dec_recommender.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import arviz as az\n",
    "import matplotlib.pyplot as plt\n",
    "from collections import Counter\n",
    "\n",
    "import jax\n",
    "import jax.numpy as jnp\n",
    "from jax import random\n",
    "from jax.scipy.special import expit\n",
    "\n",
    "import numpyro\n",
    "import numpyro.distributions as dist\n",
    "from numpyro.distributions import constraints\n",
    "from numpyro.infer import SVI, Trace_ELBO, Predictive, NUTS, MCMC\n",
    "\n",
    "rng_np = np.random.default_rng(111)\n",
    "\n",
    "n_factors_exposure = 10\n",
    "n_factors_outcome = 10\n",
    "K = 5\n",
    "\n",
    "numpyro.set_platform('cpu')\n",
    "numpyro.set_host_device_count(n=5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# MovieLens data\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(100000, 3)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>userId</th>\n",
       "      <th>movieId</th>\n",
       "      <th>rating</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>196</td>\n",
       "      <td>242</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>186</td>\n",
       "      <td>302</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>22</td>\n",
       "      <td>377</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   userId  movieId  rating\n",
       "0     196      242       3\n",
       "1     186      302       3\n",
       "2      22      377       1"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "names = ['userId', 'movieId', 'rating', 'timestamp']\n",
    "df_ratings = pd.read_csv('./ml-100k/u.data', sep='\\t', names=names)\n",
    "df_ratings = df_ratings.drop('timestamp', axis=1)\n",
    "print(df_ratings.shape)\n",
    "df_ratings.head(3)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "train-test split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(943, 1682) (943, 1682)\n"
     ]
    }
   ],
   "source": [
    "# Taken from https://docs.pymc.io/notebooks/probabilistic_matrix_factorization.html\n",
    "\n",
    "# Define a function for splitting train/test data.\n",
    "def split_train_test(data, percent_test, rng):\n",
    "    \"\"\"Split the data into train/test sets.\"\"\"\n",
    "    n, m = data.shape             # # users, # movies\n",
    "    N = n * m                     # # cells in matrix\n",
    "    # Prepare train/test ndarrays.\n",
    "    train = data.copy()\n",
    "    test = np.ones(data.shape) * np.nan\n",
    "    # Draw random sample of training data to use for testing.\n",
    "    tosample = np.where(~np.isnan(train))       # ignore nan values in data\n",
    "    idx_pairs = list(zip(tosample[0], tosample[1]))   # tuples of row/col index pairs\n",
    "    test_size = int(len(idx_pairs) * percent_test)  # use a % of data as test set\n",
    "    train_size = len(idx_pairs) - test_size   # and remainder for training\n",
    "    indices = np.arange(len(idx_pairs))         # indices of index pairs\n",
    "    sample = rng.choice(indices, replace=False, size=test_size)\n",
    "    # Transfer random sample from train set to test set.\n",
    "    for idx in sample:\n",
    "        idx_pair = idx_pairs[idx]\n",
    "        test[idx_pair] = train[idx_pair]  # transfer to test set\n",
    "        train[idx_pair] = np.nan          # remove from train set\n",
    "    # Verify everything worked properly\n",
    "    assert(train_size == N-np.isnan(train).sum())\n",
    "    assert(test_size == N-np.isnan(test).sum())\n",
    "    # Return train set and test set\n",
    "    return train, test\n",
    "\n",
    "\n",
    "all_users = np.sort(df_ratings.userId.unique())\n",
    "all_movies = np.sort(df_ratings.movieId.unique())\n",
    "df_dense_data = df_ratings.pivot_table(index='userId', columns='movieId', values='rating')\n",
    "assert all(df_dense_data.columns == all_movies)\n",
    "assert all(df_dense_data.index == all_users)\n",
    "\n",
    "n_users, n_items = all_users.shape[0], all_movies.shape[0]\n",
    "train, test = split_train_test(df_dense_data.values, 0.2, rng=rng_np)\n",
    "\n",
    "print(train.shape, test.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exposure model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(943, 1682)\n",
      "0.050437354 80000 80000\n"
     ]
    }
   ],
   "source": [
    "exposure_train = jnp.nan_to_num(train, nan=0)\n",
    "exposure_train = jnp.where(exposure_train > 0, 1, 0)\n",
    "print(exposure_train.shape)\n",
    "print(exposure_train.mean(), exposure_train.sum(), jnp.count_nonzero(exposure_train))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(943, 1682)\n",
      "0.10843464 171991 147510 25\n"
     ]
    }
   ],
   "source": [
    "def exposure_model(n_users: int, n_items: int, n_factors: int, exposure=None):\n",
    "    \"\"\"Hierarchical Poisson factorization model.\"\"\"\n",
    "    plate_users = numpyro.plate('plate_users', n_users, dim=-1)\n",
    "    plate_items = numpyro.plate('plate_items', n_items, dim=-1)\n",
    "    c = 5  # 10\n",
    "    r = 1  # 3\n",
    "    with plate_users:\n",
    "        activity = numpyro.sample('activity', dist.Gamma(c, r))\n",
    "        preferences = numpyro.sample('preferences', dist.Gamma(0.3, activity), sample_shape=(n_factors,))\n",
    "    with plate_items:\n",
    "        popularity = numpyro.sample('popularity', dist.Gamma(c, r))\n",
    "        attributes = numpyro.sample('attributes', dist.Gamma(0.3, popularity), sample_shape=(n_factors,))\n",
    "    rates = numpyro.deterministic('rates', preferences.T @ attributes)\n",
    "    obs = numpyro.sample('obs', dist.Poisson(rates), obs=exposure)\n",
    "    return obs\n",
    "\n",
    "\n",
    "\n",
    "def exposure_guide(n_users: int, n_items: int, n_factors: int, exposure):\n",
    "    \"\"\"Hierarchical Poisson factorization guide.\"\"\"\n",
    "    plate_users = numpyro.plate('plate_users', n_users, dim=-1)\n",
    "    plate_items = numpyro.plate('plate_items', n_items, dim=-1)\n",
    "    with plate_items:\n",
    "        popularity_concentration = numpyro.param(\n",
    "            'popularity_concentration',\n",
    "            5 * jnp.ones(shape=(n_items,)),\n",
    "            constraint=constraints.positive\n",
    "        )\n",
    "        popularity_rate = numpyro.param(\n",
    "            'popularity_rate',\n",
    "            1 * jnp.ones(shape=(n_items,)),\n",
    "            constraint=constraints.positive\n",
    "        )\n",
    "        popularity = numpyro.sample(\n",
    "            'popularity', dist.Gamma(popularity_concentration, popularity_rate)\n",
    "        )\n",
    "        attributes_concentration = numpyro.param(\n",
    "            'attributes_concentration',\n",
    "            0.3 * jnp.ones(shape=(n_items,)),\n",
    "            constraint=constraints.positive\n",
    "        )\n",
    "        attributes = numpyro.sample(\n",
    "            'attributes', \n",
    "            dist.Gamma(attributes_concentration, popularity), \n",
    "            sample_shape=(n_factors,)\n",
    "        )\n",
    "    with plate_users:\n",
    "        activity_concentration = numpyro.param(\n",
    "            'activity_concentration',\n",
    "            5 * jnp.ones(shape=(n_users,)),\n",
    "            constraint=constraints.positive\n",
    "        )\n",
    "        activity_rate = numpyro.param(\n",
    "            'activity_rate',\n",
    "            1 * jnp.ones(shape=(n_users,)),\n",
    "            constraint=constraints.positive\n",
    "        )\n",
    "        activity = numpyro.sample(\n",
    "            'activity', dist.Gamma(activity_concentration, activity_rate)\n",
    "        )\n",
    "        preferences_concentration = numpyro.param(\n",
    "            'preferences_concentration',\n",
    "            0.3 * jnp.ones(shape=(n_users,)),\n",
    "            constraint=constraints.positive\n",
    "        )\n",
    "        preferences = numpyro.sample(\n",
    "            'preferences', \n",
    "            dist.Gamma(preferences_concentration, activity), \n",
    "            sample_shape=(n_factors,)\n",
    "        )\n",
    "\n",
    "\n",
    "with numpyro.handlers.seed(rng_seed=1234):\n",
    "    prior_sample = exposure_model(n_users, n_items, n_factors_exposure)\n",
    "    print(prior_sample.shape)\n",
    "    print(prior_sample.mean(), prior_sample.sum(), jnp.count_nonzero(prior_sample), prior_sample.max())\n",
    "    exposure_guide(n_users, n_items, n_factors_exposure, exposure_train)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "final loss: 273203.78125\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# SVI\n",
    "n_iters = 260\n",
    "step_size = 0.1\n",
    "optimizer = numpyro.optim.Adam(step_size=step_size)\n",
    "svi = SVI(exposure_model, exposure_guide, optimizer, loss=Trace_ELBO(num_particles=1))\n",
    "\n",
    "init_state = svi.init(\n",
    "    random.PRNGKey(55), \n",
    "    n_users, n_items, n_factors_exposure, exposure_train\n",
    ")\n",
    "\n",
    "state, losses = jax.lax.scan(\n",
    "    lambda state, i: svi.update(state, n_users, n_items, n_factors_exposure, exposure_train), \n",
    "    init_state, jnp.arange(n_iters)\n",
    ")\n",
    "print(f'final loss: {losses[-1]}')\n",
    "svi_params = svi.get_params(svi_state=state)\n",
    "plt.plot(losses);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# # MCMC\n",
    "# rng_key = random.PRNGKey(1234)\n",
    "# nuts_kernel = NUTS(hpf_model)\n",
    "# mcmc = MCMC(nuts_kernel, num_samples=200, num_warmup=1000, num_chains=1)\n",
    "# mcmc.run(rng_key, n_users, n_items, n_factors_exposure, exposure_train)\n",
    "# posterior_samples = mcmc.get_samples()\n",
    "\n",
    "# for k, a in posterior_samples.items():\n",
    "#     print(k, a.shape)\n",
    "#     jnp.save(f'./exposure_samples/{k}.npy', a)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Posterior predictive checks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(200, 943, 1682)\n"
     ]
    }
   ],
   "source": [
    "# MCMC rates\n",
    "# rates = np.load('./exposure_samples/rates.npy')\n",
    "# print(rates.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(200, 943, 1682)\n"
     ]
    }
   ],
   "source": [
    "# SVI rates\n",
    "post_predictive = Predictive(\n",
    "    exposure_model, guide=hpf_guide, params=svi_params, num_samples=200,\n",
    "    return_sites=['rates']\n",
    ")\n",
    "posterior = post_predictive(\n",
    "    random.PRNGKey(90),\n",
    "    n_users, n_items, n_factors_exposure, exposure_train\n",
    ")\n",
    "rates = posterior['rates']\n",
    "print(rates.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(200, 943, 1682)"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "posterior_samples = rng_np.poisson(rates)\n",
    "posterior_samples.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 792x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(ncols=2, figsize=(11, 4), sharey=True)\n",
    "_, bins_user, _ = axs[0].hist(exposure_train.sum(axis=1), bins=10)\n",
    "axs[0].set(title='Distribution of user views');\n",
    "_, bins_movie, _ = axs[1].hist(exposure_train.sum(axis=0), bins=10)\n",
    "axs[1].set(title='Distribution of movies views');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 792x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "colors = [\n",
    "    '#c7e9c0','#a1d99b','#74c476','#31a354', '#006d2c',\n",
    "    '#31a354','#74c476','#a1d99b','#c7e9c0',\n",
    "]\n",
    "quantiles = np.arange(0.1, 1, 0.1)\n",
    "\n",
    "user_views_quantiles = np.quantile(posterior_samples.sum(axis=2), q=quantiles, axis=0)\n",
    "movie_views_quantiles = np.quantile(posterior_samples.sum(axis=1), q=quantiles, axis=0)\n",
    "\n",
    "fig, axs = plt.subplots(ncols=2, figsize=(11, 4), sharey=True)\n",
    "axs[0].hist(\n",
    "    user_views_quantiles.T, histtype='step', color=colors, linewidth=3, bins=bins_user\n",
    ")\n",
    "axs[0].set(title='Posterior distribution of user views');\n",
    "axs[1].hist(\n",
    "    movie_views_quantiles.T, histtype='step', color=colors, linewidth=3, bins=bins_movie\n",
    ")\n",
    "axs[1].set(title='Posterior distribution of movies views');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 2160x504 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(30, 7))\n",
    "axs = fig.subplot_mosaic(\n",
    "    '''\n",
    "    ..O..\n",
    "    ABCDE\n",
    "    '''\n",
    ")\n",
    "# training data\n",
    "axs['O'].spy(exposure_train)\n",
    "axs['O'].set(title='training data')\n",
    "axs['O'].set_axis_off()\n",
    "# samples from the posterior\n",
    "ids = rng_np.integers(0, posterior_samples.shape[0], size=5)\n",
    "for k, i in zip('ABCDE', range(0, 5)):\n",
    "    axs[k].spy(posterior_samples[i, ...])\n",
    "    axs[k].set(title=f'sample {i}')\n",
    "    axs[k].set_axis_off()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### TODO: \n",
    "* Measure predictive power using the median value of the rates\n",
    "* Prior predictive checks and parameter recovery\n",
    "* EDA confounders"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Outcome model\n",
    "\n",
    "* stronger prior on the final outcome"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(943, 1682)\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# expected value of the rates\n",
    "confounders = jnp.load('./exposure_samples/rates.npy').mean(axis=0)\n",
    "# print(confounders.min(), confounders.max())\n",
    "print(confounders.shape)\n",
    "plt.hist(confounders.flatten(), bins=30);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(943, 1682)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "DeviceArray([[5., 3., 0., ..., 0., 0., 0.],\n",
       "             [0., 0., 0., ..., 0., 0., 0.],\n",
       "             [0., 0., 0., ..., 0., 0., 0.],\n",
       "             ...,\n",
       "             [5., 0., 0., ..., 0., 0., 0.],\n",
       "             [0., 0., 0., ..., 0., 0., 0.],\n",
       "             [0., 5., 0., ..., 0., 0., 0.]], dtype=float32)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mask_no_nan = (~jnp.isnan(train))\n",
    "ratings_train = jnp.nan_to_num(train, nan=0)\n",
    "print(ratings_train.shape)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(943, 1682)\n",
      "5.0\n"
     ]
    }
   ],
   "source": [
    "def outcome_model(\n",
    "    n_users: int,\n",
    "    n_items: int,\n",
    "    n_factors: int,\n",
    "    exposure,\n",
    "    confounders,\n",
    "    mask,\n",
    "    ratings=None\n",
    "):\n",
    "    plate_users = numpyro.plate('plate_users', n_users, dim=-1)\n",
    "    plate_items = numpyro.plate('plate_items', n_items, dim=-1)\n",
    "    c = 5\n",
    "    r = 1\n",
    "    with plate_users:\n",
    "        activity = numpyro.sample('activity', dist.Gamma(c, r))\n",
    "        preferences = numpyro.sample('preferences', dist.Gamma(.1, activity), sample_shape=(n_factors,))\n",
    "    with plate_items:\n",
    "        popularity = numpyro.sample('popularity', dist.Gamma(c, r))\n",
    "        attributes = numpyro.sample('attributes', dist.Gamma(.1, popularity), sample_shape=(n_factors,))\n",
    "    gammas = numpyro.sample('gammas', dist.Normal(0., 1), sample_shape=(n_users, 1))\n",
    "    beta_0 = numpyro.sample('beta_0', dist.Normal(0., 1))\n",
    "    rates = (preferences.T @ attributes) * exposure\n",
    "    adjustment = jnp.exp(beta_0 + (gammas * confounders))\n",
    "    # print(rates.min(), rates.max())\n",
    "    # print(adjustment.min(), adjustment.max())\n",
    "    mean = numpyro.deterministic('mean', rates + adjustment)\n",
    "    # print(mean.min(), mean.max())\n",
    "    masked_ratings = dist.Poisson(mean).mask(mask)\n",
    "    obs = numpyro.sample('obs', masked_ratings, obs=ratings)\n",
    "    return obs\n",
    "\n",
    "\n",
    "with numpyro.handlers.seed(rng_seed=101):\n",
    "    prior_sample = outcome_model(\n",
    "        n_users, n_items, n_factors_outcome, exposure_train, confounders, mask_no_nan,\n",
    "        ratings=ratings_train\n",
    "    )\n",
    "    print(prior_sample.shape)\n",
    "    print(prior_sample.max())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "\n",
    "def outcome_guide(\n",
    "    n_users: int,\n",
    "    n_items: int,\n",
    "    n_factors: int,\n",
    "    exposure,\n",
    "    confounders,\n",
    "    mask,\n",
    "    ratings\n",
    "):\n",
    "    gammas_loc = numpyro.param('gammas_loc', 0.00001*jnp.ones(shape=(n_users, 1)))\n",
    "    gammas_scale = numpyro.param(\n",
    "        'gammas_scale', 1.0*jnp.ones(shape=(n_users, 1)), \n",
    "        constraint=constraints.positive\n",
    "    )\n",
    "    beta_0_loc = numpyro.param('beta_0_loc', jnp.array([0.0]))\n",
    "    beta_0_scale = numpyro.param('beta_0_scale', jnp.array([1.0]), constraint=constraints.positive)\n",
    "    \n",
    "    gammas = numpyro.sample('gammas', dist.Normal(gammas_loc, gammas_scale))\n",
    "    beta_0 = numpyro.sample('beta_0', dist.Normal(beta_0_loc, beta_0_scale))\n",
    "\n",
    "    plate_users = numpyro.plate('plate_users', n_users, dim=-1)\n",
    "    plate_items = numpyro.plate('plate_items', n_items, dim=-1)\n",
    "    with plate_items:\n",
    "        popularity_concentration = numpyro.param(\n",
    "            'popularity_concentration',\n",
    "            1.0 * jnp.ones(shape=(n_items,)),\n",
    "            constraint=constraints.positive\n",
    "        )\n",
    "        popularity_rate = numpyro.param(\n",
    "            'popularity_rate',\n",
    "            1.0 * jnp.ones(shape=(n_items,)),\n",
    "            constraint=constraints.positive\n",
    "        )\n",
    "        popularity = numpyro.sample(\n",
    "            'popularity', dist.Gamma(popularity_concentration, popularity_rate)\n",
    "        )\n",
    "        attributes_concentration = numpyro.param(\n",
    "            'attributes_concentration',\n",
    "            1 * jnp.ones(shape=(n_items,)),\n",
    "            constraint=constraints.positive\n",
    "        )\n",
    "        attributes = numpyro.sample(\n",
    "            'attributes', \n",
    "            dist.Gamma(attributes_concentration, popularity), \n",
    "            sample_shape=(n_factors,)\n",
    "        )\n",
    "        # print(attributes.shape)\n",
    "    with plate_users:\n",
    "        activity_concentration = numpyro.param(\n",
    "            'activity_concentration',\n",
    "            1.0 * jnp.ones(shape=(n_users,)),\n",
    "            constraint=constraints.positive\n",
    "        )\n",
    "        activity_rate = numpyro.param(\n",
    "            'activity_rate',\n",
    "            1.0 * jnp.ones(shape=(n_users,)),\n",
    "            constraint=constraints.positive\n",
    "        )\n",
    "        activity = numpyro.sample(\n",
    "            'activity', dist.Gamma(activity_concentration, activity_rate)\n",
    "        )\n",
    "        preferences_concentration = numpyro.param(\n",
    "            'preferences_concentration',\n",
    "            1 * jnp.ones(shape=(n_users,)),\n",
    "            constraint=constraints.positive\n",
    "        )\n",
    "        preferences = numpyro.sample(\n",
    "            'preferences', \n",
    "            dist.Gamma(preferences_concentration, activity),\n",
    "            sample_shape=(n_factors,)\n",
    "        )\n",
    "        # print(preferences.shape)\n",
    "\n",
    "\n",
    "with numpyro.handlers.seed(rng_seed=101):\n",
    "    outcome_guide(\n",
    "        n_users, n_items, n_factors_outcome, exposure_train, confounders, mask_no_nan,\n",
    "        ratings=ratings_train\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "final loss: 195697.1875\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# SVI\n",
    "# n_iters = 47\n",
    "# step_size = 0.07\n",
    "n_iters = 36\n",
    "step_size = 0.1\n",
    "optimizer = numpyro.optim.Adam(step_size=step_size)\n",
    "svi = SVI(outcome_model, outcome_guide, optimizer, loss=Trace_ELBO(num_particles=1))\n",
    "\n",
    "init_state = svi.init(\n",
    "    random.PRNGKey(55), \n",
    "    n_users, n_items, n_factors_outcome, exposure_train, confounders, mask_no_nan,\n",
    "    ratings_train\n",
    ")\n",
    "\n",
    "state, losses = jax.lax.scan(\n",
    "    lambda state, i: svi.update(\n",
    "        state, \n",
    "        n_users, n_items, n_factors_outcome, exposure_train, confounders, mask_no_nan,\n",
    "        ratings_train\n",
    "    ), \n",
    "    init_state, jnp.arange(n_iters)\n",
    ")\n",
    "print(f'final loss: {losses[-1]}')\n",
    "svi_params = svi.get_params(svi_state=state)\n",
    "plt.plot(losses);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# # MCMC\n",
    "# rng_key = random.PRNGKey(1234)\n",
    "# nuts_kernel = NUTS(outcome_model)\n",
    "# mcmc = MCMC(nuts_kernel, num_samples=200, num_warmup=200, num_chains=1)\n",
    "# mcmc.run(\n",
    "#     rng_key, \n",
    "#     n_users, n_items, n_factors_outcome, exposure_train, confounders, mask_no_nan,\n",
    "#     ratings_train\n",
    "# )\n",
    "# posterior_samples = mcmc.get_samples()\n",
    "\n",
    "# # for k, a in posterior_samples.items():\n",
    "# #     print(k, a.shape)\n",
    "# #     jnp.save(f'./outcome_samples/{k}.npy', a)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(100, 943, 1682)\n"
     ]
    }
   ],
   "source": [
    "# SVI rates\n",
    "post_predictive = Predictive(\n",
    "    outcome_model, guide=outcome_guide, params=svi_params, num_samples=100,\n",
    "    return_sites=['mean']\n",
    ")\n",
    "posterior = post_predictive(\n",
    "    random.PRNGKey(909),\n",
    "    n_users, n_items, n_factors_outcome, exposure_train, confounders, mask_no_nan,\n",
    "    ratings_train\n",
    ")\n",
    "rates = posterior['mean']\n",
    "print(rates.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 943, 1682)"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "posterior_samples = rng_np.poisson(rates)\n",
    "posterior_samples.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(posterior_samples[0, ...].flatten());"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "# TODO: \n",
    "# Posterior predictive checks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "# Results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "# Functions taken from https://docs.pymc.io/notebooks/probabilistic_matrix_factorization.html\n",
    "\n",
    "def rmse(test_data, predicted):\n",
    "    \"\"\"Calculate root mean squared error.\n",
    "    Ignoring missing values in the test data.\n",
    "    \"\"\"\n",
    "    I = ~jnp.isnan(test_data)   # indicator for missing values\n",
    "    N = I.sum()                # number of non-missing values\n",
    "    sqerror = jnp.power(test_data - predicted, 2)\n",
    "    mse = sqerror[I].sum() / N                 # mean squared error\n",
    "    return jnp.sqrt(mse)\n",
    "\n",
    "\n",
    "def mae(test_data, predicted):\n",
    "    \"\"\"Calculate Mean Absolute Error Ignoring missing values\"\"\"\n",
    "    I = ~jnp.isnan(test_data)   # indicator for missing values\n",
    "    N = I.sum()                # number of non-missing values\n",
    "    abserror = jnp.abs(test_data - predicted)\n",
    "    mae = abserror[I].sum() / N   # mean squared error\n",
    "    return mae"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "def pmf_predict(U, V, gammas, confounders, k):\n",
    "    mean = (U @ V.T) * 1. + (gammas * confounders)\n",
    "    scaled_mean = expit(mean)\n",
    "    preds = scaled_mean * (k - 1) + 1\n",
    "    return preds\n",
    "\n",
    "# samples\n",
    "U_samples = jnp.load('./samples/U.npy')\n",
    "V_samples = jnp.load('./samples/V.npy')\n",
    "gammas_samples = jnp.load('./samples/gammas.npy')\n",
    "beta_0_samples = jnp.load('./samples/beta_0.npy')\n",
    "\n",
    "# params\n",
    "U = np.median(U_samples, axis=0)\n",
    "V = np.median(V_samples, axis=0)\n",
    "gammas = np.median(gammas_samples, axis=0)\n",
    "beta_0 = np.median(beta_0_samples, axis=0)\n",
    "\n",
    "assert n_factors_pmf == U.shape[1]\n",
    "assert n_factors_pmf == V.shape[1]\n",
    "\n",
    "preds_pmf = pmf_predict(U, V, gammas, confounders, K)\n",
    "print(preds_pmf.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "print('RMSE:', rmse(test, preds_pmf))\n",
    "print('MAE:', mae(test, preds_pmf))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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  "kernelspec": {
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  "language_info": {
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    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
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   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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