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@npyoung
Last active July 30, 2022 05:41
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A state space model distribution for pymc3
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# A state space model for fitting dynamics in pymc3\n",
"\n",
"The goal is to create a `Distribution` subclass similar to `distributions.timeseries.GaussianRandomWalk` for modeling a dynamical system with observed varibles, unobserved state, and IID spherical Gaussian noise for each. In other words, we will be fitting\n",
"\n",
"$$\n",
"\\begin{align}\n",
"X(t+1) &= AX(t) + BU(t) + \\epsilon_s(t) \\\\\n",
"Y(t) &= CX(t) + \\epsilon_o(t) \\\\\n",
"\\epsilon_s{(t)} &\\sim \\mathcal{N} (0,\\sigma_s^2) \\\\\n",
"\\epsilon_o{(t)} &\\sim \\mathcal{N} (0,\\sigma_o^2)\n",
"\\end{align}\n",
"$$\n",
"\n",
"Our strategy is to create a class that can compute the likelihood of $x(t)$, then define the likelihood of $y(t)$ using `pymc3.Normal(mu=x, ...)`. This amounts of linear regression."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import seaborn as sns\n",
"import pymc3 as mc\n",
"import theano\n",
"import theano.tensor as T"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"theano.config.compute_test_value = 'ignore'"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Generate some toy data\n",
"\n",
"For simplicity let's start with no driving input ($U, B = 0$)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"True A: \n",
"[[ 0.86736839 -0.07095217]\n",
" [ 0.05227378 0.99177767]]\n",
"True tau: 400.0\n"
]
},
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7f06ce65a850>,\n",
" <matplotlib.lines.Line2D at 0x7f06ce65aa50>]"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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UUChhC6aCxHOJmvqa6wjxFggEAsGqyeazPH9t2GgWciWsxnLv7L6N+3vv5Z0DbyOktfHU\n51TrlnelmueVyMk5MnK2pkxzHavJRjavirfVZDV6n8c3IFtbd5vr4j2bVMvmDnbuA2AiNo2syDXX\neEPBbV4u2zyUDm9ISECIt0AgEDQ5oXS4bEvTH02+wl+/+kVemBgG4EroOgA7fFsB+MCOR/BrU7AK\n4t0FULHb2ErU06BFx262qU1N0hFcFqcxAGQjuqxFMjEkJHb4tpWcz772XQCMRSeA2mu8obLlHc3E\n+O+v/Bl/f+ZLDZ71ygjxFggEgiYmmUvx8Zf/lH86/9Vlz10JqZb2azOnkBWZq+HrdDk6DMF2WBz8\nrwc+zG7/DvZ17AFUd7HT4jBiwfVST19zHb3WO5KJ4bQ6jSYnG9FlLZqN4ra6cFmd+GxtgBr/7nR0\nAAXxrrXGG8ButmOSTMss729ePU4il2Q0uv49TYR4CwQCQRMTSofJ5DO8Pvum4QIHUBSFq+EbAFyP\njHJ24TyJXJKdmntYZ0/7Tn7j7l/GZy+UJHmsbmOSVr3U09dcR48vKygllvdGuJejmZjhpte9D0Pe\nASNZTxdaj6128ZYkCZfFWWJ5j0cnOTH5KqB+RrF1bkIjxFsgEAiamFhGFQFZkXlJEwdQ50mHMxFj\natfTl74JwM4i93AlPFYP8WwCWZFX3HYpuqu73mxzHVW89Zjx+op3Np8lmUvhtanx7G63Jt5tBfEu\ntEatXbwBTbzV81cUhacvfRMFhQFPHwBzicaGv6yEEG+BQCBoYorbiJ6YfNVITtOt7vfvfTcWyWxM\nCtvp37biPj02N7IiVxyRWQ2jNWo9bnOT1fi/0+LEZVje65uwZszp1sT7bb1v4c7AbRzs3IvdbCsR\n7HrF22l1kswmURSFqfgMF0NX2N+xhyN99wEwpyXGrRdCvAUCgaCJ0S1Dr81DKB3m9ILaj/uaJt53\n9R7igJY57ba6jGzyang1oYotiXsnskn+4exXqlqNq01Y03FZnbiNwR7ra3nrcX3dbb61bZD/dNtH\njEz54jr3etzmoL7/nJInK2dZSC0CsLd9FwFXJ1AYBrNeCPEWNC3xVJY/O3aKG9Oibafg1iWmuZbf\nM/ROAH449pIR7zZLZra3D3HPljsA2OHbVlPTE49miUaXxGXPLJzjxzMnOTH1armXAYU4tbuO7Oyl\nbnPXCjHvVC5dMsRktegjO3XLeykd9iLxXoXbHNTFTDCl5iK02310O9VsfmF5C25ZLo6GOHN1kR++\nMbnZpyIQbBq623yPfyf7O/ZwMXSFH02+zHhskiFvPzazlTu6DvJA/2EeGnqwpn3qQrU0qUpvmToe\nq/ybK4h37WKnjwUFdSJXtYQ1RVH4i5Of5Y9e/TSZMuVx9RDN6F6L8v3Diy3vet4PFMIGiWzSSCT0\n2X20O/xqGEPEvAW3Kom02uLx6mR4hS0FgpsXXWDdVjc/t/ffYzfb+OcLX0NWZLZr9dxWs5UP7/1g\nTfFuKBLvJW7zcEYV74loNfGub/Y1lFreTqsLh15qVcZtfm7xIqPRCRZTQV7U6tdXi96gpa2C5a2L\nt0Uy4zDb69p3seWti3e7w4dJMtHp7BSWt+DWRRfv8dk46Wx+k89GINgcjGxom5tOZwc/u/tRoze3\nLt71orvNK1ne4Uy0Yh34atzmdnMhYc1lcRqlVuUS1r4/9iIAVpOV5278gFQuXfNxlqK/h4puc0c7\noC6M6u2xrot3ski89TryblfnupeLCfEWbBo/uTBLLFnZLZbUxFtWFBH3FtyyxDMJrCaLkbF9uPde\n7ug6iNVkNVp+1kshYa28eENl13kim8RismAtyiBfidKYtwNQxT++RNwmY9OcW7zIbv8OHhp6J7Fs\nnB+Ov1TzcZYSMSzvCm5zLeZdb7IalLZIDaXDeKxurNoiJaDHvdcxaU2It2BTuDYV4a/+9QzffOl6\nxW0SqcJkpKuTqx9fKBC0MrFsvMQylCSJjx76BT5++L9WFKWV0MVqaaOWEvGu4DqPa+Mz67FUS2Le\nmsXusrhI5NRSK53vjb0AwE8NvYN3Dz2Ay+Lku6M/XLX1bVjeFfqWd2hu83qT1aDQpCaRSxJMh42u\ndlAk3sn1i3sL8RasK6cuz3P22uKyx6cW1BX3jenKoqxb3gBXp4R4C25N4tn4MnExm8wlHdPqxVPG\n8lYUhXAmYrjDK1ne8VyiLpc5LM82B9XyVieLqcKcyCZ4bfok3c4uDnbuw2lxcrj3LVq70bG6jqcT\nycaqzulus3k5uu09vHvwgbr3rb+PhdQimXymRLy7jf7xwvIWtCCKovC5b57lH549t+y52aAa6xqb\ni5esvIvRY95Wi4lrImlNcAuSlXOk8ulVWYbVsJlt2EzWkphsMpckK+fY3rYVh9nORGxq2evycp5k\nLrUK8S5u0lJwm0Ohy9qb8yPklDz3996LSVKlaWvbIKCOOq2HK6HrPHvteywmFyvGu0H1Yvy7HQ9z\nqGt/XfuHgtt8MjYNgN9RbHmrtd7rmbQmxFuwbixEUiTTeRYjabK50jaMsyFVvJPpHAvh8l2edMt7\nz6CfhUiacGz1iSsCQSsSNzLN6xPLWvDYPCXiHdJc5n6Hjz5PLzOJuWWlWnqDlnrLqvQmLSbJhF3L\n6tbFL6zFpU/Ongbgru7bjNcNetVWo5Vc+OWYjs/wZ6//Nd+6dpyMnGWPNj1srdEtb12824ss740o\nFxPiLVg3JubUG4OCKuTFzAULWaZjs+WzWhOpHDaLiT0D6o9CxL0Ftxp6ZvdqEqpWwmN1E8sWPF96\nmZjf1saApw9ZkZmKT5OX8+TkXMn5uOtojQoFt7meaQ4YIzqHJ18lmUtxfvEi/Z5eurXhIQBdzk4c\nZrsx+asWZjRX9QP9h/mjI/8XH9r703Wda63oiw89b6DYbW6STHQ5O5lNzlf0LDaKEG/BujExX1jV\nz4VKS0JmQzWIdzqH025hR58m3iLuLbjF0GPS9Vq6teCxucnJOdJazFm3vH32Nga8vQB8Z/SH/N5L\n/52/OPn/Aatr0AKF3ua6yxzgzsAhtrgCvDL9Oi+OD5NT8twZOFTyOpNkot/Tx0xijnQ+U9OxwlrZ\n1i7fNnz2trrOsx7sZjsShaS9YvEGdYJZMpckssrRqyshxFuwbkzMFb60xeKdTOeIJrIMBNQbQCXx\nTqZzuBwWtve2IUlwYSxU9XjrtcIVCDaL1U68qgU9A1s/RrhYvLXJWCdn3ySajXEtPEpezq/ajV+w\nvAuvM0kmHt76LvJKnm9c/TYAd3Xfvuy1Q95+FJSyMfhyFBYhvhW2bAyTZCrp775UvPs86gJookq3\nuoaOvy57FQgouM2hVLz1/+8e9ONxWsuKt6IoJFKq5e1yWNjZ7+PKRLhiXXg8leV3/voEz758Y43f\nhUCweaymm1mt6AsCvYWoId62Nvo8vez0beOOwCH2tu9CQSGUjhQs7zpmeUNBqB8cPFLy+Fu23EWn\nox0FhR5XN73uLcteO2DEvWtznesNU5aK6XpQPFnNv8TKH9DEu1qr2UYQ4i1YF/KyzORCgo42NTll\nLlSIeeuZ5t1+J4PdHmZDyZKyMIBsTiYvK7jsFgDu2NmJosCbV8pnb569tkgwmhaudcFNRXFr1LVG\nj6PHtJitHvP22duwmiz81j3/B//7bb9oZHwvpoLEc/V3V9N5dOdR3tpzd8ljZpOZh7Y+CJS3ugEG\nvf0ANce9C33G189lrqNb3k6LA0dRSAAKi45KWfuNegqFeAvWhdlgklxeZt9QO3aruazlrYs3lFrp\nUCgTczlU8b5zl1o3eepy+exNvZY8lRFtVAU3D/pEsfVwm3t0t3mR5W2WzMuEWW8hupgKGpa3aw09\nAUf67uOXb3+Ch7e+q+zzPa5uLCYLYzVasKG0WqteXJ62XujiXc7K73C04zDbGV8i3nk5z8df/lOe\nvvzNho5taejVAkEFdDEeCHgYnYkyF1I7KUmSZCSrBdqdhkiPzkZZjKaQFYX7D/QYlrhTs7z7utx0\n+RycubpALi9jMRfWnYqiMHJdF+9SC14gaGXiRX3N1xqvrXSyWDgdwWdvM2qsdQriHSpkv6+heJsk\nE7d1Haj4vNlkps/dw0Rsipycw2KqLlvhdJhOZ8eanV81dLd5OfE2SSb6PL1cC98gk88ai4lQOsxC\nanFZa9p6EZa3YF2Y1DLN+wNuAn4nqUzeiFfrbvNAkeX9z9+/zGe/fpbPfXOEdDZvtEbV3eaSJHHn\nri5SmTwXlySuTS8mWIioGbPC8hbcTBjZ5nXGmGvBiHlnY8iKTDgTMQZrFKO3EA2mg6vONm+UQW8/\neSXPVHy26napXIpUPr0hLnOobnkDDHj6UFCYik8bjy2mgkBhUbRaGhbv48ePMzw8zLFjx8o+f+zY\nMY4dO8YnP/nJRg8laCHGdfHuUsUbCnHv2WASv8eG3Wqmt9ONzWIim5Nx2S0oCoRi6WWWN8Adu3XX\neWnce+R60Ph/Ki3EW3DzEM/GsZttxsCLtaTYbR7PJpAVuazolVre6u+6OMt6Ixg04sfVXedGoxnb\n+ierQS3irWecF1zniynV+OgomiW+GhoS75GRESRJ4vDhwwCcO1faBnN4eJi3ve1tPP7444yNjTE8\n3NhsVkHrMDEXw2k30+61F4m3GgdfjKbo1h6zWkz89ofv5Hc/cg/vvkdNTAlF08ti3gB7B/04bGbe\nvFIa99bj3S67RbjNBTcVsWxiXeLdUJywFi+p8V6K3WzDbXUZMW+nxVGxV/h60eFQ3eDBVPU2yYVM\n8w2yvDW3eXsF8e73Ls84bwrL+5lnnsHrVZvjDw4OcuLEiZLniwV7cHCQ8fHxRg4naBGyOZmZxST9\nXR4kSSLgV7Mw50JJ5sMpFEWNd+vsHvCzq9+H36NmpgdjBfEutrwtZhO7+n3MBpOGWz2Xlzk/GmRL\nu5OeTpdwmwtuKvSJYuuBw2zHIpmJZeJGYxN/Gbc5QIfdb8S8Xevgwl8JXYz1jPhK6OVuG1EmBrCv\nfTdbXN0VW7D2uXuQkBiPFlveTSDekUgEv79g+odCpbHIxx9/nMceewxQrfRDh0q75whuTm7MRJEV\nxYhnF1vexWViS2nXxDsUzZBcEvPW6etSb2ST2lSya1MRUpk8B7Z34LCZycvKsj7qAkErkslnyMrZ\ndbO8JUnS+pvHSsrEytHhaCcrZ0umjm0k+nkVjywtx0aWiQEMtQ3wB/f/DgFXZ9nnbWYb3a4Ak/Ep\nozRswRDvTXSb18rIyAgHDx5k//76J7cIWo8zV1W39oFtqqury1ewvF87ryacbOlYfgPwezXxjpV3\nm4MaQ4dC97bLE+qPdd9QOw6buq1wnQtuBtazxlvHY3WzkApy7OLXgerirbMZ4u22uLCYLIY4VyK0\nwZZ3LQx4eknmUobFvZgK4rG6S8akroaGSsV8Pp9hbS+1wosZHh7mt3/7t2vaZyCw+hm1gs1Fv3YX\nxsKYTBIP3DOI26km2nT6HFwYC3F+NMS23jbefd+2Epc4gEkT30QmT5tVjan19/hKvhOH9nTDs+cJ\nxrMEAl4mF1VL/p6DvVwYV3/YLo+DQOfGZsPeDIjfXnMRXVRv9gGff8Vrs9pr99MHH+Y7V14kkU3i\nMNu4e/s+3Lbl4jy4uAW0qGenx7cp35UOp49oLlr12IkL6oJnZ38/bfbKo0A3kr092/nJ7BuETYvs\n6RokmA6z1dff8GfYkHgfPXqUs2fPAmp8+8gRtfVdNBo1YuHHjh3jox/9KKCKuJ7cVom5uWgjpyTY\nJAIBL3NzUWLJLBdHg+we8JGIpUjE1AzzTq+dhbCaqPbrP3MbsUiSpU1R87KMJMHMQpxcTo1dpxLp\nku+EU8uTuTQaZG4uyoXri3icVqRcDmTVXT45HcEsC9d5PejXT9A8jC/MAWDOWatem0au3X73Afbf\nXqixToTzJFi+L1uuIOhm2bYp3xWPxcu18A2mZ0IVE+ZmIwtYTBZSYZm01Bzf506TOiXt9PglOukm\nJ+fwWtqMz3C1It6Q2/zAAfWiDw8P4/P5DLf4E088YTz+qU99ioceeoj77ruvkUMJWoSR64sowKEd\npTGgO3cH6O108VsfvhOfFtteitlkwue2EYymjYS0pda5w2ahy+dgcj5OLJllPpxiW48XSZKMbYXb\nXHAz8MqQGBnlAAAgAElEQVT0TwDY4ure5DMpjc+6N7hMTMdvb0NBMUZwliOcDuOztRljR5uBIa29\n62hk3HCddzaYrAZr0GFNT0gr5umnnwbg8OHDvPLKK40eQtBCnNbi3bctEe/33jfEe+8bWvH17V47\nY7Nx/B47kgQO2/IVdl+XmzevLHDmmnqsbb1qnE7fNilqvQUtzuXQNX48c5Ih7wB3BA5u9uksiXlv\nTkiqOGmtXEw7L+eJZGLGnPBmwWV1EXB2ciM6XpSs1rh4iw5rgjVDURTOXF2kzWVlcMvq4k1+j51c\nXmYunMRlt5RdQfdro0RPnFa7Fm3vUd1OImFNcDMgKzJf1RLIHt/z6LJ2pZuBx+rGqs3k3oyENSgk\noYUqZJxHMlEUlA2r8a6HrW2DJHNJLgavAI1nmoMQb0EDfOm5i/zDs4XGPGOzMcLxDAe3d2JapdtK\nzzgPxzLLXOY6esb5Wa2f+VLLW9R6C1qZl6deYzw2yX0997Ddt3WzTwdQy8p0wdks8dZbt1YqF2vG\nTHOdIe8AAG/MnQGE5S3YRE5enON7r4/z4htThqWr9xw/sG31X0x/UTx8aZmYTn+XatUrCvjcNvwe\nteRCiLfgZuDV6dcB+MCORzb5TEppt2+ueBuNWiqUi4U3uLtaPehjVfXyPyHegk0hncnz5e9eBEAB\nxrUJYjdm1OxJ3RJeDe3F4l3B8u7tdKEb9nqyGgi3uaD1SWSTXAlfZ2vbIO1r4FpdS4baBrCarGsi\nPKtBj3mHKnRZW0yHtO2az/Ie8PQhod2nzA6jrWojCPEW1M03XrrGQiRNb6e6Ah/TRHt0JobNYqK3\nTAOWWvF7C40LKrnNbVaz0bWteKEgLG9Bq3Nu8SKyInNbZ/M1tHrf9of4w8P/Ba9tc+qndVGu5Da/\nERkDYEAbYtJMOCx2etxq1cBaxLuhhcQ7lUvx+bNfZio+s9mnckuTzuR57sdjdLY5+I/vU28wo7Mx\nsrk8k/NxBrs9mEyrL9OoxfKGQtx7W0+hRlKIt6DVObOg5pAc7Nq3yWeyHKvJsqnxZLvZhtPiqCje\n18I3cFtddDu7NvjMamOrV3Wdr5XnomXE+3zwMq/NnOLE5KubfSq3NKFYmryssH9bO9t6vJhNEqMz\nMW5MRcnLCkNbGusapCesATgrxLwB3naol31DfvYMFlaxwm0uaGVkRebswnl8tjYGPf2bfTpNic/W\nVrZFajgdYSEVZHvb1qaq8S5mqE1NWlsr8W64znujCGmj4ITlvblEEhkA2lw2LGYT/QE343MxLo2p\n9YtbexoTb5fdgs1iIqPN967EPXsD3LM3UPKYw65Z3qLOW9CCXI+MEs8mONL31qYVoM3Gb/cxnZgl\nk89iK5pxfi18A6BpsvPLcbBzL202L/s6dq/J/lrG8tZXW9PxWeOxnJwjL4sb9UYSiWcBaHOpP5yh\nbi/ZnMwLpybUv1dZ360jSZKRcV5NvMtRcJsLy1vQepyeV13mh5ow3t0s6ElrkSVJa1c18d7RxOLd\n5ezkj9/++2vWdKflxDuYDpHKqf2y/+7Ml/iT1z6zmad1yxHVLG+vW00s05uxnLmygNkkGWVcjaC7\nzqu5zcthNpmwWkwi5i1oSS4sXsYimdm7RpbZzYiRcb4k7n0tcgOTZDJKsm4FWk68AWYSc2TlHCML\n55mITSErYgjFRlHsNgcY6i6IdV+XG6ul8a+UXrddr+UN4LSZhXgLWg5ZkZmMT9Pj3oK9wVGRNzO+\nMrXeWTnHaGScfnfPLfXZtUzMO1h0sabjs+QVmZyi3qQTueS6DawXlBLV3OZezW0+2F2IcW9tMFlN\np8Orzv92OawrbLkch80i3Oa3MJlsnmQ6V3H4TbMyn1wgK2fp8/Rs9qk0NeVapI5HJ8gpebY3WU/z\n9aYlLG9FUQilw0aP36n4DNe1GAdAPJvYrFO75TAsb81t7nJYCPhVsW003q3z4F19vPe+IXYP1F+W\n4hCW9y3NsR9c5r/+7ctE4pnNPpW6mNQScfvcQryrUa5F6lUjWW3lwUc3Ey0h3vFcgpycY3ubenGm\nEzNcjYwazyeEeG8Yeszb4yxYxUOa9d1omZhOd7uLx9+1C4u5/q+nLt6yoqzJuQhai2tTEdKZPCM3\nFlf1+sVIyhhHu5FMxqYAhOW9AgFnJxISV8LXjccuBi8DNN00sfWmJcRbLxPr9/ThsbqZjs8apQEg\nLO+NJJrI4nZYSoT1vfcP8cEHd7Grf/PbEjq0OHlaWN+3JHMhNZn13PVg3a/N5mT+779/lS9958Ja\nn9aKTMbUCXnC8q6Ox+ZmX8durkdGmYnPEkqHObtwgSHvAF3Ojs0+vQ2lNcRbi3e32330uLuZSy6U\nJLAJ8d44IomM4TLX2dnn43/7wMGGOqutFaLLWvPw6rkZ/vG5C2W9IIqirLl3JJHKEUuqORkj14Mo\nde4/HE8TT+WYnN/4+8lkfAanxdGUE7Gajft77gHg5emfMDz5GgoKR/reuslntfG0hHjryWp+h48e\n9xbjcb3dXDwnxHutmVqIc2G01HqRZYVYIovX1bwZnaLWuzmYmIvx5LfO8YPXJ5hZLP19KorCxz//\nYz779bNresy5UNL4/0IkVfJ3LUQTqvCH4+k1Pa+VyOazzCXn6XP3iOYsNXB74CAOs51Xp19neOpV\nbGYb9265c7NPa8NpCfEuHvXW6yqI9yGt/6+Iea89X/j2BT751KmS+F8smUWh0KClGSm0SBWWd62E\nYmkSqeya7S+Xl/nct0bI5dUSztGZWMnzqUye0dkYr52fNWayrwW6WG/RBuOM1Ok615PcIvHshuZM\nTCdmkRWZXhHvrgmb2cbd3bcTSodZSAW5t/sOHBbHZp/WhtMS4m1Y3prbHMAkmdjfsQeAeLa+FbZg\nZWYWE+RlhUvjIeOxyJIGLc2IcJvXRziW5vc+9wqffupkxW2S6Rw/uTDLYiRV0z6/8dJ1RmdiDATU\n6oOx2VLxDhdlgv/PH1xZM6HUxfudd6hTpUZurE68ZUUx3O8bgR7v7hfx7pq5r/de4/9H+u/bxDPZ\nPFpCvPWEtWLx7nf3GPNu49qAc8HakMnmjRvshdGCeEfjpQ1amhExnKQ+vjV8g2Q6Z4x1LSaVyfG3\n3zzLb/zlj/irfz3D5585V9M+f3hqAq/Lyq/97G0AjM6W7jscU93SZpPEjZkor55bm3kFs5p4H9rR\nQUebnfM3gqSz6rQ73QtQDX1xChCJbVyp2WRcS1bz9G7YMVudHb6tDHj62OnbZoRPbzVaoklLKBPB\nZXFiM9uwmW08uuMoA94+XBbVPZbICct7LVkosrAujBWsl0iitK95MyIs79qZDyd5/qTakz4YXR7n\nff7kJC+fnWFLh4tMNs+5GyHiqSzuKs1zdKt1V7+PLp+TjjZ7Rcv7PfcO8N3XxvnaC9e4b/+WmuK9\nsqJgqrCdbnkH/E4ObO3gR6en+M9/9gKyovCzD+7kffdX73ut9+3Xz3FgxbNZGwzxLsrnEVTHJJn4\nL/f+KsAtmyfQMpZ3cRbmw9vexYHOvdjMVqwmq7C815iFcEG8r09HSaZVK9Zwmze15S3Eu1a+8aPr\n5GUFq8VEPJklmyv9zE6cmcZ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hOj5LwNkJrL/lrSiKMSFrvS3v86NBbFYTO/punrp1j9NC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\niIjIZP4PUvTPcoR6duQAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f06ce4fd990>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"N = 200\n",
"\n",
"# we'll use a dynamics matrix with a decaying rotational component plus a small perturbation\n",
"theta = 5. / 180 * np.pi\n",
"rot_comp = np.array([[np.cos(theta), -np.sin(theta)], [np.sin(theta), np.cos(theta)]])\n",
"true_A = 0.9 * rot_comp + 0.05 * np.random.randn(2, 2)\n",
"true_sigma = 0.05\n",
"true_tau = 1./true_sigma**2\n",
"true_x0 = np.zeros(2)\n",
"\n",
"x = np.zeros((N, 2))\n",
"x[0] = true_x0\n",
"\n",
"for t in range(1, N):\n",
" x[t] = np.dot(true_A, x[t-1].T).T + np.random.randn(2) * true_sigma\n",
"\n",
"print \"True A: \\n{}\".format(true_A)\n",
"print \"True tau: {}\".format(true_tau)\n",
"plt.plot(x)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Define the `StateSpaceModel` class (based heavily on `GaussianRandomWalk`)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"from pymc3 import Normal, Flat, Continuous\n",
"\n",
"class StateSpaceModel(Continuous):\n",
" \"\"\"\n",
" A state space model with Gaussian noise.\n",
" \n",
" This models only the state variables so that the form of the observation\n",
" noise can be specified separately.\n",
" \n",
" Parameters\n",
" ----------\n",
" tau : tensor\n",
" tau > 0, innovation precision\n",
" sd : tensor\n",
" sd > 0, innovation standard deviation (alternative to specifying tau)\n",
" A: tensor\n",
" state update matrix\n",
" B : tensor\n",
" input matrix\n",
" u : tensor\n",
" (time x dim), inputs to the system\n",
" init : distribution\n",
" distribution for initial value (defaults to Flat())\n",
" \"\"\"\n",
" def __init__(self, tau=None, sd=None, A=None, B=None, \n",
" u=None, init=Flat.dist(), *args, **kwargs):\n",
" super(StateSpaceModel, self).__init__(*args, **kwargs)\n",
" self.tau = tau\n",
" self.sd = sd\n",
" self.A = A\n",
" self.B = B\n",
" self.u = u\n",
" self.init = init\n",
" self.mean = 0.\n",
" \n",
" def random(self, point=None, size=None):\n",
" tau, sd, A, B, u, init = draw_values([self.tau, self.sd, self.A, self.B, self.u, self.init], point=point)\n",
" \n",
" T, D = size\n",
" x = np.zeros(T, D)\n",
" x[0,:] = init\n",
" \n",
" for t in range(1, T):\n",
" x[t,:] = np.dot(A, x[t-1,:].T).T + np.dot(B, u[t-1,:].T).T + np.random.randn(1, D) * sd\n",
" \n",
" return x\n",
" \n",
" def logp(self, x):\n",
" tau = self.tau\n",
" sd = self.sd\n",
" A = self.A\n",
" B = self.B\n",
" u = self.u\n",
" init = self.init\n",
" \n",
"\n",
" x_im1 = x[:-1]\n",
" x_i = x[1:]\n",
" u_im1 = u[:-1]\n",
"\n",
" innov_like = Normal.dist(mu=T.dot(A, x_im1.T) + T.dot(B, u_im1.T), tau=tau, sd=sd).logp(x_i.T)\n",
" return T.sum(init.logp(x[0])) + T.sum(innov_like)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Testing the model for $x(t)$ observed directly"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Applied log-transform to tau and added transformed tau_log_ to model.\n",
"Assigned NUTS to A\n",
"Assigned NUTS to tau_log_\n",
" [-----------------100%-----------------] 10000 of 10000 complete in 11.0 sec"
]
}
],
"source": [
"with mc.Model() as model:\n",
" A = mc.Normal('A', mu=np.eye(2), tau=1e-5, shape=(2,2))\n",
" Tau = mc.Gamma('tau', mu=500, sd=100)\n",
" X = StateSpaceModel('x', A=A, B=T.zeros((1,1)), u=T.zeros((x.shape[0],1)), tau=Tau, observed=x)\n",
" \n",
" trace = mc.sample(10000, start=mc.find_MAP())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note the speed: **hundreds of steps per second**"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([[<matplotlib.axes._subplots.AxesSubplot object at 0x7f06b8667390>,\n",
" <matplotlib.axes._subplots.AxesSubplot object at 0x7f06b78826d0>],\n",
" [<matplotlib.axes._subplots.AxesSubplot object at 0x7f06b44368d0>,\n",
" <matplotlib.axes._subplots.AxesSubplot object at 0x7f06b7af0310>]], dtype=object)"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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VDIhncDtE+7RHtE97RPu0R7TPg2HfCaqxsTGuX7/OpUuXOHfuHGfPngWsqEvZrFhH0Exl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avKMGeLWEX8KeKCzI70E/L3Ls8AyO5+ZOOHEjk/Mo0yiQjbU9wjwB3FtbFGzvv3MmG2e3FjwobO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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f06b8c27350>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"mc.traceplot(trace)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 0.82924495, -0.11186985],\n",
" [ 0.00330255, 0.96797908]])"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"trace['A'].mean(axis=0)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 0.86736839, -0.07095217],\n",
" [ 0.05227378, 0.99177767]])"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"true_A"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Testing the model with $x(t)$ hidden and only $y(t)$ observed"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"True C: \n",
"[[-0.61404953 2.41103216]]\n",
"True tau_o: 25.0\n"
]
},
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7f06b40b7d10>]"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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N0+HDTNJJten9udt8TDDeA3CbM+XNXPHtuqwFdd7du82LFYNvPAwho/4Pv34Bv/OVs22V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\nP4lX/9vfoQV360VRIi0549O+Me9ae7m8XG2g7pkKJMa6a57HNsp135S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w3FkFjvO8iYjC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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f06cbbef890>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"true_sig_o = 0.2\n",
"true_tau_o = 1./true_sig_o**2\n",
"true_C = np.random.randn(1, 2)\n",
"y = np.random.randn(x.shape[0], true_C.shape[0]) * true_sig_o + np.dot(true_C, x.T).T\n",
"\n",
"print \"True C: \\n{}\".format(true_C)\n",
"print \"True tau_o: {}\".format(true_tau_o)\n",
"plt.plot(y)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Applied log-transform to tau and added transformed tau_log_ to model.\n",
"Applied log-transform to tau_o and added transformed tau_o_log_ to model.\n",
"Assigned NUTS to A\n",
"Assigned NUTS to tau_log_\n",
"Assigned NUTS to x\n",
"Assigned NUTS to C\n",
"Assigned NUTS to tau_o_log_\n",
" [ 0% ] 22 of 10000 complete in 158.1 sec"
]
}
],
"source": [
"with mc.Model() as model:\n",
" A = mc.Normal('A', mu=np.eye(2), tau=1e-5, shape=(2,2))\n",
" Tau = mc.Gamma('tau', mu=100, sd=100)\n",
" \n",
" X = StateSpaceModel('x', A=A, B=T.zeros((1,1)), u=T.zeros((x.shape[0],1)), tau=Tau, shape=(y.shape[0], 2))\n",
" \n",
" C = mc.Normal('C', mu=np.zeros((1,2)), tau=1e-5, shape=(1,2))\n",
" Tau_o = mc.Gamma('tau_o', mu=100, sd=100)\n",
" \n",
" Y = mc.Normal('y', mu=T.dot(C, X.T).T, tau=Tau_o, observed=y)\n",
" \n",
" trace = mc.sample(10000, start=mc.find_MAP())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This is problematic. Why is it taking **several seconds per step** in the chain? Initially steps take < 1 second, but slow to a standstill. What's going on?"
]
}
],
"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": "2.7.12"
},
"widgets": {
"state": {},
"version": "1.1.2"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
@DanielWeitzenfeld
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did you ever get an answer to your question?

@Nilavro
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Nilavro commented Mar 1, 2018

Try this piece of code out instead of the mcmc sampling

Replace : trace = mc.sample(10000, start=mc.find_MAP())
With: inference = mc.ADVI()
%%time approx = mc.fit(n=30000, method=inference)

ADVI is faster

@michael-ziedalski
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Did this end up going anywhere? The code looked promising.

@tanmoy7989
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tanmoy7989 commented Mar 22, 2019

Same question as above. Did you develop this further?
I am using this with the ADVI suggestion by Nilavro and it isn't slow!

@Nilavro
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Nilavro commented Mar 25, 2019

I used this code for my research. Check the package BSSPy for the work https://arxiv.org/pdf/1901.07469.pdf.

Just remember the caveats that if you use a mean-field VI then it does not preserve the Markov dependency. i.e. $N(x_t | x_t-1 )$
More elaborate discussions about mean-field and structured mean field here. http://www.ee.columbia.edu/~sfchang/course/svia-F03/papers/factorial-HMM-97.pdf

I think the full rank ADVI may preserve this dependency but can be slower.

Also, I would ask for some thoughts regarding the Tau initialization -


    A = mc.Normal('A', mu=np.eye(2), tau=1e-5, shape=(2,2))
    **Tau = mc.Gamma('tau', mu=100, sd=100)**
    
    X = StateSpaceModel('x', A=A, B=T.zeros((1,1)), u=T.zeros((x.shape[0],1)), tau=Tau, shape=(y.shape[0], 2))

It seems like a single random variable for the Precision term is being broadcasted. I would prefer to declare it as a covariance matrix instead. I am trying to put together a code with reparameterization trick and will push a new module soon.

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