notebooks/time_series/MvGaussianRandomWalk_demo.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Multivariate Gaussian Random Walk"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pymc3 as pm\n",
    "import theano\n",
    "\n",
    "from scipy.linalg import cholesky\n",
    "\n",
    "np.random.seed(42)\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Simulate the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "D = 3\n",
    "N = 300\n",
    "sections = 5\n",
    "period = N / sections\n",
    "\n",
    "Sigma_a = np.random.randn(D, D)\n",
    "Sigma_a = Sigma_a.T.dot(Sigma_a)\n",
    "L_a = cholesky(Sigma_a, lower=True)\n",
    "\n",
    "Sigma_b = np.random.randn(D, D)\n",
    "Sigma_b = Sigma_b.T.dot(Sigma_b)\n",
    "L_b = cholesky(Sigma_b, lower=True)\n",
    "\n",
    "# Gaussian Random walk:\n",
    "alpha = np.cumsum(L_a.dot(np.random.randn(D, sections)), axis=1).T\n",
    "beta = np.cumsum(L_b.dot(np.random.randn(D, sections)), axis=1).T\n",
    "sigma = 0.1\n",
    "\n",
    "t = np.arange(N)[:, None] / N\n",
    "alpha = np.repeat(alpha, period, axis=0)\n",
    "beta = np.repeat(beta, period, axis=0)\n",
    "y = alpha + beta * t + sigma * np.random.randn(N, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12, 5))\n",
    "plt.plot(t, y)\n",
    "plt.title(\"Three Correlated Series\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Scaler:\n",
    "    def __init__(self):\n",
    "        mean_ = None\n",
    "        std_ = None\n",
    "\n",
    "    def transform(self, x):\n",
    "        return (x - self.mean_) / self.std_\n",
    "\n",
    "    def fit_transform(self, x):\n",
    "        self.mean_ = x.mean(axis=0)\n",
    "        self.std_ = x.std(axis=0)\n",
    "        return self.transform(x)\n",
    "\n",
    "    def inverse_transform(self, x):\n",
    "        return x * self.std_ + self.mean_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def inference(t, y, sections, n_samples=100):\n",
    "    N, D = y.shape\n",
    "\n",
    "    # Standardies y and t\n",
    "    y_scaler = Scaler()\n",
    "    t_scaler = Scaler()\n",
    "    y = y_scaler.fit_transform(y)\n",
    "    t = t_scaler.fit_transform(t)\n",
    "    # Create a section index\n",
    "    t_section = np.repeat(np.arange(sections), N / sections)\n",
    "\n",
    "    # Create theano equivalent\n",
    "    t_t = theano.shared(np.repeat(t, D, axis=1))\n",
    "    y_t = theano.shared(y)\n",
    "    t_section_t = theano.shared(t_section)\n",
    "\n",
    "    with pm.Model() as model:\n",
    "        packed_L_α = pm.LKJCholeskyCov(\"packed_L_α\", n=D, eta=2.0, sd_dist=pm.HalfCauchy.dist(2.5))\n",
    "        L_α = pm.expand_packed_triangular(D, packed_L_α)\n",
    "\n",
    "        packed_L_β = pm.LKJCholeskyCov(\"packed_L_β\", n=D, eta=2.0, sd_dist=pm.HalfCauchy.dist(2.5))\n",
    "        L_β = pm.expand_packed_triangular(D, packed_L_β)\n",
    "\n",
    "        α = pm.MvGaussianRandomWalk(\"alpha\", shape=(sections, D), chol=L_α)\n",
    "        β = pm.MvGaussianRandomWalk(\"beta\", shape=(sections, D), chol=L_β)\n",
    "        alpha_r = α[t_section_t]\n",
    "        beta_r = β[t_section_t]\n",
    "        regression = alpha_r + beta_r * t_t\n",
    "\n",
    "        sd = pm.Uniform(\"sd\", 0, 1)\n",
    "        likelihood = pm.Normal(\"y\", mu=regression, sigma=sd, observed=y_t)\n",
    "        trace = pm.sample(n_samples, cores=4)\n",
    "\n",
    "    return trace, y_scaler, t_scaler, t_section"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/env/miniconda3/lib/python3.7/site-packages/theano/tensor/subtensor.py:2197: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  rval = inputs[0].__getitem__(inputs[1:])\n",
      "/env/miniconda3/lib/python3.7/site-packages/theano/tensor/subtensor.py:2339: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  out[0][inputs[2:]] = inputs[1]\n",
      "Only 100 samples in chain.\n",
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "/env/miniconda3/lib/python3.7/site-packages/theano/tensor/basic.py:6611: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  result[diagonal_slice] = x\n",
      "/env/miniconda3/lib/python3.7/site-packages/theano/tensor/subtensor.py:2339: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  out[0][inputs[2:]] = inputs[1]\n",
      "/env/miniconda3/lib/python3.7/site-packages/theano/tensor/subtensor.py:2197: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  rval = inputs[0].__getitem__(inputs[1:])\n",
      "/env/miniconda3/lib/python3.7/site-packages/theano/tensor/basic.py:6611: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  result[diagonal_slice] = x\n",
      "/env/miniconda3/lib/python3.7/site-packages/theano/tensor/subtensor.py:2339: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  out[0][inputs[2:]] = inputs[1]\n",
      "/env/miniconda3/lib/python3.7/site-packages/theano/tensor/subtensor.py:2197: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  rval = inputs[0].__getitem__(inputs[1:])\n",
      "/env/miniconda3/lib/python3.7/site-packages/theano/tensor/subtensor.py:2339: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  out[0][inputs[2:]] = inputs[1]\n",
      "/env/miniconda3/lib/python3.7/site-packages/theano/tensor/basic.py:6611: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  result[diagonal_slice] = x\n",
      "/env/miniconda3/lib/python3.7/site-packages/theano/tensor/subtensor.py:2197: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  rval = inputs[0].__getitem__(inputs[1:])\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [sd, beta, alpha, packed_L_β, packed_L_α]\n",
      "/env/miniconda3/lib/python3.7/site-packages/theano/tensor/subtensor.py:2339: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  out[0][inputs[2:]] = inputs[1]\n",
      "/env/miniconda3/lib/python3.7/site-packages/theano/tensor/subtensor.py:2339: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  out[0][inputs[2:]] = inputs[1]\n",
      "/env/miniconda3/lib/python3.7/site-packages/theano/tensor/subtensor.py:2339: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  out[0][inputs[2:]] = inputs[1]\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "    <div>\n",
       "        <style>\n",
       "            /* Turns off some styling */\n",
       "            progress {\n",
       "                /* gets rid of default border in Firefox and Opera. */\n",
       "                border: none;\n",
       "                /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
       "                background-size: auto;\n",
       "            }\n",
       "            .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
       "                background: #F44336;\n",
       "            }\n",
       "        </style>\n",
       "      <progress value='4400' class='' max='4400' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
       "      100.00% [4400/4400 01:25<00:00 Sampling 4 chains, 0 divergences]\n",
       "    </div>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/env/miniconda3/lib/python3.7/site-packages/theano/tensor/basic.py:6611: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  result[diagonal_slice] = x\n",
      "/env/miniconda3/lib/python3.7/site-packages/theano/tensor/subtensor.py:2339: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  out[0][inputs[2:]] = inputs[1]\n",
      "/env/miniconda3/lib/python3.7/site-packages/theano/tensor/basic.py:6611: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  result[diagonal_slice] = x\n",
      "/env/miniconda3/lib/python3.7/site-packages/theano/tensor/subtensor.py:2197: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  rval = inputs[0].__getitem__(inputs[1:])\n",
      "/env/miniconda3/lib/python3.7/site-packages/theano/tensor/subtensor.py:2197: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  rval = inputs[0].__getitem__(inputs[1:])\n",
      "/env/miniconda3/lib/python3.7/site-packages/theano/tensor/basic.py:6611: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  result[diagonal_slice] = x\n",
      "/env/miniconda3/lib/python3.7/site-packages/theano/tensor/basic.py:6611: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  result[diagonal_slice] = x\n",
      "/env/miniconda3/lib/python3.7/site-packages/theano/tensor/subtensor.py:2197: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  rval = inputs[0].__getitem__(inputs[1:])\n",
      "/env/miniconda3/lib/python3.7/site-packages/theano/tensor/subtensor.py:2197: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  rval = inputs[0].__getitem__(inputs[1:])\n",
      "Sampling 4 chains for 1_000 tune and 100 draw iterations (4_000 + 400 draws total) took 87 seconds.\n"
     ]
    }
   ],
   "source": [
    "trace, y_scaler, t_scaler, t_section = inference(t, y, sections)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Predict the mean expected y value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "a_mean = trace[\"alpha\"][-1000:].mean(axis=0)\n",
    "b_mean = trace[\"beta\"][-1000:].mean(axis=0)\n",
    "\n",
    "y_pred = y_scaler.inverse_transform(a_mean[t_section] + b_mean[t_section] * t_scaler.transform(t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12, 5))\n",
    "plt.gca().set_prop_cycle(\"color\", [\"red\", \"green\", \"blue\"])\n",
    "plt.plot(t, y, \".\")\n",
    "plt.plot(t, y_pred)\n",
    "plt.title(\"Mean Prediction of Three Correlated Series\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "theano 1.0.4\n",
      "numpy  1.18.5\n",
      "pymc3  3.9.0\n",
      "last updated: Fri Jun 12 2020 \n",
      "\n",
      "CPython 3.7.7\n",
      "IPython 7.15.0\n",
      "watermark 2.0.2\n"
     ]
    }
   ],
   "source": [
    "%load_ext watermark\n",
    "%watermark -n -u -v -iv -w"
   ]
  }
 ],
 "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": "3.7.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}