PGLDM_Demo.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import evaluation.evaluate as evaluate\n",
    "import matplotlib.pyplot as plt\n",
    "import math_utils.matrix_utils as matrix_utils\n",
    "import models.regression_models as reg_models\n",
    "import models.PLDS as PLDS\n",
    "import numpy as np\n",
    "import os\n",
    "import PGLDM.PGLDM as PGLDM\n",
    "import PGLDM.SDP_optimize as SDP_optimize\n",
    "import visualization.visualization as viz_utils"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Utility methods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def extract_shared_disjoint(params, pgldm_params, sid_params):\n",
    "  \"\"\"Extracts shared and disjoint modes in primary and seconday observations to compare against learned modes.\"\"\"\n",
    "  shared_primary_inds = np.isin(params['rev_statesy'], params['rev_statesz'])\n",
    "  shared_states = params['rev_statesy'][shared_primary_inds]\n",
    "  shared_eigs = np.linalg.eigvals(matrix_utils.extract_block(params['A'], shared_states))\n",
    "\n",
    "  private_primary_states = np.delete(params['rev_statesy'], shared_primary_inds)\n",
    "  primary_only_eigs = np.linalg.eigvals(matrix_utils.extract_block(params['A'], private_primary_states))\n",
    "  \n",
    "  if 'eps_sysz' in params:\n",
    "    secondary_only_eigs = np.linalg.eigvals(params['eps_sysz']['A'])\n",
    "  else:\n",
    "    shared_secondary_inds = np.isin(params['rev_statesz'], params['rev_statesy'])\n",
    "    private_secondary_states = np.delete(params['rev_statesz'], shared_secondary_inds)\n",
    "    secondary_only_eigs = np.linalg.eigvals(matrix_utils.extract_block(params['A'], private_secondary_states))\n",
    "\n",
    "  pgldm_eigs = np.linalg.eigvals(pgldm_params['A'])\n",
    "  sid_eigs = np.linalg.eigvals(sid_params['A'])\n",
    "  return {\n",
    "    'shared_eigs': shared_eigs, 'primary_only_eigs': primary_only_eigs, 'secondary_only_eigs': secondary_only_eigs,\n",
    "    'pgldm_eigs': pgldm_eigs, 'sid_eigs': sid_eigs\n",
    "  }\n",
    "\n",
    "\n",
    "_TITLE_STR = lambda n1, nx: f'n1={n1},nx={nx}'\n",
    "def plot_true_and_learned_eigeninfo(params, pgldm_params, sid_params, title, sid_variant='sid'):\n",
    "  \"\"\"Visualizes the identified modes by both learning algorithms vs groud truth modes.\"\"\"\n",
    "  extracted_eigen_info = extract_shared_disjoint(params, pgldm_params, sid_params)\n",
    "\n",
    "  colors = { # Colors for visualizing the modes.\n",
    "    'shared': '#39b54a', 'primary only': '#e5542c', 'secondary only': '#0071bd',\n",
    "    'pgldm': '#39b54a', 'sid': '#e5542c'\n",
    "  }\n",
    "\n",
    "  viz_utils.plot_eigenvalues(\n",
    "    [extracted_eigen_info['shared_eigs'], extracted_eigen_info['primary_only_eigs'],\n",
    "     extracted_eigen_info['secondary_only_eigs'], extracted_eigen_info['pgldm_eigs'],\n",
    "     extracted_eigen_info['sid_eigs']],\n",
    "     title, labels=['shared', 'primary only', 'secondary only', 'pgldm', sid_variant],\n",
    "     markers=['o', 'o', 'o', 'x', 'x'],\n",
    "     edgecolors=[colors['shared'], colors['primary only'], colors['secondary only'], None, None],\n",
    "     facecolors=['None', 'None', 'None', colors['pgldm'], colors['sid']],\n",
    "     alpha_vals=[0.4, 0.4, 0.4, 0.8, 0.8],\n",
    "     bound_lims_to_circle=False, show_legend=True, legend_location='upper left', fig=None, ax=None)\n",
    "  plt.xlim([0.6, 1.0])\n",
    "  plt.ylim([-0.35, 0.35])\n",
    "  plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bernoulli-Gaussian system identification example\n",
    "\n",
    "Here we demonstrate PGLDM's usage with joint Bernoulli-Gaussian observations as primary-secondary time-series. Using the first stage only, we learn a latent model corresponding to true shared dimensionality using both PGLDM and bestLDS (the appropriate single time-series SSID algorithm for Bernoulli observations). We then visualize the learned modes on a pole-zero diagram alongside the true shared vs private modes to qualitatively evaluate learning."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = np.load(os.path.join(os.getcwd(), 'sample_data', 'sample_berngaus_sys.npz'), allow_pickle=True)\n",
    "\n",
    "### Prepare the data.\n",
    "Y, Z, params = data['Y'], data['Z'], data['params'][()]\n",
    "\n",
    "num_train = int(Y.shape[0]/2)\n",
    "Ytrain, Ztrain = Y[:num_train, :].astype('float64'), Z[:num_train, :]\n",
    "Ytest, Ztest = Y[num_train:, :].astype('float64'), Z[num_train:, :]\n",
    "\n",
    "##### Without loss of generality, demean the Gaussian observations.\n",
    "Zmean = np.mean(Ztrain, axis=0, keepdims=True)\n",
    "Ztrain -= Zmean\n",
    "Ztest -= Zmean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "n1 = nx = np.sum(np.isin(params['rev_statesz'], params['rev_statesy'])) # Shared dynamics dimensionality.\n",
    "i = 10 # horizon\n",
    "\n",
    "### PGLDM Stage 1 only.\n",
    "pgldm_params = PGLDM.PGLDM(i, nx, Ytrain.T, PGLDM.ObservationType.BernGaus, T=Ztrain.T, n1=n1, T_horizon=i)\n",
    "\n",
    "### bestLDS.\n",
    "bestLDS_params = PGLDM.PGLDM(i, nx, Ytrain.T, PGLDM.ObservationType.SingleBernoulli, n1=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Ignoring fixed x limits to fulfill fixed data aspect with adjustable data limits.\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_true_and_learned_eigeninfo(params, pgldm_params, bestLDS_params, _TITLE_STR(n1, nx), sid_variant='bestLDS')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Poisson-Poisson system identification example\n",
    "\n",
    "Here we demonstrate PGLDM's usage with joint Poisson-Poisson observations as primary-secondary time-series. Using the first stage only, we learn a latent model corresponding to true shared dimensionality using both PGLDM and PLDSID (the appropriate single time-series SSID algorithm for Poisson observations). We then visualize the learned modes on a pole-zero diagram alongside the true shared vs private modes to qualitatively evaluate learning."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = np.load(os.path.join(os.getcwd(), 'sample_data', 'sample_poispois_sys.npz'), allow_pickle=True)\n",
    "\n",
    "### Prepare the data.\n",
    "Y, T, params = data['Y'], data['T'], data['params'][()]\n",
    "\n",
    "num_train = int(Y.shape[0]/2)\n",
    "Ytrain, Ttrain = Y[:num_train, :].astype('float64'), T[:num_train, :]\n",
    "Ytest, Ttest = Y[num_train:, :].astype('float64'), T[num_train:, :]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0  1  8  9 10 11] [0 1 2 3 4 5 6 7]\n"
     ]
    }
   ],
   "source": [
    "print(params['rev_statesz'], params['rev_statesy'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "n1 = nx = np.sum(np.isin(params['rev_statesz'], params['rev_statesy'])) # Shared dynamics dimensionality.\n",
    "i = 10 # horizon\n",
    "\n",
    "### PGLDM Stage 1 only.\n",
    "pgldm_params = PGLDM.PGLDM(i, nx, Ytrain.T, PGLDM.ObservationType.PoisPois, T=Ttrain.T, n1=n1, T_horizon=i)\n",
    "\n",
    "### PLDSID.\n",
    "pldsid_params = PGLDM.PGLDM(i, nx, Ytrain.T, PGLDM.ObservationType.SinglePoisson, n1=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_true_and_learned_eigeninfo(params, pgldm_params, pldsid_params, _TITLE_STR(n1, nx), sid_variant='pldsid')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Poisson-Gaussian system identification example\n",
    "\n",
    "Here we demonstrate PGLDM's usage with joint Poisson-Gaussian observations as primary-secondary time-series. Using the first stage only, we learn a latent model corresponding to true shared dimensionality using both PGLDM and PLDSID (the appropriate single time-series SSID algorithm for Poisson observations). We then visualize the learned modes on a pole-zero diagram alongside the true shared vs private modes to qualitatively evaluate learning."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = np.load(os.path.join(os.getcwd(), 'sample_data', 'sample_poisgaus_sys.npz'), allow_pickle=True)\n",
    "\n",
    "### Prepare the data.\n",
    "Y, Z, params = data['Y'], data['Z'], data['params'][()]\n",
    "\n",
    "num_train = int(Y.shape[0]/2)\n",
    "Ytrain, Ztrain = Y[:num_train, :].astype('float64'), Z[:num_train, :]\n",
    "Ytest, Ztest = Y[num_train:, :].astype('float64'), Z[num_train:, :]\n",
    "\n",
    "##### Without loss of generality, demean the Gaussian observations.\n",
    "Zmean = np.mean(Ztrain, axis=0, keepdims=True)\n",
    "Ztrain -= Zmean\n",
    "Ztest -= Zmean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "n1 = nx = np.sum(np.isin(params['rev_statesz'], params['rev_statesy'])) # Shared dynamics dimensionality.\n",
    "i = 10 # horizon\n",
    "\n",
    "### PGLDM Stage 1 only.\n",
    "pgldm_params = PGLDM.PGLDM(i, nx, Ytrain.T, PGLDM.ObservationType.PoisGaus, T=Ztrain.T, n1=n1, T_horizon=i)\n",
    "\n",
    "### PLDSID.\n",
    "pldsid_params = PGLDM.PGLDM(i, nx, Ytrain.T, PGLDM.ObservationType.SinglePoisson, n1=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_true_and_learned_eigeninfo(params, pgldm_params, pldsid_params, _TITLE_STR(n1, nx), sid_variant='pldsid')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Stage 3 Demonstration\n",
    "\n",
    "Using the same Poisson-Gaussian simulation, we now demonstrate usage of the optional 3rd state to learn the latents private to the secondary time series. Here we run all three stages, but stage 3 can be used without the inclusion of stage 2 (e.g., stage 1 + 3 only). After learning the private modes, we visualize them in a pole-zero diagram to visually inspect how well the private modes were learned."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "n1 = np.sum(np.isin(params['rev_statesz'], params['rev_statesy']))\n",
    "nx = len(params['rev_statesy'])\n",
    "# Please refer to Appendix A.7.1 for how private latents x3 were simulated for Gaussian observations.\n",
    "n3 = params['eps_sysz']['A'].shape[0]\n",
    "\n",
    "i = 10 # horizon\n",
    "\n",
    "### PGLDM Stage 1 + 2 + 3.\n",
    "pgldm_params = PGLDM.PGLDM(i, nx, Ytrain.T, PGLDM.ObservationType.PoisGaus, T=Ztrain.T, n1=n1, T_horizon=i, n3=n3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eigeninfo = extract_shared_disjoint(params, pgldm_params, pldsid_params)\n",
    "pgldm_stage3_modes = np.linalg.eigvals(pgldm_params['secondary_private_params']['A'])\n",
    "\n",
    "colors = {'secondary only': '#0071bd', 'pgldm': '#39b54a'}\n",
    "\n",
    "viz_utils.plot_eigenvalues(\n",
    "  [eigeninfo['secondary_only_eigs'], pgldm_stage3_modes],\n",
    "  f'n1={n1},n2={nx-n1},n3={n3}', labels=['secondary only', 'pgldm stage 3'],\n",
    "   markers=['o','x'],\n",
    "   edgecolors=[colors['secondary only'], None],\n",
    "   facecolors=['None', colors['pgldm']],\n",
    "   alpha_vals=[0.4, 0.8],\n",
    "   bound_lims_to_circle=False, show_legend=True, legend_location='upper left', fig=None, ax=None)\n",
    "plt.xlim([0.7, 1.0])\n",
    "plt.ylim([-0.35, 0.35])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Demonstration of secondary time-series decoding and primary time-series self-prediction using the same system.\n",
    "\n",
    "Using a different simulated Poisson-Gaussian system with more observations and larger difference between the numer of shared vs private primary states, we demonstrate PGLDM's ability to improve decoding performance due to the explicit modeling of shared dynamics."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = np.load(os.path.join(os.getcwd(), 'sample_data', 'sample_sys.npz'), allow_pickle=True)\n",
    "\n",
    "### Prepare the data.\n",
    "Y, Z, params = data['Y'], data['Z'], data['params'][()]\n",
    "\n",
    "num_train = int(Y.shape[0]/2)\n",
    "Ytrain, Ztrain = Y[:num_train, :].astype('float64'), Z[:num_train, :]\n",
    "Ytest, Ztest = Y[num_train:, :].astype('float64'), Z[num_train:, :]\n",
    "\n",
    "##### Without loss of generality, demean the Gaussian observations.\n",
    "Zmean = np.mean(Ztrain, axis=0, keepdims=True)\n",
    "Ztrain -= Zmean\n",
    "Ztest -= Zmean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The optimal value is 46.35446703999908 with status: optimal\n",
      "The optimal value is 6.152844128904781 with status: optimal\n"
     ]
    }
   ],
   "source": [
    "n1 = nx = np.sum(np.isin(params['rev_statesz'], params['rev_statesy'])) # Shared dynamics dimensionality.\n",
    "i = 10 # horizon\n",
    "\n",
    "### PGLDM Stage 1 only.\n",
    "pgldm_params = PGLDM.PGLDM(i, nx, Ytrain.T, PGLDM.ObservationType.PoisGaus, T=Ztrain.T, n1=n1, T_horizon=i)\n",
    "\n",
    "### PLDSID.\n",
    "pldsid_params = PGLDM.PGLDM(i, nx, Ytrain.T, PGLDM.ObservationType.SinglePoisson, n1=0)\n",
    "\n",
    "## Use convex optimization (Appendix A.3) to compute noise covariances necessary to construct the point-process\n",
    "## filter (Eden & Brown, 2008).\n",
    "pgldm_params = SDP_optimize.optimize(pgldm_params)\n",
    "pldsid_params = SDP_optimize.optimize(pldsid_params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Warning: no baseline d is provided...will set d=0.\n"
     ]
    }
   ],
   "source": [
    "### NOTE: This block will take some time to run as we're testing on 1e6 contiguous samples and the point-process\n",
    "### filter runs recursively.\n",
    "\n",
    "#### PLDS model using PGLDM parameters.\n",
    "pgldm_sys = PLDS.update_missing_params_and_construct_PLDS(pgldm_params)\n",
    "\n",
    "### Predict the test data.\n",
    "other_out = {'Z': pgldm_params['Cz']}\n",
    "pgldm_y_pred, _, other_est = pgldm_sys.predict(Ytest, other_out)\n",
    "pgldm_z_pred = other_est['Z']\n",
    "\n",
    "pgldm_z_evalres = evaluate.evaluate_results(Ztest, pgldm_z_pred, ['CC'])['CC']\n",
    "\n",
    "#### Handle prediction covariances to compute AUC.\n",
    "Pp = other_est.get('Pp', None) # Prediction error covariance.\n",
    "assert (Pp is not None)\n",
    "log_rate_covariances = Pp @ pgldm_params['C'].T # (time, nx, nr)\n",
    "log_rate_covariances = np.transpose(log_rate_covariances, (0, 2, 1)) @ pgldm_params['C'].T # (time, nr, nr)\n",
    "pgldm_y_evalres = evaluate.evaluate_results(\n",
    "                      Ytest, pgldm_y_pred, ['AUC'], predicted_covariances=log_rate_covariances)['AUC']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "#### PLDS model using PLDSID parameters.\n",
    "pldsid_sys = PLDS.update_missing_params_and_construct_PLDS(pldsid_params)\n",
    "\n",
    "##### First fit Cz.\n",
    "_, x_pred, _ = pldsid_sys.predict(Ytrain, {}) # Predict xTrain.\n",
    "reg_kwargs = {'fit_intercept': True}\n",
    "regression = reg_models.RegressionModel(reg_models.RegressionMethod.OLS_REG)\n",
    "## Must be (num_samples, num_features)\n",
    "regression.fit(x_pred, Ztrain, **reg_kwargs) # Regress training data onto the estimated latent states.\n",
    "reg_weights, reg_intercept = regression.weights()\n",
    "pldsid_params['Cz'] = reg_weights\n",
    "\n",
    "##### Now predict test data.\n",
    "other_out = {'Z': pldsid_params['Cz']}\n",
    "pldsid_y_pred, _, other_est = pldsid_sys.predict(Ytest, other_out)\n",
    "pldsid_z_pred = other_est['Z']\n",
    "\n",
    "pldsid_z_evalres = evaluate.evaluate_results(Ztest, pldsid_z_pred, ['CC'])['CC']\n",
    "\n",
    "#### Handle prediction covariances to compute AUC.\n",
    "Pp = other_est.get('Pp', None) # Prediction error covariance.\n",
    "assert (Pp is not None)\n",
    "log_rate_covariances = Pp @ pldsid_params['C'].T # (time, nx, nr)\n",
    "log_rate_covariances = np.transpose(log_rate_covariances, (0, 2, 1)) @ pldsid_params['C'].T # (time, nr, nr)\n",
    "pldsid_y_evalres = evaluate.evaluate_results(\n",
    "                    Ytest, pldsid_y_pred, ['AUC'], predicted_covariances=log_rate_covariances)['AUC']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PGLDM Z prediction CC 0.46216264610683616, PLDSID Z prediction CC 0.40961546633248686\n",
      "PGLDM Y prediction AUC 0.5447589112937984, PLDSID Y prediction AUC 0.5592364736580343\n"
     ]
    }
   ],
   "source": [
    "print(f'PGLDM Z prediction CC {pgldm_z_evalres.mean()}, PLDSID Z prediction CC {pldsid_z_evalres.mean()}')\n",
    "print(f'PGLDM Y prediction AUC {pgldm_y_evalres.mean()}, PLDSID Y prediction AUC {pldsid_y_evalres.mean()}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Next, we demonstrate decoding and self-prediction performance when including stage 2 to model the private dynamics in the primary time-series."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The optimal value is 6.034638926763588 with status: optimal\n",
      "The optimal value is 2.5482397391823426 with status: optimal\n"
     ]
    }
   ],
   "source": [
    "n1 = np.sum(np.isin(params['rev_statesz'], params['rev_statesy']))\n",
    "nx = len(params['rev_statesy'])\n",
    "i = 10 # horizon\n",
    "\n",
    "# PGDLM Stage 1 + 2.\n",
    "pgldm_params = PGLDM.PGLDM(i, nx, Ytrain.T, PGLDM.ObservationType.PoisGaus, T=Ztrain.T, n1=n1, T_horizon=i)\n",
    "pgldm_params = SDP_optimize.optimize(pgldm_params)\n",
    "\n",
    "# PLDSID.\n",
    "pldsid_params = PGLDM.PGLDM(i, nx, Ytrain.T, PGLDM.ObservationType.SinglePoisson, n1=0)\n",
    "pldsid_params = SDP_optimize.optimize(pldsid_params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Warning: no baseline d is provided...will set d=0.\n"
     ]
    }
   ],
   "source": [
    "### NOTE: This block will take some time to run as we're testing on 1e6 contiguous amples and the point-process\n",
    "### filter runs recursively.\n",
    "\n",
    "#### PLDS model using PGLDM parameters.\n",
    "pgldm_sys = PLDS.update_missing_params_and_construct_PLDS(pgldm_params)\n",
    "\n",
    "#### Predict test data.\n",
    "other_out = {'Z': pgldm_params['Cz']}\n",
    "pgldm_y_pred, _, other_est = pgldm_sys.predict(Ytest, other_out)\n",
    "pgldm_z_pred = other_est['Z']\n",
    "\n",
    "pgldm_z_evalres = evaluate.evaluate_results(Ztest, pgldm_z_pred, ['CC'])['CC']\n",
    "\n",
    "#### Handle prediction covariances to compute AUC.\n",
    "Pp = other_est.get('Pp', None) # Prediction error covariance.\n",
    "assert (Pp is not None)\n",
    "log_rate_covariances = Pp @ pgldm_params['C'].T # (time, nx, nr)\n",
    "log_rate_covariances = np.transpose(log_rate_covariances, (0, 2, 1)) @ pgldm_params['C'].T # (time, nr, nr)\n",
    "pgldm_y_evalres = evaluate.evaluate_results(\n",
    "                      Ytest, pgldm_y_pred, ['AUC'], predicted_covariances=log_rate_covariances)['AUC']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "#### PLDS model using PLDSID parameters.\n",
    "pldsid_sys = PLDS.update_missing_params_and_construct_PLDS(pldsid_params)\n",
    "\n",
    "##### First fit Cz.\n",
    "_, x_pred, _ = pldsid_sys.predict(Ytrain, {}) # Predict xTrain.\n",
    "reg_kwargs = {'fit_intercept': True}\n",
    "regression = reg_models.RegressionModel(reg_models.RegressionMethod.OLS_REG)\n",
    "## Must be (num_samples, num_features)\n",
    "regression.fit(x_pred, Ztrain, **reg_kwargs) # Regress observations onto estimated latents.\n",
    "reg_weights, reg_intercept = regression.weights()\n",
    "pldsid_params['Cz'] = reg_weights\n",
    "\n",
    "##### Now predict test data.\n",
    "other_out = {'Z': pldsid_params['Cz']}\n",
    "pldsid_y_pred, _, other_est = pldsid_sys.predict(Ytest, other_out)\n",
    "pldsid_z_pred = other_est['Z']\n",
    "\n",
    "pldsid_z_evalres = evaluate.evaluate_results(Ztest, pldsid_z_pred, ['CC'])['CC']\n",
    "\n",
    "#### Handle prediction covariances to compute AUC.\n",
    "Pp = other_est.get('Pp', None) # Prediction error covariance.\n",
    "assert (Pp is not None)\n",
    "log_rate_covariances = Pp @ pldsid_params['C'].T # (time, nx, nr)\n",
    "log_rate_covariances = np.transpose(log_rate_covariances, (0, 2, 1)) @ pldsid_params['C'].T # (time, nr, nr)\n",
    "pldsid_y_evalres = evaluate.evaluate_results(\n",
    "                    Ytest, pldsid_y_pred, ['AUC'], predicted_covariances=log_rate_covariances)['AUC']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PGLDM Z prediction CC 0.4773237849353172, PLDSID Z prediction CC 0.47613448679244974\n",
      "PGLDM Y prediction AUC 0.5711734082729463, PLDSID Y prediction AUC 0.5711118238927165\n"
     ]
    }
   ],
   "source": [
    "print(f'PGLDM Z prediction CC {pgldm_z_evalres.mean()}, PLDSID Z prediction CC {pldsid_z_evalres.mean()}')\n",
    "print(f'PGLDM Y prediction AUC {pgldm_y_evalres.mean()}, PLDSID Y prediction AUC {pldsid_y_evalres.mean()}')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "pgldm_demo",
   "language": "python",
   "name": "pgldm_demo"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}