3gv81yTP\nllK+0oPXm2RkZITFixdPaluzZk2vX1aSpFlhdHSU0dHRSW27du2qPl8vgsS1wH8upfyP9vn3krwT\n+AzwFeB5IDSzDp2zEkuAx9uvnwcWJFnUNSuxpO07qPXr17NixYpJbdu2bWN4eLjqm5EkaS4ZGhpi\naGhoUtuWLVtYuXJl1fl6sUfiWOD1rrb9E69VSnmaJgycPdHZbq48g2Z/BcBjwGtdY5YBJwMP9aBm\nSZJUoRczEt8Ark6yHfgesAIYAf60Y8yGdsxTwDPAOmA7cAc0my+T3ARcl2QnsBu4HnjAKzYkSRoc\nvQgSV9AEgxuAE4FngT9p2wAopVyb5FjgRuA44D7g3FLKvo7zjNDMbGwEFgJ3AZf3oF5JklRp2oNE\nKWUP8Hvt41Dj1gJrD9H/KnBl+5AkSQPIe21IkqRqBglJklTNICFJkqoZJCRJUjWDhCRJqmaQkCRJ\n1QwSkiSpmkFCkiRVM0hIkqRqBglJklTNICFJkqoZJCRJUjWDhCRJqmaQkCRJ1QwSkiSpmkFCkiRV\nM0hIkqRqBglJklTNICFJkqoZJCRJUjWDhCRJqmaQkCRJ1QwSkiSpmkFCkiRVM0hIkqRqBglJklTN\nICFJkqoZJCRJUjWDhCRJqmaQkCRJ1QwSkiSpmkFCkiRVM0hIkqRqBglJklTNICFJkqoZJCRJUjWD\nhCRJqmaQkCRJ1QwSkiSpmkFCkiRVM0hIkqRqBglJklTNICFJkqoZJCRJUjWDhCRJqmaQkCRJ1QwS\nkiSpmkFCkiRVM0hIkqRqBglJklTNICFJkqr1JEgkOSnJV5LsSPJKkieSrOgac02SZ9v+u5Oc2tW/\nMMkN7Tl2J9mY5MRe1CtJkupMe5BIchzwAPAqcA6wHPgPwM6OMVcBVwCXAquAPcCmJAs6TrUBOA+4\nAFgNnATcPt31SpKkekf34JyfBsZKKZ/oaNvWNWYYWFdK+SZAko8D48D5wG1JFgGXABeWUu5tx1wM\nbE2yqpSyuQd1S5KkKerF0sY/Bx5NcluS8SRbkvwsVCQ5BVgK3DPRVkp5GXgEOLNtOp0m5HSOeRIY\n6xgjSZL6rBdB4l3AJ4EngQ8AfwJcn+Rft/1LgUIzA9FpvO0DWALsawPGwcZIkqQ+68XSxlHA5lLK\n59rnTyR5D3AZ8JUevN4kIyMjLF68eFLbmjVrev2ykiTNCqOjo4yOjk5q27VrV/X5ehEkngO2drVt\nBf5F+/XzQGhmHTpnJZYAj3eMWZBkUdesxJK276DWr1/PihWTLhBh27ZtDA8PT+V7kCRpThoaGmJo\naGhS25YtW1i5cmXV+XqxtPEAsKyrbRnthstSytM0YeDsic52c+UZwINt02PAa11jlgEnAw/1oGZJ\nklShFzMS64EHknwGuI0mIHwC+HcdYzYAVyd5CngGWAdsB+6AZvNlkpuA65LsBHYD1wMPeMWGJEmD\nY9qDRCnl0SS/DfwR8DngaWC4lPIXHWOuTXIscCNwHHAfcG4pZV/HqUaA14GNwELgLuDy6a5XkiTV\n68WMBKWUO4E732TMWmDtIfpfBa5sH5IkaQB5rw1JklTNICFJkqoZJCRJUjWDhCRJqmaQkCRJ1QwS\nkiSpmkFCkiRVM0hIkqRqBglJklTNICFJkqoZJCRJUjWDhCRJqmaQkCRJ1QwSkiSpmkFCkiRVM0hI\nkqRqBglJklTNICFJkqoZJCRJUjWDhCRJqmaQkCRJ1QwSkiSpmkFCkiRVM0hIkqRqBglJklTNICFJ\nkqoZJCRJUjWDhCRJqmaQkCRJ1QwSkiSpmkFCkiRVM0hIkqRqBglJklTNICFJkqoZJCRJUjWDhCRJ\nqmaQkCRJ1QwSkiSpmkFCkiRVM0hIkqRqBglJklTNICFJkqoZJCRJUjWDhCRJqmaQkCRJ1QwSkiSp\nmkFCkiRVM0hIkqRqBglJklTNICFJkqoZJCRJUrWeB4kkn06yP8l1Xe3XJHk2yStJ7k5yalf/wiQ3\nJNmRZHeSjUlO7HW9kiTp8PU0SCT5DeBS4Imu9quAK9q+VcAeYFOSBR3DNgDnARcAq4GTgNt7Wa8k\nSZqangWJJL8I3AJ8Avi7ru5hYF0p5ZullO8CH6cJCue3xy4CLgFGSin3llIeBy4G3p9kVa9qliRJ\nU9PLGYkbgG+UUr7T2ZjkFGApcM9EWynlZeAR4My26XTg6K4xTwJjHWMkSVKfHd2Lkya5EHgvTSDo\nthQowHhX+3jbB7AE2NcGjIONkSRJfTbtQSLJO2j2N6wppfx0us//ZkZGRli8ePGktjVr1sx0GZIk\nDaTR0VFGR0cnte3atav6fL2YkVgJnABsSZK27S3A6iRXAL8ChGbWoXNWYgnwePv188CCJIu6ZiWW\ntH0HtX79elasWDGpbdu2bQwPD1d+O5IkzR1DQ0MMDQ1NatuyZQsrV66sOl8v9kh8G/g1mqWN09rH\nozQbL08rpfyQJgycPXFAu7nyDODBtukx4LWuMcuAk4GHelCzJEmqMO0zEqWUPcD3O9uS7AFeKqVs\nbZs2AFcneQp4BlgHbAfuaM/xcpKbgOuS7AR2A9cDD5RSNk93zZIkqU5PNlseQJn0pJRrkxwL3Agc\nB9wHnFtK2dcxbAR4HdgILATuAi6fmXIlSdLhmJEgUUr5pwdoWwusPcQxrwJXtg9JkjSAvNeGJEmq\nZpCQJEnVDBKSJKmaQUKSJFUzSEiSpGoGCUmSVM0gIUmSqhkkJElSNYOEJEmqZpCQJEnVDBKSJKma\nQUKSJFUzSEiSpGoGCUmSVM0gIUmSqhkkJElSNYOEJEmqZpCQJEnVDBKSJKmaQUKSJFUzSEiSpGoG\nCUmSVM0gIUmSqhkkJElSNYOEJEmqZpCQJEnVDBKSJKmaQUKSJFUzSEiSpGoGCUmSVM0gIUmSqhkk\nJElSNYOEJEmqZpCQJEnVDBKSJKmaQUKSJFUzSEiSpGoGCUmSVM0gIUmSqhkkJElSNYOEJEmqZpCQ\nJEnVDBKSJKmaQUKSJFUzSEiSpGoGCUmSVM0gIUmSqhkkJElSNYOEJEmqZpCQJEnVDBKSJKnatAeJ\nJJ9JsjnJy0nGk3wtybsPMO6aJM8meSXJ3UlO7epfmOSGJDuS7E6yMcmJ012vJEmq14sZibOALwJn\nAGuAtwLfSvILEwOSXAVcAVwKrAL2AJuSLOg4zwbgPOACYDVwEnB7D+qVJEmVjp7uE5ZSPtj5PMnv\nAi8AK4H72+ZhYF0p5ZvtmI8D48D5wG1JFgGXABeWUu5tx1wMbE2yqpSyebrrliRJUzcTeySOAwrw\nE4AkpwBLgXsmBpRSXgYeAc5sm06nCTmdY54ExjrGSJKkPutpkEgSmiWK+0sp32+bl9IEi/Gu4eNt\nH8ASYF8bMA42RpIk9dm0L210+TLwq8D7e/w6PzMyMsLixYsnta1Zs2amXl6SpIE2OjrK6OjopLZd\nu3ZVn69nQSLJl4APAmeVUp7r6HoeCM2sQ+esxBLg8Y4xC5Is6pqVWNL2HdT69etZsWLFpLZt27Yx\nPDxc9X1IkjSXDA0NMTQ0NKlty5YtrFy5sup8PVnaaEPER4DfKqWMdfaVUp6mCQNnd4xfRHOVx4Nt\n02PAa11jlgEnAw/1omZJkjR10z4jkeTLwBDwYWBPkiVt165Syt726w3A1UmeAp4B1gHbgTug2XyZ\n5CbguiQ7gd3A9cADXrEhSdLg6MXSxmU0myn/qqv9YuBmgFLKtUmOBW6kuarjPuDcUsq+jvEjwOvA\nRmAhcBdweQ/qlSRJlXrxORKHtVxSSlkLrD1E/6vAle1DkiQNIO+1IUmSqhkkJElSNYOEJEmqZpCQ\nJEnVDBKSJKmaQUKSJFUzSEiSpGoGCUmSVM0gIUmSqhkkJElSNYOEJEmqZpCQJEnVDBKSJKlaL24j\nrllibGyMHTt2vKH9+OOP5+STT+5DRZKk2cYgMU+NjY2xbNly9u595Q19xxxzLE8+udUwIUl6Uy5t\nzFM7duxoQ8QtwGMdj1vYu/eVA85USJLUzRmJeW85sGLKR7ksIkkCg4QquCwiSZpgkJjl+jEzMHlZ\nZHlHz1b27r2IHTt2GCQkaZ4wSMxi/Z8ZqFsWkSTNHW62nMXcMClJ6jdnJOYEZwYkSf1hkNCM8moP\nSZpbDBKaMf3f0yFJmm7ukdCMcU+HJM09zkioD9zTIUlzhTMSkiSpmkFCkiRVM0hIkqRq7pHQrOGl\no5I0eAwSmhW8dFSSBpNLG5oVvHRUkgaTMxKaZeouHXVZRJJ6wyChOc9lEUnqHZc2NOe5LCJJveOM\nhOYRP1FTkqabQUJ6E+6vkKSDM0hIh+D+Ckk6NIPEAPAv3sE1eX/F8o6erezdexE7duzwfyNJ85pB\nos/8i3e2cH+FJB2IQaLP/It3bnO2SdJcZ5AYGP7FO9c42yRpPvBzJKQe8fMrJM0HzkhIPTd9H+vt\nkoikQWOQkAbQwZZFXBKRNGhc2pAG0IGXRVwSkTR4nJGQBpqbcCUNNoPENPEyP0nSfGSQmAZe5qdB\nYqiVNJMMEtPAD5XSoDDUSpppbracVhPr2ROP5YcePieM9ruAeeeuu+46aN+RfnbF2NgYW7ZsecNj\nbGxsGr+D2Wd01J/zmeZ7PnsM/IxEksuB3weWAk8AV5ZS/k9/q9LPjQJD/S5iXtm0aROf/exn32TU\n1DdpHulsxpEsqQz6cszo6ChDQ/6czyTf89ljoINEkt8B/hi4FNgMjACbkry7lOI1cNI0OpIluiMJ\nIfNtOWbQQ5M0VQMdJGiCw42llJsBklwGnAdcAlzbz8KkuWvqsxlHEkKOdI9R7S/mfvxCn2+hSfPD\nwAaJJG8FVgJ/ONFWSilJvg2c2bfCJB3CkXzuxcwtx/TrF7obszUXDWyQAI4H3gKMd7WPA8sOMP4Y\ngIcffphHH310UsdLL73UfPG3wM6Ojl3Nf7Zu3QrAiy++eMC/UI466ij279//xgKPP54TTjjhZ8fD\nncDWjhFPN6133tkxZq4dux249ZDHDla9s/nY5rjx8XFuvfXWKRw3G7/Xwz+2+cX8b4G3d4x4jr17\nb+Lmm2/mlFNOOeLjtm/fzqZNmzjhhBOA6fi34umuEW/+vR7J6/bi2F6/5gsvvPCGn/N+fa+9PvZI\nXnO6dPzcHTPVY1NKmdZipkuStwM/Bs4spTzS0f5fgNWllDO7xn+Un/9GkyRJU/exUspXp3LAIM9I\n7ABeB5Z0tS8Bnj/A+E3Ax4BngL09rUySpLnlGOCdNL9Lp2RgZyQAkjwMPFJKGW6fBxgDri+lfKGv\nxUmSpIGekQC4DvizJI/x88s/jwX+rJ9FSZKkxkAHiVLKbUmOB66hWdL4a+CcUsqL/a1MkiTBgC9t\nSJKkwea9NiRJUjWDhCRJqjYngkSSy5M8neT/JXk4yW/0u6a5LMlZSb6e5MdJ9if5cL9rmuuSfCbJ\n5iQvJxlP8rUk7+53XXNZksuSPJFkV/t4MMk/63dd80WST7f/vlzX71rmsiSfb9/nzsf3p3KOWR8k\nOm7s9Xng12nuELqp3aSp3ngbzcbXTwFuspkZZwFfBM4A1gBvBb6V5Bf6WtXc9iPgKprP7V4JfAe4\nI8nyQx6lI9b+MXgpzb/n6r3v0lzQsLR9/JOpHDzrN1se5LMmfkTzWRPe2KvHkuwHzi+lfL3ftcwn\nbVB+geZTXu/vdz3zRZKXgN8vpfz3ftcyVyX5ReAx4JPA54DHSym/19+q5q4knwc+UkqpvUnO7J6R\n6Lix1z0TbaVJRt7YS3PdcTSzQT/pdyHzQZKjklxI8zk2D/W7njnuBuAbpZTv9LuQeeSX26Xq/5vk\nliT/aCoHD/TnSByGqd7YS5r12lm3DcD9pZQprWVqapK8hyY4HAPsBn67lPKD/lY1d7Vh7b3A6f2u\nZR55GPhd4EmaO9itBf53kveUUvYczglme5CQ5qMvA78KvL/fhcwDPwBOAxYD/xK4Oclqw8T0S/IO\nmoC8ppTy037XM1+UUjrvrfHdJJuBbcC/Ag5rCW+2B4mp3thLmtWSfAn4IHBWKeW5ftcz15VSXgN+\n2D59PMkqYJhm/V7TayVwArClnXWDZsZ5dZIrgIVltm/qmwVKKbuS/C1w6uEeM6v3SLSp9THg7Im2\n9gfwbODBftUl9UIbIj4C/FYpZazf9cxTRwEL+13EHPVt4NdoljZOax+PArcApxkiZka72fVU4LD/\nUJntMxLgjb1mXJK30fygTfzV8K4kpwE/KaX8qH+VzV1JvgwMAR8G9iSZmIXbVUrZ27/K5q4kfwj8\nL5o7Dv894GPAbwIf6Gddc1W7Hj9pz0+SPcBLpZSt/alq7kvyBeAbNMsZ/xD4T8BPgdHDPcesDxLe\n2KsvTgf+kuaqgULzOR4Afw5c0q+i5rjLaN7rv+pqvxi4ecarmR9OpPmZfjuwC/gb4ANeTTCjnIXo\nvXcAXwV+CXgRuB94XynlpcM9waz/HAlJktQ/s3qPhCRJ6i+DhCRJqmaQkCRJ1QwSkiSpmkFCkiRV\nM0hIkqRqBglJklTNICFJkqoZJCRJUjWDhCRJqmaQkCRJ1f4/ZjwtUQlcm98AAAAASUVORK5CYII=\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x7f7dc5cc6dd8>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"plt.hist(qalpha.sample(1000).eval(),bins=30)\n", | |
"plt.show()" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"### The automatic relevance determination in higher dimensions\n", | |
"\n", | |
"The ARD might seem like an overkill but it comes in handy in higher dimensions, where the dimensionality of the latent space is not a prior known. Let us generate a higher dimensional data set and see how ARD determines the latent dimensionality." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 306, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"[[ 1. 0. 0. ]\n", | |
" [-1. 0.5 0. ]\n", | |
" [ 0. -0.5 0.33333333]\n", | |
" [ 0. 0. -0.33333333]\n", | |
" [ 0. 0. 0. ]\n", | |
" [ 0. 0. 0. ]\n", | |
" [ 0. 0. 0. ]\n", | |
" [ 0. 0. 0. ]\n", | |
" [ 0. 0. 0. ]\n", | |
" [ 0. 0. 0. ]]\n" | |
] | |
} | |
], | |
"source": [ | |
"# DATA\n", | |
"\n", | |
"Dhigh = 10\n", | |
"Ktrue = 3\n", | |
"\n", | |
"x_high = build_toy_dataset(N, Dhigh, Ktrue, sigma = 0.1)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 263, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"Iteration 1 [ 0%]: Loss = 21631782.000\n", | |
"Iteration 1000 [ 10%]: Loss = 110226.578\n", | |
"Iteration 2000 [ 20%]: Loss = 48362.117\n", | |
"Iteration 3000 [ 30%]: Loss = 15400.440\n", | |
"Iteration 4000 [ 40%]: Loss = -4317.944\n", | |
"Iteration 5000 [ 50%]: Loss = -6210.043\n", | |
"Iteration 6000 [ 60%]: Loss = -9394.196\n", | |
"Iteration 7000 [ 70%]: Loss = -12650.920\n", | |
"Iteration 8000 [ 80%]: Loss = -10626.010\n", | |
"Iteration 9000 [ 90%]: Loss = -15246.326\n", | |
"Iteration 10000 [100%]: Loss = -12622.543\n", | |
"Inferred principal axes (columns):\n", | |
"[[ -9.47400033e-01 -2.27103228e-04 -4.84446093e-04 -2.61202746e-04\n", | |
" 1.26546517e-01 2.35039950e-03 2.36805320e-01 -9.86780578e-05\n", | |
" -5.83961082e-04 7.35060967e-05]\n", | |
" [ 1.08158708e+00 -3.62846738e-04 -3.73822346e-04 -5.52089594e-04\n", | |
" 1.14145666e-01 2.18318868e-03 1.36531740e-01 -2.96724211e-05\n", | |
" -6.28667010e-04 5.09225465e-05]\n", | |
" [ -1.45155460e-01 -1.46481441e-04 -5.70291886e-05 -1.91689269e-05\n", | |
" 3.93552752e-03 4.10213470e-05 -5.50909400e-01 -1.93324468e-05\n", | |
" 1.47016963e-05 -8.70729564e-05]\n", | |
" [ 1.18359150e-02 8.01008253e-04 7.46513135e-04 1.06196094e-03\n", | |
" -2.42707178e-01 -4.67475457e-03 1.77586958e-01 2.74501363e-04\n", | |
" 1.16129871e-03 -1.86616613e-04]\n", | |
" [ -3.85368650e-04 8.14004670e-05 1.65667116e-05 -1.17582975e-04\n", | |
" 8.21503345e-04 -7.31311084e-05 -1.80058042e-03 -3.74936963e-06\n", | |
" 9.45753272e-05 1.02860489e-04]\n", | |
" [ 1.37489231e-03 5.24255520e-05 6.44143583e-05 -1.05127924e-07\n", | |
" 1.65358768e-03 1.34771763e-04 1.69831183e-04 4.41989650e-05\n", | |
" 1.02313534e-04 -6.09083800e-05]\n", | |
" [ 2.75859667e-04 8.10626807e-05 1.41651879e-04 -1.63655443e-07\n", | |
" 1.23207434e-03 1.19314063e-04 -1.54425376e-04 9.74498835e-05\n", | |
" 3.76220414e-05 8.22164220e-05]\n", | |
" [ 6.77114760e-04 -2.97158229e-04 -1.73837499e-04 9.41494545e-06\n", | |
" 3.64849082e-04 3.80107667e-05 -4.76350804e-04 -1.09225992e-04\n", | |
" 8.56654078e-05 1.22045458e-04]\n", | |
" [ 9.57225711e-05 -5.07429941e-05 -5.67338429e-05 4.76397254e-05\n", | |
" 5.55574188e-05 4.47914863e-05 -3.23144428e-04 -2.13330699e-04\n", | |
" -6.35642864e-05 -2.19060839e-05]\n", | |
" [ -1.99448108e-03 1.52135122e-04 -1.21356839e-04 9.68520399e-05\n", | |
" -8.27554089e-04 -1.48708088e-04 2.75092345e-04 1.65813268e-04\n", | |
" -8.07100423e-06 2.34402047e-04]]\n", | |
"[[ 6.85583509e-05 4.11421875e-04 3.12137679e-04 3.49760638e-04\n", | |
" 4.79560949e-05 1.71191350e-05 1.00877820e-04 2.09858525e-04\n", | |
" 1.15960975e-04 1.33785989e-05]\n", | |
" [ 7.29684543e-04 3.60367674e-04 4.51261294e-05 7.77532914e-05\n", | |
" 4.77808098e-05 1.23217207e-04 8.40232606e-05 1.54905778e-04\n", | |
" 1.20147910e-04 1.77172624e-04]\n", | |
" [ 1.52203691e-04 4.09944681e-04 3.39910803e-05 7.57988846e-06\n", | |
" 1.03272314e-05 2.68745262e-05 5.14794265e-05 2.85498281e-05\n", | |
" 7.49161918e-05 6.26635374e-05]\n", | |
" [ 2.45623203e-04 2.40652851e-04 2.01488765e-05 1.13515227e-04\n", | |
" 1.93556152e-05 1.03209575e-04 6.33113959e-04 1.91680938e-05\n", | |
" 1.05856401e-04 7.95219239e-05]\n", | |
" [ 9.20693681e-04 2.26508710e-05 2.68376516e-05 2.48127180e-04\n", | |
" 1.17369418e-05 4.66144593e-05 1.65109930e-04 2.76065897e-04\n", | |
" 6.33168165e-05 4.61864460e-04]\n", | |
" [ 7.82688367e-05 5.60193694e-05 4.61548298e-05 1.20106568e-04\n", | |
" 1.18799791e-04 1.41630308e-05 4.43231227e-04 2.33843733e-04\n", | |
" 8.77666753e-05 1.02534505e-04]\n", | |
" [ 6.41343795e-05 1.98620532e-04 3.50299117e-04 1.38945732e-04\n", | |
" 1.45300774e-05 3.10315256e-04 1.06754160e-04 5.88275143e-04\n", | |
" 2.74684484e-04 5.60175977e-05]\n", | |
" [ 1.89547864e-04 1.01341156e-03 3.92760521e-05 5.45676194e-05\n", | |
" 1.12662303e-04 8.06320240e-05 4.68994331e-05 5.06380806e-04\n", | |
" 1.22814468e-04 1.51032174e-04]\n", | |
" [ 1.24489816e-04 1.74949877e-04 3.13361270e-05 4.24618993e-05\n", | |
" 5.57363455e-05 3.08436342e-04 2.76857376e-04 3.48645495e-04\n", | |
" 5.82599314e-04 2.97959814e-05]\n", | |
" [ 5.84719419e-05 6.30939612e-04 2.50513578e-04 7.79430266e-05\n", | |
" 1.99316870e-04 9.12206378e-05 1.40835864e-05 6.03439112e-04\n", | |
" 1.10315059e-05 3.45541339e-04]]\n", | |
"Inferred center:\n", | |
"[ 4.65760054e-03 9.99053574e+00 4.17116145e-03 -2.13712352e-04\n", | |
" -1.45088031e-03 1.57464109e-03 -8.83906905e-04 -4.91537678e-04\n", | |
" 2.11652849e-04 6.69048110e-04]\n", | |
"[ 6.35485267e-05 6.47690695e-06 1.71059582e-04 3.06870759e-04\n", | |
" 1.83340569e-04 1.44911719e-05 1.11422751e-05 1.05987543e-04\n", | |
" 1.49283282e-04 7.02186517e-05]\n" | |
] | |
} | |
], | |
"source": [ | |
"# MODEL\n", | |
"\n", | |
"D=Dhigh\n", | |
"K=D\n", | |
"\n", | |
"ds = tf.contrib.distributions\n", | |
"\n", | |
"sigma = ed.models.Gamma(1.0,1.0)\n", | |
"\n", | |
"alpha = ed.models.Gamma(tf.ones([K]),tf.ones([K]))\n", | |
"w = Normal(mu=tf.zeros([D, K]), sigma=tf.reshape(tf.tile(alpha,[D]),[D,K]))\n", | |
"z = Normal(mu=tf.zeros([K, N]), sigma=tf.ones([K, N]))\n", | |
"mu= Normal(mu=tf.zeros([D]), sigma=tf.ones([D]))\n", | |
"x = Normal(mu=tf.matmul(w, z)+\n", | |
" tf.transpose(tf.reshape(tf.tile(mu,[N]),[N,D])), sigma=sigma*tf.ones([D, N]))\n", | |
"\n", | |
"# INFERENCE\n", | |
"qalpha = ed.models.TransformedDistribution(\n", | |
" distribution=ed.models.NormalWithSoftplusSigma(mu=tf.Variable(tf.random_normal([K])),\n", | |
" sigma=tf.Variable(tf.random_normal([K]))),\n", | |
" bijector=ds.bijector.Exp(),\n", | |
" name=\"qalpha\")\n", | |
"\n", | |
"qw = Normal(mu=tf.Variable(tf.random_normal([D, K])),\n", | |
" sigma=tf.nn.softplus(tf.Variable(tf.random_normal([D, K]))))\n", | |
"qz = Normal(mu=tf.Variable(tf.random_normal([K, N])),\n", | |
" sigma=tf.nn.softplus(tf.Variable(tf.random_normal([K, N]))))\n", | |
"\n", | |
"# initial conditions for qmu, improves convergence\n", | |
"data_mean = np.mean(x_high,axis=1).astype(np.float32,copy=False)\n", | |
"\n", | |
"qmu= Normal(mu=tf.Variable(data_mean+tf.random_normal([D])),\n", | |
" sigma=tf.nn.softplus(tf.Variable(tf.random_normal([D]))))\n", | |
"\n", | |
"qsigma = ed.models.TransformedDistribution(\n", | |
" distribution=ed.models.NormalWithSoftplusSigma(mu=tf.Variable(0.0),\n", | |
" sigma=tf.Variable(1.0)),\n", | |
" bijector=ds.bijector.Exp(),\n", | |
" name=\"qsigma\")\n", | |
"\n", | |
"inference = ed.KLqp({alpha: qalpha, w: qw, z: qz, mu: qmu, sigma: qsigma}, data={x: x_high})\n", | |
"inference.run(n_iter=10000, n_samples=10)\n", | |
"\n", | |
"print(\"Inferred principal axes (columns):\")\n", | |
"print(qw.mean().eval())\n", | |
"print(qw.variance().eval())\n", | |
"print(\"Inferred center:\")\n", | |
"print(qmu.mean().eval())\n", | |
"print(qmu.variance().eval())" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 264, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"def hinton(matrix, max_weight=None, ax=None):\n", | |
" \"\"\"Draw Hinton diagram for visualizing a weight matrix.\"\"\"\n", | |
" ax = ax if ax is not None else plt.gca()\n", | |
"\n", | |
" if not max_weight:\n", | |
" max_weight = 2 ** np.ceil(np.log(np.abs(matrix).max()) / np.log(2))\n", | |
"\n", | |
" ax.patch.set_facecolor('gray')\n", | |
" ax.set_aspect('equal', 'box')\n", | |
" ax.xaxis.set_major_locator(plt.NullLocator())\n", | |
" ax.yaxis.set_major_locator(plt.NullLocator())\n", | |
"\n", | |
" for (x, y), w in np.ndenumerate(matrix):\n", | |
" color = 'white' if w > 0 else 'black'\n", | |
" size = np.sqrt(np.abs(w) / max_weight)\n", | |
" rect = plt.Rectangle([x - size / 2, y - size / 2], size, size,\n", | |
" facecolor=color, edgecolor=color)\n", | |
" ax.add_patch(rect)\n", | |
"\n", | |
" ax.autoscale_view()\n", | |
" ax.invert_yaxis()" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 266, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAUkAAAFKCAYAAACQHq0GAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nap0mAAAAAElFTkSuQmCC\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x7f76f6f939e8>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"hinton(qw.mean().eval())\n", | |
"plt.show()" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 284, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAgUAAAFkCAYAAACw3EhvAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQ4EkSar6/7VOmrnLXpt3AAAAAElFTkSuQmCC\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x7f76e7172048>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"alphas=tf.exp(qalpha.distribution.mean()).eval()\n", | |
"alphas.sort()\n", | |
"plt.plot(range(alphas.size),alphas)\n", | |
"plt.show()" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 268, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAhkAAAFkCAYAAACNTikJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nw5ZMvD8mxRcAAAAASUVORK5CYII=\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x7f76e8a3ad30>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"plt.hist(qalpha.sample(1000).eval(),bins=20)\n", | |
"plt.xlim(0,2)\n", | |
"plt.show()" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 285, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAhAAAAFkCAYAAABxWwLDAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nZoCQJEnVDBCSJKmaAUKSJFX7/8lnvzdSJ4wAAAAAAElFTkSuQmCC\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x7f76e6e4da20>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"plt.hist(qsigma.sample(1000).eval(),bins=20)\n", | |
"plt.xlim(0,2)\n", | |
"plt.show()" | |
] | |
} | |
], | |
"metadata": { | |
"anaconda-cloud": {}, | |
"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": "3.5.3" | |
} | |
}, | |
"nbformat": 4, | |
"nbformat_minor": 2 | |
} |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
Very nice notebook on using Edward for PPCA.
However, the statements about original working version of PPCA is not very true.
Ref:
[1]PPCA original paper: https://www.microsoft.com/en-us/research/publication/probabilistic-principal-component-analysis/