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Last active June 28, 2019 00:29
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
"import seaborn as sns; sns.set()\n",
"\n",
"from jax import grad, jit, lax, random\n",
"from jax.config import config; config.update('jax_platform_name', 'cpu')\n",
"from jax.experimental import optimizers\n",
"import jax.numpy as np\n",
"from jax.scipy.special import logsumexp\n",
"from jax.tree_util import tree_map\n",
"\n",
"from numpyro.contrib.autoguide import AutoDiagonalNormal, AutoIAFNormal, init_to_feasible\n",
"import numpyro.distributions as dist\n",
"from numpyro.distributions import constraints\n",
"from numpyro.handlers import sample, param\n",
"from numpyro.infer_util import log_density\n",
"from numpyro.mcmc import mcmc\n",
"from numpyro.svi import elbo, svi\n",
"from numpyro.util import control_flow_prims_disabled, fori_loop, fori_collect"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"def dual_moon_pe(x):\n",
" term1 = 0.5 * ((np.linalg.norm(x, axis=-1) - 2) / 0.4) ** 2\n",
" term2 = -0.5 * ((x[..., :1] + np.array([-2., 2.])) / 0.6) ** 2\n",
" return term1 - logsumexp(term2, axis=-1)\n",
"\n",
"\n",
"def dual_moon_model():\n",
" x = sample('x', dist.Uniform(-10000 * np.ones(2), 10000 * np.ones(2)))\n",
" pe = dual_moon_pe(x)\n",
" sample('log_density', dist.Delta(log_density=-pe), obs=0.)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"opt_init, opt_update, get_params = optimizers.adam(0.001)\n",
"rng_guide, rng_init, rng_train = random.split(random.PRNGKey(1), 3)\n",
"guide = AutoIAFNormal(rng_guide, dual_moon_model, get_params, hiddens=[10, 10], num_flows=8)\n",
"svi_init, svi_update, _ = svi(dual_moon_model, guide, elbo, opt_init, opt_update, get_params)\n",
"opt_state, _ = svi_init(rng_init)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"def body_fn(val):\n",
" i, loss, opt_state_, rng_ = val\n",
" loss, opt_state_, rng_ = svi_update(i, rng_, opt_state_)\n",
" return i + 1, loss, opt_state_, rng_\n",
"\n",
"losses, opt_states = fori_collect(0, 100000, jit(body_fn), (0, 0., opt_state, rng_train),\n",
" transform=lambda x: (x[1], x[2]), progbar=False)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"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": [
"plt.plot(losses[-1000:]);"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"last_state = tree_map(lambda x: x[-1], opt_states)\n",
"samples = guide.sample_posterior(random.PRNGKey(0), last_state, sample_shape=(1000,))"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"x1 = np.linspace(-3, 3, 100)\n",
"x2 = np.linspace(-3, 3, 100)\n",
"X1, X2 = np.meshgrid(x1, x2)\n",
"P = np.clip(np.exp(-dual_moon_pe(np.stack([X1, X2], axis=-1))), a_min=0.)\n",
"\n",
"plt.figure(figsize=(8, 8))\n",
"plt.contourf(X1, X2, P, cmap='OrRd')\n",
"sns.kdeplot(samples['x'][:, 0], samples['x'][:, 1])\n",
"plt.xlim([-3, 3])\n",
"plt.ylim([-3, 3])\n",
"plt.gca().set_aspect('equal');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Mixture of Gaussians"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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/ZfjjOVKmQiFT8kKgs7s/5xtuvn7Ly1xzy8uu37eeCXizJlDoDAYCPPz8Vjq77QlbIXuIQUJuKXkh8O07VvHtO1flOhmueeqV3ZaupBNMREvUb8Sbm5t5+pXd/OnZzblOSslQqgOOQqPkhUBvgW+2sRQAwOOrd8b8zueG6fP5MqZaiYQ6MJD6eE3HYeegTPP4MwoFRskLgULD6WD91U0HY367WYRry/FpY15gZ3NvMBjknsffYevew47Clg5ZKGRECJQYbkatz7y6x/uEZJnIuomVOqy7d5BVGw7wq6XrspUs1xSx5i5ryIJ+CFvHSyqlbgY+CUwH5mqtN4Sv7wR6wv8Avqu1fiZ873TgLqAa2Al8TmsdOywVHJNutS3Veu+PuH22kX/HZVSqhVrgyFcLYXcm8ChwFpDMzeOntNYnhf9FBIAfeBD4mtZ6NvASsNiLBAvpkevRz76mztxEHBUC3udfOpMCRT4cYFMIaK1XaK2d6ATmAz1a6xXh30uAS5wmTvCedIyDvNhk8+iKHa7jT4eIOkjaff6Q6wmU1IUQttRBKfijUsoHrAC+r7U+BEzFMGvQWjcrpfxKqTFa61a7AdfX17hOVENDbUafzwR20jByf3q7dkfWVZvGU1VVYfludfWwtMtp2DDzKldZVU55eey4JFV8dtMzurkLgIqKMtN3joT3EPh8PlvhloV1TKNHj8hq/WloqKU/LDLLyvx5UXeT4U+RtsrKUF0YObLKs+9sK13+UB0bM2YEY0ZWeRau12Tru6YrBBZprfcopSqBW4DbgM+ln6wQLS2dBFw4eWpoqKWpqcPRO06fzwR20tDRnt7Gtra2IzQ1DUt6ryfFruXu7r60y6nX4jzk3t6BBBNOq/icfOf29u5oHGbvdIXzHwwGbYUbcUDW2nqEEeXm85jNew7R0zfACbPG2kqrFZE8t7aGhNrgYCAv6m4yAinS1hf24tne3uPZd7ZDRCXY3NzJYG9+bh50m2e/3+d48JyWdVBERaS17gXuAM4I39oNTIs8p5QaCwSczAJKhY6uvqzGl/MpeI4S4LOxJuA0ZUNmp9ZvLv7jG9yytPBPABOKE9dCQCk1QilVF/7bB3wGiNjWrQWqlVJnhn9fDSxNJ6HFyjdvW5nV+CzPE8hDu0OvhMaQiahVXM7CjH/81U2NrN/e4iyQEqZUByT5hl0T0VuBTwATgGeVUi3ARcAjSqkyoAx4B/g3AK11QCl1OXCXUqqKsImo98kvfJz6NE+32nq/X9YZbjpaL2STnVF7up3Cksc2AnDvdeemFY4dCqH7kj62MLAlBLTW1wLXJrl1ssU7q4C5LtMlZArLhmnd3XrRqB13tB5Jgah1kIczAeMu5Kdf2e0uYS6JlOPBtm46u/upqbZe1M9Hcj3ztPSjVULIjmEHdPX0s/yNvQU9jcx12q1iT9YneOVr3p+BNQHj8w8/v9VxmrziT/8Qp3iuKNxm7ClemIiWDL9/WvP6uweZOq6Wo4+qy0ka0h08FdqJel7LLCt1WK4FpBOMSS1UJ4i5Lu7C+dqZRWYCDugMW/L0DxRmo4Pcd3Q5b/iWawLOwho6Yjj7mSqmDizbaqGopVh2o81bRAiUGDnvhHPc9LzMf65ysr/5SHRAUgzkqk6+tbU554OifEDUQS4o5GqTcxNRy0WBxAR41UYjarBUrqTdkO1+5If3vJLdCB3QHbMZ0LpgcrUwHIn2oWe3UFlRxlknTspNQvIEmQk4IB/8z6RtIprzmUCK+wkPeJPgv760PRy+9+ogYYi/vrzd9rP5MAg/1FH4Z2WkiwiBkiP9lhcMBl2b11nOREhMnVcdxdZ9h1OG53QmkAd9WN4xMOi8VLyYEazVTVxzy0uO1+usHBqWCiIECox024sXnepdyzby5V88n5X4ve5ovTQRHQrT5Yse4UuzF/3Gb1bwk/te9SYxJoVx7a9f5sYH1jp5xRF/Xr6FIz0DHOr0bq0kGAzyt5U7OGRxst7AYK63X6aPCAE3FPAQ0IsNMvFHVmYUj8t698FOU0HgdCaQS+sgI+kubrYf6WN3Y2bPeejs7o/OxiJ4uSaQCUG8q7GDv768g7uXbUx6f+/BTv71phdYW+BnZYkQcECudzh6Qa5HrV5ZY7R19HLnI28xGHA+Elurm5Jed52yAh4UZJKW9l7L75OzumizIUdcupjtw9hxIOTWfd3WZm/SlSNECLgg1yO/dEilk88U/3htD1csXs6AY19JyZ//w9Pv8uSqnbyzs81xWlpN3HE77ZQiqoeOrty6I05XHZRJevoKd09NqSBCwAGZbmr7mjr53l2rac+gDXg6o690+prIAlyvw07BLL1OHe8ZqapMbhkdEZB2Qj5s0BPf+oi4iY6wv/lIzG+fjVbj5aAqf8Vh/iJCwA0Zmghc/7tXaWzrZt2WzE0vLdcEMjSi7B8YjLMf9y56NymuGlbm4q1Y+gcKf0EwE2zeezj1Q/EU7sS6KBAh4ARDL9Xa3sOuA5k50an5cA9XLF7O29u8902fCz1s82H3p6GZpjeNjAyrSC4EnEwupN+yi5RUviNCwAVB4D/vWMVPf/9aRsLfFraiWLXhPc/DzvV6Rsq+O+EBE0ueyB8upgKRs4FTx22OdG32sCNYs12WdquMHVUW4EkG9jUfyaga2AoRAg4oBn1jtmYCT6zeSWP4HNyY+D1u8rYbqjENpiaijgJxHG+myOd6acsazJOizN73+O6SVSxb6e0ms+vveYUf5cgdiAiBPMaLfubCBVPjwsy8ddCRnn4eeXE7v3zozYR7Xm0WS6dszEan+dOtFw/Nh3vo6bNeD/J0YJAFidh0qIdHXzYIAY/ibM+RlZk4kLPJ7sYONuxoBTI/CLRaIL3niXcchTVz0siY39kYwEaSn6zxB5yaiKZ63EUD9GKzmAgMe/zsD68zbUJtrpORWQq8MshMwCY/uc+o/8/OV08WS1+/U6uU2F7SS9e5ZmFZHepu7cU0O4oNsyQ4Uwd5kpSSIJUBhacDkyx+l/uefDd7kWUQEQIesOSxDVyxeLln4XnZFcb3q+l4Ef37a3tifqdU1SR5wKnbimRC45EXt7FpV2iTmJsKbCoEHPQgIgOyQyAQpKsntZrEosol4rCBZWI2Ght+bmtTUQuBQCDIYyt20NWT2kbdisMWDqQgg750PKgc8fUzGzOBSGearMN36uUhWQxPrN419MPF7CHVwnBv32DOG6YZqepiIWJV1Pc/o7n0B0/aViN6+dWytRE71wfeF7UQWLu5icdW7Ej7EPA34zZvmX2zl97azxWLl6e/kSiu9vX1D/LAM5ojNkZEiUHFqYMsH04dnrHCplKrJOtIHS8CZqB92FlsfnLNLpOnIs/mpuF+7sdP5yTeXLFyfchM2nZH6eK7pOMaPRSA+1fBnfttLylqITAQ7oz70j0T2OaIIHJwiZvOOhmRqrFi/Xs8/+Y+/rzchTCLS3u6fVdP71BZmguBYMx94yAu1YjOafLcDNZSzWAgPadgjzo4WEWwNzCwK3Td1O+Hnt3i2jW6FwzmWAiktA5SSt0MfBKYDszVWm8IX58N/AGoB1qAz2utt6S6V4gkqFRSPG+siK+9e5CGUVVMnzDS/IVU8YXDW/G29eaxn315AdfH2RrHh/Xc2j1ccOoU22mJp6t3SMCZd6YhIqOroKHjt/RaYRGWl5iO+hxEZiXMlq3cyccWzXSYqhLGRrnbXctyU1+eXbs39G4w6M44IU21kRtPuF5iZybwKHAWED8/XgLcrrWeDdwO3GXzXtZwtNDnZAhhHNlavPfw8q3c+egG/uv3r9sP2yQeO0weOyLhWnydbjrk3oUDELO+kkqtEgyGfNUby8jad5FFYGavuDIRdXY93WczTj7vFrOBnaJMOYO0UEHGY+bE0LQ+pwqw2NVBWusVWusYsxCl1DhgHvBQ+NJDwDylVIPVPe+S7Qw7bcTqM1iNDpJVzsjjT7+620bMySJMnSbbQXm8umU0UTVtcIbr9z65KabDzPXJYqE0pFYHpSLXi3kx5FFS0qH5UHeC7/5I9fVqDaazu9/UvXWu1nmMM4FdBzp48O86q2lxuyYwBdintR4ECP+/P3zd6l7+EtFfB4Lc8/g77Dlo76SlTHysiCsEL8J2IgLsPNtrWF95c3Mzr7+baBlllIs9fYOxMwGLEV1ndz8H27pjrmWiLdiaCaSIN59kQKHR2d1PZ3fiutl3lqzm10vfSvqOXXVQquc6LPzzxH9Tu4J+b9OR1A9ZYHSLvn57C8vf2JfV2UFe7xiur69x/W5DQy21tSFb8sqqChoarHctjh1bQ1mZn70HO1i14QA7D3Rw1/c+CEBtbVXMsyNHDv0ePWYojf6wY7IxY0ZQX1edkB67VIb93VdWlofyUVNp671kcdSNGm7rOYCWjtTmh9XVw6J///bx0O7lv/33xTHP+IcNVavKYeWMMqTBqmpv2N6acK2+PrEsjYwaNdxR2QLU1FQlfaexfSj/5RVlluEe7rE2Nkj2rtN02qWyqtyTsDOVvvg4rvjWYwCceeIkAGpqKqNxv7v7UFw6fECQMWNGUGfRDiJOAUePtq4PPRbq9427D/HB06ZFf7eE3ThUlPstw9zV2MGOpiOcdvwE88At6DZ0+NXDQ+3L78vO9wD3QmAPMFkpVaa1HlRKlQGTwtd9Fvcc0dLS6djNAIQKr6mpg/bwCVK9PQM0NVnvWjzY1EF5mZ+2tpDTs8HBQPSdzo5YPfrhw0Oj1YMHh8KNjByamzsJxLlMSBW/kb7wu729oXR32LQNTxZH++HuhGsbtxxk3KjEjvUtG+cYNLUkjnqM8X71f16MWZvo7x+gtXXoHaffM1lZGjl0qCsa/8r173Hi0WOpqa6wDLO9vTtpWUW+PcBA/6DlN2tptR79JXvXSR1wQqSepEum0mcWR2/4jIn2jp6Y60nLrrmTvm7zUXxkNN3aeoThZeZz2laL7/brP6/jxBljor/bwg4Q+weG+gKz2fmfntrEjIbENTk7NDUPaR06w23d7/e5+h5+v8/x4NmVOkhrfRBYB1wWvnQZ8KbWusnqnpu4soXlzM9i1+0r7xxwFpYNvDxHINmSwHVLVrNhewu3/t/bjlVOfSbnrUbo7Rtk+/52Q/w++wvDLogE917LEX73xKakh4Jv2Xso9h2zsBzFK/qgeJyWSYz2LcW7VoOHrp5+BgYD4XCs41y72X43lGyNyCz8bfvb2brPxYE6xKqDIvnM5pGhKYWAUupWpdRe4CjgWaVUpJVdDVyjlNoMXBP+jY17eYp57Ul0Vzz07AN/3zx0NXy5fzBxzrl5z6GEaylT5KKf+eczpsf8NqtKv1r6Fuu2Nkc75YEkaU5Gn4uNcLELwx4LgfD/kQ16hzr7eHLNLn77tyFh8HDc/gozQeTIgZzIgATclsmTq3dFz2uOJ9XC8IbtLXz9lpej5zyn+oaRvTx2SBaUlfHAjQ+std2OjAxGO/5Q3fRn+czolOogrfW1wLVJrr8LLDB5x/ReLrBTplZ1R++JPcw81SapH/3uVe7+9gdi7i3+4xvce925qROSJhcumMaylTuHLqTIfCQvqUb4Eew+F2HTrjY+snBIz+rYOijlAm3sAz4f/N8L2wC46qI5jsK0sy7c1tFLWZkvv6yD8gSnu8EjNbP5cA93JZnBGTEr73d2tSW97gWRurXrQAeNrV2MHzM8ZX3s6OpndK29NbwI0dE/PoJB8Gd5C29R7xh2afqf8Hvl+liVj/lIMvS/m9GAFY4GBj7LnwlE/eXY9E7aZeOs4HiMvn4cO5BL0bG46YqTjRYb27psbWr71u0r+catK2zNGgKBIP/7XOb3SK7VTXkhlNJJQir/XmbaoHg1kVfFsGFHS8yxqN+7e42n4RuJ1KXITCCbqiDIc+sgr7BVpEEHz5oFYVFDKspzI2/N6lP85pp4+2wzXnmn0XEaWtuHGpPjRuRwJmCnM4x/JOIBds700baTZWd9+7ePv+OqvNzw4pv7OGfeUQAsfX4r77V0ce2nTshK3BHS2QNi/I4H27oYNzpkUeZLct8qTq8OqPmfPyc3VU0l/N2oO43qoGAO1EFFPRNwQnzlibdXN5JqJpCMYS6EQHSE4OAdp9UnkhezXZTxdCeRVKIsAAAeR0lEQVSZCaTybJlR31xRYRb6f58Nm22zhqr32F/YS9XY9x7szJoAAGJ06k+9sjst30dOCASDhkVZZx96h8GAwNimDh5KbHtmC8PxbTHdkfoL6/ZZ3s/EfGsoDz4Cgex5L41Q1EIg1ajAWNmSVZ5kHZ7Zs6niG1ZRZpkWr3BagaJrAjad7CWbMfzHbSst30lHVbFl7yG27h3qnOMbqTt1UPLrxo5mx3vtSTc0pQojwo/ufdVFytyT7Y4jwt3LNvKvN70AOP8WLYYZYkwnbwwonC/TI0E91s/c/7S2vJ8Jq7DIhuFcLQwXrRC4/xk9dPKPSZmueHt/wjXjJzbV7ZvUA6tTv1zNBML/O9PDx2Y2lX4xUqnbbGwUA3d+TtIRAvc8vokbH1wb/f1HgzUWwJqNiSa6RrbuO8w2w4gTzBtyfDr/8uI203DFRDSE8SwNO2ViVs+cGgBEiBcOmf4sqdPpPMxIvYuog2Qm4BEvvGk9rYsnmQMqs+9p1qkZ7X3jF7rK01gTeOTFzLkmDgShsbWLJY9ZW2ekQyYb5uqNjfT2DyacehbhxgfWJlyzu19twOJBNye0ZVJwZHsxMRl2snfdXauTXg+kaHem6qCEheHMSoFUwbsZ8ETy0NcfYP32lqjngWxRtELAOYkf77ZH1id/0sZ3fui52BFrWZY+rHN1UDDGCiIT2J1luOWvL21ndYoZgRG7i4dWHYqbxn4kzRPudh5oN72XexFgr12YHbhkel511I9W8vAS1gRSJyFNrGNIRwhAyMuvqIMyQOJmrxAxm5jC/9/75KboNbMdgHZGG/EzgWx/WLuE7JLzM212MVOXOV3TSXzQ/NaSRzfYDGSIa3/9sq3nOrv7k9Y9S5fkNj7hy2/vj1lfSUYwGGTl+vfosXDVYfG2i3dCxCwJJAnmoee2cNNDbybGmGgelFFSzQDduLmJFxyiDsoRke+wbZ/5aCvCqg2pR53xR1LGd7RHevpT7iJ2M7ONr0CpKlRoIcp5PMn4x+uO3UN5glny7zTpqLfZ3N5v1Z7d7Jy2y/97cG2CGuuJ1Tst30lWBu/sjHXId9+T78asryRj+/52fvfEJh54ZrPlc8mIHM7ihkGzwg5nbPOeQ2xKsjEs/jwWL0xErQZ5Kd1buFkTiHtJ1EGZwOMy1S5cQMTPBG55+C0W//ENr5JkitksKEIwCGUebVF86NnMb4xK1gbNBN3uxuQOuOIFtGlcBOnq6eer//0ib2/LjsklwHstIcdlxg4n5bpQkkK4+X/XOY67J2z9dcjhgfbBYJBHX97hOD7j+xG27D3EX14yX5SPeS+u0/diScBKpZMqeDdrEgkzgSwr90pis5gdMr2gFC/ddzWmPq/AzajGaQUKBoOeHG/3g9+uSTsMt2RqUTQQCNJ0qIfe/kFuWfo2C44fn5F4jLQb/N0HgkHKfD4e/Lu12SJ4N85JtTnLjHR3yRuji+ww/8RZs1K+l4mFYasgUi4Mu1EHxRWduI3IIsnWBDJF/AwvY3q/+HBTxNPdO8Av/pSoa3VKZPSaCzJVlMFg7HfKxuavb9y6Ivp3pENZ/kZqSzev6pPbYNpMHMDZJZk6aG9TZ8pNjE76/PhFabMyszz4PeWOYfvpiRA/E5CF4Qxgp0i7egZcLobZ493dh2LCt/Od29p72WvzhDMzUkXT3evMIVw+kqmZQDAYZMOOxINuskUuzh+PlGV8ZzYYCFiqSezuODcj2Qj+R79L3HB3xeLlMRsW49PU0zfI06/sJhAI0tjaxRsG19GPr9oZ8+xJR4/lrBMnJsTx8PNbE65FSKUKNiujl97ab6pSjJ89ZNvctySEgBlGdcv3717Dt+9YlfDMN36zIuGaW7YYLDPsqG32NR9xvPM0IdRU0RSIYZCluiFDeQgGhzyS5gLTxdIk7Gs6wp2PbrCl2ntx3T6uWLw8qUdYM9fNV/3yBX73+KaE5yOYmX7axYlppfGIyPgOdNnKnTz8/FZWbzzA9+9ew21/GTLz7kiyAzxZh/takiNTI6TaT2OmDvr9U+9yy9K3k78TPxOQhWHvsStYk9lxtx9Jb5prxPitMyXsnY4iBj32eJopfvr710zvmeXYqls50hPqEKzOkk7XM2e6n9hJ/GveaeS1dw8mqOWSWUhFXI13dPWbO2Yz/B1xAGi1F6PfptsRM6x228djTHL8DvaIYDvSM5BSxTtj4sikqhc3ev0INzywlm/fYe1GJZ6dB2INGMRENCPky3B3qHJ5/aF/8fUzXb1ntSs2n7ByDOdm+hzZCPjHf5ibQqa7xpjutN7JTMCMZKPaSMcXCAYT8hhVBxmu/eC3r6SMJ5Mms/EYhWO88CkLHy2ZbI9IvBeBDy+clnSQl0z4jhxewYFWe+teLeGzqjftamPZytQWUyvefi/mt6wJZJj121u4YvFy9jZ1ZmN7YQzGNu21GdjxM+qTXk8Vj+UiWIGQyl12MvY2hWYAVjPvdC1N0m3Luyx2CJvGaXLdmJfI7vXBQDCJiWXEf8rQNTtuxp2M5NPl6Vd2D8UbJ3zKy0Jd2rIVQ51vfCcbwe/zJd0tn0wIjBsz3LYQAPj7q7u56aE3XZnNihDwgNuWmttHrw0fdZxq52SmydZ3ThVPoaiDIORnPlkDNd8Rbt6JR0a8Vu480h2IpzuSN9MhW5HU704wGFNuvnCeBwYCMYJy2/7DtNs8pjGeZOqgqmGZ8Zz74rohx4/xwiciBIypN3oBiCdZ+0i2rOK0uf5fGv6+RB3kAc+s2RXz21io0YUvsj4R4FBnb1QXnQ8OvwCed+hoL5dcd1fyvQhmRWnVB0fe6bVQYxSLp9BAIMiB1iG36ZHi6hsIxBzreMP9a6NrCE2HurnxgbXR+pqKu//2TsxvH3DHN8/mp1ecllbazYjo7eOFT3mZs3aVrB0m++6BYJAeB95809k3IQvDGWbIBC77Dfz+pzXfuTO5F8VckUsTSK8wVweZf+OOrn4WP7jWckaY7bI52ObBXoskWR4MBLn+nlcMv0Md1P7mI9GZcTztXSH/RWb37ZKp/izSyfbHdbZOd78nS1+yGdy2fe0Jgs4Ltu9PVPnJTCADbNrZFnOOJ4T1xRmWAyfMStTTRxassiXs82TCkVHM1EHJVEfGb7I5xyrBeF5Yl3i+hVPufyZxd3G8tUvEosZKTRIhvmSbk5z6lYxIjJka1fb0D9LbN0hre6x7i/XbWxyF48tCQ4zfTf/E6p08F/az9PP7E50CyppABjh4qJtXNoV2e/rJ3kzA8mNm6UMbO8gvffjYrMSZbZwsDH/0/dMzmpZ0iIxuv/AhFb1m5T46Gcm8j8aPbNNRVViZ1CYjU0Lg5ofW0ehg5mRWjtnoAOPNdh95cbulVZoIgQwRHTGEy3fPwU627s/sSDAdGVCZgUW1IlFxJ2JTHTRtQi1HT65j5IhhWUiUc9qP9DF+dDUjhw+l72dW7qNtYjYTsEP8YT1O17Iy1aHtbepMUAVZYeqGO4dTZaOfKCPOThJMn7QdyCmldgI94X8A39VaP6OUOh24C6gGdgKf01qbb8XLML64/182MRvLBr39gymtDeZMHxOz5d0L3GyCGV1bmZFDYWqqK5gxcSTrt7fwjU+f4MoSJoKpOsikj0i2UzZbNB3qZsveQ5yixiWcOz0wGKSi3B8zevZCbsfPBJzUg33NcfszHPaZmRzVemLenMOR0Z+fG3JPMW50NQfbQqo2p7OtdPFqJvAprfVJ4X/PKKX8wIPA17TWs4GXgMUexeWKyAgmE1Y5F5w6Jel1s/r15OpdKdORiWm0mx2w55+SPG9e8O+fOoG7v/0BTpg1Nq1wzPKVcD38M10/N+nw3SWruefxTdz31LsJ9wYGA5SV+T0/hc4LL7ERbv0/Z8I6k5YuTTbXJ6zI5V5J43eZa9jnM3V8TVbTkSl10HygR2sdcbyzBLgkQ3HZItLnei0DKoeVOXYx3Ns/mDIdXnVUxnjcDHq8OKTDDL/fF7XrTge7I6eIeigftGLJDhQaHAxQXubzfLEywd1yFksgk+uuv3si9cJ2KnJpBmys+xWGM8jPm3dUVtPhlRD4o1LqbaXUHUqpUcBUIGqsr7VuBvxKqTEexeeYyMg7XZO3BIIhHyTHTRsNwIULpg7dshihptrJ69TKwQ7p+ETxGi8b30abppyZzr0Tgeb3hcpg78FOmg9309bRy8BgkHK/P6UKZeo4ZyPFeHVQurt7//SPzXTZ3D+QDeubdLDTJGqqKzISt3HGV24QAl4MjJzgxaEyi7TWe5RSlcAtwG3AXz0Il/p676ZFtbWVNDTU0tLu8aHqPmhoqOWcU6eyaVcbF545k6fC29orhoWK97xTp/CcYYGtqqqCYR4s/J518mReMmz2amioTXhmzJgR0b+Hu1gQHTG80l3iUuD3+5KmN5OUl/tdx/kvFyj+lOJwl8oKP2NHVXHAxtkK5eVlvL61hTsfGVKvqGmjqa4sp6LSutMZU1dN0Odjj8nJafG8tD71cahOeHbtXqZMrOMT5xxt+VxDQy1VJouf+UBDQ23U15AVXqrTjPWvtmaobY2qq4r+PXr08IRnM0naQkBrvSf8f69S6g5gGfBrYFrkGaXUWCCgtXa0+6alpdOz0WtnZy9NTfYajV1mTBzJRxdOo6mpg/mzxnDnt87GZxhvRupXZZmfX169kO8sCW0U6+rqo9swkqofWRl1OmXFT750Kj+5b8ib5hf/ScUIgWT5a20dWtjrcLHA23kk/UXhKz9yHP2DAe5/eqgTDQSCnn+PVPT3B1zF+dH3T4v5XmYMBoIM2HSk1tjaFSMAAPSuNk6YVU9Ts7V6a+KYalrb7evD43fQe4E/mLosm5o6bM8YckFTU4ctI4HePu+EgLHMeg1WQD0GN9dHwkd7uqmrfr/P8eA5rXmHUmqEUqou/LcP+AywDlgLVCulIq4trwaWphNXugQCQc/1f9d/4RROnt0AhNRNlRVlMVO5k44ey5UfOY6Lz5zB2FHV0evL39jHIcNJTF/68HEJYSdTCbixtDAuQDtZGC4v81M3Yhine3Ck4sI5E5g5cWTa4aSLW134zIl1lp3Fnd88OxR+MH1jk/IyP6ccO87ymY+fNTPrKoN4BgNBm/XJXp0dXpmbk27tZKG+zrvZ8MtvD20INDrmM/ZNTl1fpEu6NWk88IJS6m1gAzAb+DetdQC4HLhTKbUFOBu4Ls240uLPy7dy35OxFhn1I71XdcSa9wU5Y+7EmEWfZBw/PXGp5KdXnJpwzSgDjmqwJ+2N1WmKhS45fnfzhDHV/OqaMxkzssrkjRDXfHJu6jQkqdOFtGfB57PWo0fyFwgG0z5rt6Orj4pyP+fNT744OLq2kvIyf3QNKlWazBhWkV7T//1T7/LlXzyf8rlIh1Y3Yphle/v+5fNtx734K6fH/F44x/lA5Sv/PAdIvTb1jU+f4GldNfZBRq+ktYa9IdkW8GnFprXerrU+WWt9gtZ6jtb601rr98L3Vmmt52qtj9Fan6+1zvwBrUm46avvj/69Yn3s3oDxY4YnPO900c2K4Sl0u1ZMbqhhvmqIvWho2dd99mTHYc6dWc/1Xzgl6b0Pnz4t5rdxQ5VVpYx3Mzy5YQTvmxEr1Hw+X9Z3QSbFZmO+97pzY377fL4ER2VXXzwn+nd5uZ+J9cO54sPHmW4Askt0d6lJWiMd0scXzbQMJ9nA45NnD70zoiozi53xDKso42dXnsbiqxdy9kmTTZ9z0s9Wxc0aLvvgbMeO6iIWfcYO/tZ/X8S82UNtrq5mGHNn1qct2M3Yuvcw82c38P3PzY8RZF6bCKei6HYMdxp0a6cdN476OvORbLLzdctTjNqdMHdmesZQ8eshsVPmUEX59DmzuPIjieqkuMeiNBjUUkaMI6LP/5OKjpQg+awkQk98GQaHZkOfOe+YIRcIvoTHUjJ/dkPqh8IkOys2nkicl5gsaJrN2Px+6I2bCRgFtN/n44arTmfB8eNNR412zf4iQjVgUkIRFYzf7+O2b5zF7f9xVtLnks1cKsqHjBGqU6hfxpnUE7tcdt4x0b8nN9RQWVHGwjkTOKphyFChdngFlZENcw6G29XDYtNe5vdZLt6eM89c+IyoGgqrprqCCYaB4VknTMLn8yXdwbtwzgQuev90xoRnNzMmulvEXXTiRI4+qo6K8jJmTQ6pTKcUyT6BnPGT+4bO5E21pjxl3IiY35ecc3S0r0q2AWze7AbGj07dOD57/mx+8Pn5aW9Mu+Sco5kzY0xU9TO6tpKzTpwEDE3nL1wwjTPmmneA8bpWsxG50YzwAydPjpmeTqwfKqePnzWTf/ngUAOfrxqYNqE2OpIJGuJoGFUVHf25KQvjCOx9cQI1Xh0yeexQwxlRVc5H3x87swGiwvJDBjNeIzdctYBfXZN4QpvP5+NDC6YyuraSb192Mp88eyZlfj/TxtcmNP454VnQmSfEfpNUB7NEBFP0rN64urv46oWhy4bOcnhVuWlnfuVHjuPskybFXGts7Yqma3RtomomMhusGzGMH33RXPAbqR9ZFR1VTx47gms+MZd7vnMO5ydpP/V1VfzXlQuiJpc/u3IBY8ODtPim+rWPD6kZz4sLK15Yl5f5LM9uaKirjqk/RoH81Y+9L+ZZY7ksCg8sIgJ1Yv3wmOc+ftZMfvKl0/j5lxdw/RdO5eqL5/DvnzrBNB3JMG6U/MHlp3DvdedmbZYWITerMRlk5qQ6WttD3ikiDeYXVy/ku0tiXTj/4PL5TBlXw0tvDamIpoyrYe3m0LunqHFccOoUnn51N8++HvL49/VPhCrmtv2HLW2HzfS5Vnz6nFksW7EzprMYP2Y437r0JLp7B6LnvH7xwmP54oX2HMFd/4VTEnT6xr74s+fPprWjh6fW7Kauxnp9ZO7Mek46up5zwg3oT89u4bhpo6kdPowff/FU9jUfYfXGRoLBIMdPH826rc001A0JzMTyim20d37zbLr7BugfCES/VVlYDTWsws9nz5/NyvXv8fiqXcyZPpr/uPSkqE76knOO5rxTjuKh57YA8JtvnMUaw3m4v7h6IYFgkPGjE9V/EOqwX3mnkdG1lVFXxOfMm8zzb4Qsr/yE6sZ/f+0MYEgA/fhLiR3ltZ88gd7+QV7d1Bg90erKjxwXGk2uT3gcgM+cG0r/w88PuREwdvYT64dTF1bPzT069e7qupphnDF3ImfMnchnz5/NP17bw9IXtnHstNG0H+ljBe8lFQLlZT7OPmkSHzhpMlWViSbMRx9Vl+B6+4y5E/jYopm8b8YYjp8+Jmm48Zw7bzLLVu6kalgZH1s0g9v/uoGxdVXccNUCdjd20trew3zVEFXLNTTU8tnzjuHn97+eoMO/4sPHUVFeFjNrPn76aN7Z2Rb9/cFTjqK+rooN20PGif9y/tAgpq6mku/+y8lRYTojbMBw2XnHMLYudsD3sysX8OJb+3ngGc3w8AyiproiWrdPOy712sQNVy2IHtc5cnh2O3szik4IfHD+UbwePlc1MtVrGFXNPd89h2UrdrBs5U5OP348sybXASH9b2/fIHubO5k1qY7HwsfSBQkyZmQVnzn3GM6dd1RM5Zs1qc5V2k49dlz0zNeqYWX09A1y6bmhEeCFC6Zx4YJpXLF4ecJ71ZXlTLa5EBxh3uyGaIW+8iPH0Ro2D42oanyEhFUgEOSM901k0tgRXPXR49lh4m3xPy45Meb3/3z9jJhZxtiwsLn4zBmceuw45s1uiBFAxgpf5vdx6blDDRFCO68jTvM+dNpURo4YxsL3TWBi/XA+vmgmfr+PCxdMY/22Vj521kz8Ph/jxwynsbWLebPHJsxw5qtxzN3YyAmz6pOqwL556Yms3nCAi8+cwbjRIX2+kcsvUJw37yiWPr+Vo4+y/70ryv1UlPs5/fgJ7HivnffPmcBx08cQDAaZOGY4qzYe4PILFHcv28hb20IbAi84bWq0XD6yMDQaP33OhKhr6ROPHktlRRk3XLUANauB9kOx+xB+9MVTeHNzM6NqK5k2vpZRNbHrOReePo1/WjAVv8/H1r2HqawoY97shqiQWnz1QpYu38qiEybFqE+v/dQJvLqpkTUbG5lYP5zrPjuP/31uC1Maalh04iTaOnqjwslqNhrPxWfO4J/PmIHf72O+Ghft7CfWl8fMOuP54eeH1rOu+ujxdPUORGc2RiHwn585me/cuYrmwz387MsLKC/zc+qx4yj7xFw6uvoSZqVq6tCscuakkdxw1YKY9cJZk0aybX87fr+Ps0+cBMEgi06MnWUZueXaMxkcDPKt21cydXwNP7j8FP7tf15kMBBkwpjhfGzRDB59eQc/v+p00zCyiS9PT0+aDuxwu0/gcM8gf1+9g48snB6V2BGaDnWb6sUBbnxgLVv3Hea6z85j9pRRjuO2YjAQoK8/QGVFGT5fchXJfU9uoq2jl29eepKjsBsaaqN2xf0DAcr8vqR+W/oHBvnKzS9S5vfx2++c4y4jLlm98QD1I6s8K9c/PreF517bw63/voia6gpeXLePyooyTp8zwZPwM01ndz9HevpNZygQOo1u5PBh0W9p/M7pEggETethhGAwyJqNjZxybEPMmkI2sZPnxrYuvhc+eS5+YT9devsG6e4bYFSK2XI8XT0DVJT7EsotGAwyGAhaGly4/c6GfQIzCDnuTEnRzQQAjp4yirqq5It/VgIAcH6YqAPK/H6qK62XYZLtGXCKlUlqpMHbNTH1koUed85f+9SJnHvSpOh03Mr6JB8xqhLMcNrxOMGOczefz8fC9+W/UB0/ejg3ffX9jM6A2bdxluqE+AFoBJ/Pl/W9AFYUpRBIh1NmN7B17+HoglWxUV7m5z8/cxJTx2fXZUMmqCgvs1QfCKWFlSWgYI4IgTjOP3UKi06clNKErpBJtjlNEITSpOhMRNPF5/MVtQAQBEEwIkJAEAShhBEhIAiCUMKIEBAEQShhRAgIgiCUMCIEBEEQShgRAoIgCCVMvtpCloG9HY1mpPNuoSJ5Lg0kz6WBmzwb3rG9xTlffQedCbyc60QIgiAUKIuAFXYezFchUAmcCrwHpD4JWhAEQYDQDGAi8BrQa+eFfBUCgiAIQhaQhWFBEIQSRoSAIAhCCSNCQBAEoYQRISAIglDCiBAQBEEoYUQICIIglDAiBARBEEqYfHUb4Qql1GzgD0A90AJ8Xmu9JbepSg+lVD3wADAL6AO2AF/RWjcppU4H7gKqgZ3A57TWB8Pvmd4rJJRSPwZ+AszVWm8o5jwrpaqAXwEfBHqA1Vrrf7Wq14Ve55VSHwV+BvjC/36qtf5LMeVZKXUz8ElgOuF6HL7uKo9e57/YZgJLgNu11rOB2wl1CIVOEPil1lpprecC24DFSik/8CDwtXB+XwIWA1jdKySUUvOA04Fd4d/FnudfEur8Z4e/9fXh61b1umDrvFLKR2iAc7nW+iTgcuAP4W9ZTHl+FDiLcD024DaPnua/aISAUmocMA94KHzpIWCeUqohd6lKH611q9b6BcOlNcA0YD7Qo7WO+AdZAlwS/tvqXkGglKokVMG/arhctHlWStUAnweu11oHAbTWjVb1ukjqfACoC/89ipCrmLEUUZ611iu01nuM19x+10zkv2iEADAF2Ke1HgQI/78/fL0oCI+QvgosA6ZiGFlorZsBv1JqTIp7hcJ/AQ9qrXcarhVznmcRmtr/WCn1ulLqBaXUmVjX64Ku82FhdwnwmFJqF6ER8+cp4jwbcJtHz/NfTEKgFPgN0AncluuEZBKl1ELgFOCOXKcli5QBM4E3tdanAN8F/gLU5DRVGUQpVQ58D7hYaz0NuAh4mCLOcz5STEJgDzBZKVUGEP5/Uvh6wRNeXDoGuFRrHQB2E1ILRe6PBQJa69YU9wqBs4HjgB1KqZ3AUcAzwNEUb553AwOEp/la61eAZqAb83pd6HX+JGCS1nolQPj/I4TWRYo1zxGs8uH2niuKRgiErUDWAZeFL11GaFTVlLtUeYNS6kZCOu+Paa0j7mHXAtVhlQHA1cBSG/fyHq31Yq31JK31dK31dGAv8E/ATRRvnpuB54HzIWoBMg7YjEm9LoI6vxc4SimlAJRSxwHjCVnAFWueAev+yu09t2kpKlfSSqljCZlOjQbaCJlO6dymKj2UUnOADYQ6g+7w5R1a648rpd5PyDKgiiGTyMbwe6b3Co3wbOCjYRPRos2zUmomcC8h079+4Ada66es6nWh13ml1GeB6wgtEAP8WGv9aDHlWSl1K/AJYAKh2V2L1nqO2zx6nf+iEgKCIAiCM4pGHSQIgiA4R4SAIAhCCSNCQBAEoYQRISAIglDCiBAQBEEoYUQICIIglDAiBARBEEoYEQKCIAglzP8He56z5peyKGgAAAAASUVORK5CYII=\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 576x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"def mixture_pe(x):\n",
" lp1 = np.sum(dist.Normal(np.array([-1., 0]), np.ones(2) * 0.3).log_prob(x), axis=-1)\n",
" lp2 = np.sum(dist.Normal(np.array([+1., 0]), np.ones(2) * 0.3).log_prob(x), axis=-1)\n",
" return - logsumexp(np.stack([lp1, lp2], axis=-1), axis=-1)\n",
"\n",
"\n",
"def mixture_model():\n",
" x = sample('x', dist.Uniform(-10000 * np.ones(2), 10000 * np.ones(2)))\n",
" pe = mixture_pe(x)\n",
" sample('log_density', dist.Delta(log_density=-pe), obs=0.)\n",
"\n",
"\n",
"opt_init, opt_update, get_params = optimizers.adam(0.001)\n",
"rng_guide, rng_init, rng_train = random.split(random.PRNGKey(1), 3)\n",
"guide = AutoIAFNormal(rng_guide, mixture_model, get_params, hiddens=[10, 10], num_flows=8)\n",
"svi_init, svi_update, _ = svi(mixture_model, guide, elbo, opt_init, opt_update, get_params)\n",
"opt_state, _ = svi_init(rng_init)\n",
"\n",
"\n",
"def body_fn(val):\n",
" i, loss, opt_state_, rng_ = val\n",
" loss, opt_state_, rng_ = svi_update(i, rng_, opt_state_)\n",
" return i + 1, loss, opt_state_, rng_\n",
"\n",
"losses, opt_states = fori_collect(0, 100000, jit(body_fn), (0, 0., opt_state, rng_train),\n",
" transform=lambda x: (x[1], x[2]), progbar=False)\n",
"\n",
"\n",
"plt.plot(losses[-1000:]);\n",
"\n",
"\n",
"last_state = tree_map(lambda x: x[-1], opt_states)\n",
"samples = guide.sample_posterior(random.PRNGKey(0), last_state, sample_shape=(1000,))\n",
"\n",
"\n",
"x1 = np.linspace(-3, 3, 100)\n",
"x2 = np.linspace(-3, 3, 100)\n",
"X1, X2 = np.meshgrid(x1, x2)\n",
"P = np.clip(np.exp(-mixture_pe(np.stack([X1, X2], axis=-1))), a_min=0.)\n",
"\n",
"plt.figure(figsize=(8, 8))\n",
"plt.contourf(X1, X2, P, cmap='OrRd')\n",
"sns.kdeplot(samples['x'][:, 0], samples['x'][:, 1])\n",
"plt.xlim([-3, 3])\n",
"plt.ylim([-3, 3])\n",
"plt.gca().set_aspect('equal');"
]
}
],
"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": "3.6.8"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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