{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.linalg import cholesky\n",
    "\n",
    "import pymc3 as pm\n",
    "import theano\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": "iVBORw0KGgoAAAANSUhEUgAAAsUAAAE/CAYAAACuKr76AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nwu5JUCyEEEIIIeze/wf9HnXl+rzPcAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f22e5c53588>"
      ]
     },
     "metadata": {},
     "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,   \n",
    "                                 eta=2., 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,   \n",
    "                                 eta=2., 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, sd=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": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      " 99%|█████████▉| 594/600 [08:32<00:05,  1.16it/s]/home/jovyan/pymc3/pymc3/step_methods/hmc/nuts.py:429: UserWarning: Chain 1 contains only 100 samples.\n",
      "  % (self._chain_id, n))\n",
      "/home/jovyan/pymc3/pymc3/step_methods/hmc/nuts.py:459: UserWarning: Chain 1 reached the maximum tree depth. Increase max_treedepth, increase target_accept or reparameterize.\n",
      "  'reparameterize.' % self._chain_id)\n",
      "/home/jovyan/pymc3/pymc3/step_methods/hmc/nuts.py:451: UserWarning: The acceptance probability in chain 1 does not match the target. It is 0.536618056712, but should be close to 0.8. Try to increase the number of tuning steps.\n",
      "  % (self._chain_id, mean_accept, target_accept))\n",
      "/home/jovyan/pymc3/pymc3/step_methods/hmc/nuts.py:467: UserWarning: Chain 1 contains 19 diverging samples after tuning. If increasing `target_accept` does not help try to reparameterize.\n",
      "  % (self._chain_id, n_diverging))\n",
      "/home/jovyan/pymc3/pymc3/step_methods/hmc/nuts.py:429: UserWarning: Chain 2 contains only 100 samples.\n",
      "  % (self._chain_id, n))\n",
      "/home/jovyan/pymc3/pymc3/step_methods/hmc/nuts.py:459: UserWarning: Chain 2 reached the maximum tree depth. Increase max_treedepth, increase target_accept or reparameterize.\n",
      "  'reparameterize.' % self._chain_id)\n",
      "/home/jovyan/pymc3/pymc3/step_methods/hmc/nuts.py:451: UserWarning: The acceptance probability in chain 2 does not match the target. It is 0.691331874096, but should be close to 0.8. Try to increase the number of tuning steps.\n",
      "  % (self._chain_id, mean_accept, target_accept))\n",
      "/home/jovyan/pymc3/pymc3/step_methods/hmc/nuts.py:467: UserWarning: Chain 2 contains 8 diverging samples after tuning. If increasing `target_accept` does not help try to reparameterize.\n",
      "  % (self._chain_id, n_diverging))\n",
      "100%|██████████| 600/600 [08:38<00:00,  1.16it/s]/home/jovyan/pymc3/pymc3/step_methods/hmc/nuts.py:429: UserWarning: Chain 0 contains only 100 samples.\n",
      "  % (self._chain_id, n))\n",
      "/home/jovyan/pymc3/pymc3/step_methods/hmc/nuts.py:459: UserWarning: Chain 0 reached the maximum tree depth. Increase max_treedepth, increase target_accept or reparameterize.\n",
      "  'reparameterize.' % self._chain_id)\n",
      "/home/jovyan/pymc3/pymc3/step_methods/hmc/nuts.py:467: UserWarning: Chain 0 contains 5 diverging samples after tuning. If increasing `target_accept` does not help try to reparameterize.\n",
      "  % (self._chain_id, n_diverging))\n",
      "\n",
      "/home/jovyan/pymc3/pymc3/step_methods/hmc/nuts.py:429: UserWarning: Chain 3 contains only 100 samples.\n",
      "  % (self._chain_id, n))\n",
      "/home/jovyan/pymc3/pymc3/step_methods/hmc/nuts.py:459: UserWarning: Chain 3 reached the maximum tree depth. Increase max_treedepth, increase target_accept or reparameterize.\n",
      "  'reparameterize.' % self._chain_id)\n",
      "/home/jovyan/pymc3/pymc3/step_methods/hmc/nuts.py:451: UserWarning: The acceptance probability in chain 3 does not match the target. It is 0.550616532328, but should be close to 0.8. Try to increase the number of tuning steps.\n",
      "  % (self._chain_id, mean_accept, target_accept))\n",
      "/home/jovyan/pymc3/pymc3/step_methods/hmc/nuts.py:467: UserWarning: Chain 3 contains 18 diverging samples after tuning. If increasing `target_accept` does not help try to reparameterize.\n",
      "  % (self._chain_id, n_diverging))\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": "iVBORw0KGgoAAAANSUhEUgAAAsUAAAE/CAYAAACuKr76AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nCCGEkJzn/wOkY7BvrfVhaAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f22e5b5e710>"
      ]
     },
     "metadata": {},
     "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": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
