examples/02_model_collaborative_filtering/cornac_bivae_deep_dive.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<i>Copyright (c) Microsoft Corporation. All rights reserved.</i>\n",
    "\n",
    "<i>Licensed under the MIT License.</i>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bilateral Variational Autoencoder (BiVAE)\n",
    "\n",
    "This notebook serves as a tutorial on Bilateral Variational Autoencoder (BiVAE) model for collaborative filtering. The research paper of BiVAE [1] is presented at WSDM'21 conference. For all experiments related to BiVAE model, please refer to [this repository](https://github.com/PreferredAI/bi-vae).\n",
    "\n",
    "The implementation of the model is from [Cornac](https://github.com/PreferredAI/cornac) [2], which is a framework for multimodal recommender systems focusing on models that utilize auxiliary data (e.g., item descriptive text and image, social network, etc)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 0 Global Settings and Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "System version: 3.6.11 | packaged by conda-forge | (default, Nov 27 2020, 18:57:37) \n",
      "[GCC 9.3.0]\n",
      "PyTorch version: 1.4.0\n",
      "Cornac version: 1.11.0\n"
     ]
    }
   ],
   "source": [
    "import sys\n",
    "import os\n",
    "import torch\n",
    "import cornac\n",
    "import papermill as pm\n",
    "import scrapbook as sb\n",
    "import pandas as pd\n",
    "from recommenders.datasets import movielens\n",
    "from recommenders.datasets.python_splitters import python_random_split\n",
    "from recommenders.evaluation.python_evaluation import map_at_k, ndcg_at_k, precision_at_k, recall_at_k\n",
    "from recommenders.models.cornac.cornac_utils import predict_ranking\n",
    "from recommenders.utils.timer import Timer\n",
    "from recommenders.utils.constants import SEED\n",
    "\n",
    "print(\"System version: {}\".format(sys.version))\n",
    "print(\"PyTorch version: {}\".format(torch.__version__))\n",
    "print(\"Cornac version: {}\".format(cornac.__version__))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "tags": [
     "parameters"
    ]
   },
   "outputs": [],
   "source": [
    "# Select MovieLens data size: 100k, 1m, 10m, or 20m\n",
    "MOVIELENS_DATA_SIZE = '100k'\n",
    "\n",
    "# top k items to recommend\n",
    "TOP_K = 10\n",
    "\n",
    "# Model parameters\n",
    "LATENT_DIM = 50\n",
    "ENCODER_DIMS = [100]\n",
    "ACT_FUNC = \"tanh\"\n",
    "LIKELIHOOD = \"pois\"\n",
    "NUM_EPOCHS = 500\n",
    "BATCH_SIZE = 128\n",
    "LEARNING_RATE = 0.001"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1 Theory behind BiVAE\n",
    "\n",
    "### 1.1 Motivation from Dyadic Data\n",
    "\n",
    "Preference data in collaborative filtering (CF) typically consists of a set of users, a set of items, and a set of interactions, e.g., ratings, clicks, purchases between some user-item pairs.  Most of the time, preference data is being represented as an interaction matrix between user and item.  Generally, it is a form of dyadic data, with measurements associated with pairs of elements arising from two discrete sets of objects.  Naturally, there are two ways to view such data, by users (row-wise) and by items (column-wise).\n",
    "\n",
    "<img alt=\"Dyadic Data\" width=\"600\" style=\"display: block;margin-left: auto;margin-right: auto;\" 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Arz/4Uf8AM6/9jbf/APslegUAFFFFABRRRQAUUUUAFFFFAHn/AMGf+RKvf+w1f/8Ao9q9Arz/AODP/IlXv/Yav/8A0e1egUAFFFFAHlnjjwH4ktfH0Pj/AOHMlq2rCD7PfafdnbHeRgcYbjB4UckfdBzxg5Os+GviT8V5LbSvGWnWXhTw3HMkt1BBdLcT3W3naGUkAZ9cY6/NgCvaaKErfIbbZHb28VpaxW1sgjhhQRxovRVAwB+VSUUUb6kpWVkFFFFAzz/4G/8AJGNC/wC3j/0okr0CvP8A4G/8kY0L/t4/9KJK9AoAKKKKAPJ/FPgbxXoPxGl8d/Db7Ld3F7EItS0m7fYtxjADK3AB4HUjBGeckVQv/CPj/wCKuq2EXxBsLPw54bsZxcPptvciea7cdAzKSuOo7YyeCeR7PRRHS3lsD1v5iKoRQqgBQMADtS0UUAFUdb/5AGof9esn/oJq9VHW/wDkAah/16yf+gmgDm/hF/yR/wAMf9g+P+VdlXG/CL/kj/hj/sHx/wAq7KgArlPG2oeNbGfSR4H0iy1KOW426gbpwphiyPmXMiZP3vXp0rq6KAKOty6lBoF9LoVvHc6klu7WkMpwkkoU7VPI4Jx3H1qh4Mu/El74Wtp/G2n22nayzP51vasGRQGO3BDv1XB+8a3aKAOT0fUPGs3xB1a01nSLK38MRR50+9jcGWZvl4YeYSOrfwDoK6yiijokHVsK5/x9/wAk28S/9gm6/wDRLV0Fc/4+/wCSbeJf+wTdf+iWoAPAP/JNvDX/AGCbX/0StdBXP+Af+SbeGv8AsE2v/ola6CgAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKAEZVdSrgMrDBBGQRXzr8Kwfhr+0J4g8DzHy7DUwZLIMeDjMkWD/ANc2dT6lRX0XXg37RmlXOiaj4b+ImkR/6VpN0kM5HdQ2+PPtnep/3wKAOu+Pviv/AIRf4T36Qvtu9VP2CHHXDg7z/wB8BufUir3wW8I/8Ib8LdMs5o/LvLtftl2COfMkAOD7hQq/8BrzDxheW/xg+PXhfQLJvtGiadapf3PdWV1WVs+xXyk9ixr6MoA+eLv/AJPisf8Argf/AEhem/tC+I5dX8c6D8Pzqcel6XcGKfUbmSUIgDuQN5JAwiqWweCSPQU67/5Pisf+uB/9IXrI+PGladYfHfw/q3iq1a48PahDFHc/OyjCsVcZUgjaGRuDzQB6Jp+ifAnT9HXTUufB08YTa01zfW8kzepMhbcD9CPbFcD4A1Sw8A/tDN4Y8JazDqfhXWxmNYLpZ0icoSvzAkbgy7fXaRnPFemQ/AL4WXEKTW/h1JYpFDI6ajcsrA9CCJeRXN+H9M+DukfGODw94b8P3Z8Q2MhZLqG4mlgicIWbJMpHyjg5XGTjrQBmKn/CCfthcfu7LxPbk+26QZ/MzRf+PVb/AGgo5/F3i/wd8P7GXZJfTtdTHrsXlVbHsolP4VP+0vpk1ppPh3xlp6/6VoeoLk/7LEMpPsHjUf8AAqq/D+/h+Iv7Smt+K7c+bp2kaekFo3XYzqF6+/7/APOgDT/Zj1lrj4b3ujXXyTaPfOhRjyiP8/Pp83mflWT8E0/4TP4weM/H0oDwCU2tmx/useCPcRxoP+BVyGt6+3wn+JPxM06ItEms2LS2RH/PWUgqV/3RNL/3xXtHwI8Nf8I18IdJSSMJcagpvpuMZMnKZ99gQfhQB6LXiX7Vf/JLNN/7DUX/AKInr22vEv2q/wDklmm/9hqL/wBET0Aa3wy+DXhfTPBdjc+INItNY1a+t0nup7+IT7SyghFDZACg4yOTjPpjz3xto8HwQ+NXh3XfC2610nWHMdzZBiU2hlWVR/s4dWAOcMOOwr3fwBrtl4j+H+i6lp0ivFJaRqwByY3VQGQ+4IIrxL9oCWHxn8VPB/g3S9tzeQSN9pVDkRiZo+G9MJGWPsRQBu/tN+HZn8O6T4v03KXmiXSq8i9Vjcja3/AXC4/3jXqnhzxVZ654DsfE7SLFaz2QupmJ4iwuZAf90hgfpVvxLodv4m8L6jot5/qb63eFjj7pI4Ye4OD+FfJ+neOr7w58DfEvgG53Lq0WpiwiiHLCOQsZVA7jMbg/9dRQB6R8AbSbxZ408V/EnUY2DXtw1taB/wCBSQzD/gKiNQfrXvdcx8OfCy+DPh7pGiBQJoIA1wR3mb5nP/fRIHsBXT0AeJftV/8AJLNN/wCw1F/6Inr1PwZ/yIegf9g22/8ARS15d+1RE8nwpsWRSyx6xEzkfwjyphn8yB+Nel+ArqC9+HXh6e0lWWJtNtwGU8ZEYBH1BBGPagDyH4if8nc+CP8Arxi/9G3FM/aikuEPhMXy3D+HvtbterBxuYbcDP8Ae2eZt/GqHi3WrXWP2wvDkdlOkw04RWkjIcgOPMdlz6jfg+hyO1ereP8Ax34Q0PUbDwz4ztGuItZKqvm26vbgFwuXLHACkgk9hzQBy+jRfAnxfow03S7fw9GZo9ipJEtvdKcY4ZwHLD1BPrzWx8G/h3rnw4sdU07VNWt7/Tp5xLZRwliYuoJOQB8w2ZA4yDWVr/7NPgTWA8mmLeaNK3Km1m3x591fPHsCK5X9nvUdX0j4keJfA0mqNqekabFIYpclkR45VjGzk7QwYkr6r9aAOftdR0H4qfHLVr34h63Z2fh/R2eOxs7u9WBJgH2qASR1wXbHOcDpXo/iLw78Dtf0GXT49R8IadKUIhurK8topImxw2VYbvo2c15Z8OvBXhOf4zeI/CHxC07zrjznGn+bcyQ5IcnA2MuS6MrDPYe9ezXnwI+FGn2M15feH0t7aBDJLLJqNyFRQMkk+Z0oA579mbxbe6r4d1Xw3qdz9qbQ5UFtNv3gwtuAUN3VShx7MMcDjhfAfg7T/GX7SnjC31yEXOnWOoXt29q7fJLILgom4dwN7H/6xIr1X4Jy/Dy9j1a8+G2h32mIDHFdSXbSESH5ioXdI4yOScY+8M1xvwX/AOTkPiL/ANd7z/0roA9D8eeF7Tw18L/Fc/gPRrbTNQubHEn9nQLEzovXAUDkIz9OefWvKPgvqnwdTwfb2Xie20pNdLP9qk1m3V1fLHaUdwUUbdoxkHg/U/QXizxRYeDPDVzrmrrO1nbbfM8iPew3MFHGR3IH4159H8Mvhh8WNBg8SadpRtBfAt51k/kSK2TuDopKbgc5yDQBU0f4RrpXxdsvGfw81PT7Xw/JH/pNpDKziTcCHVNoK7T8rDnhu3Ar2WvlDW/DF38Dfi34ch8Ja/cXUWqTJ5lnIfmKGQIVkVeGDZODgcg46Zr6voAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACs7X9Qk0rRJr2FVZ4ih2t0ILgEfkTWjWH4z/AORRvf8AgH/oxaa3JlpFl/StVttYsVubRsjo6Hqh9DV2vJtLur7QvJ1O1O6GTIkTsQCRg/0NemaVqttrFitzaNkdGQ9UPoaco2Ip1FIu0UUVJqFFFFABRRRQAUUUUAcv4lbx6NSj/wCEOj8ONY+SPMOqyTrL5mTnHlgjbjb75zWPv+MP/PDwP/3+u/8A4mvQKKAPP9/xh/54eB/+/wBd/wDxNG/4w/8APDwP/wB/rv8A+Jr0CigDz/f8Yf8Anh4H/wC/13/8TRv+MP8Azw8D/wDf67/+Jr0CigDz/f8AGH/nh4H/AO/13/8AE0b/AIw/88PA/wD3+u//AImvQKKAPP8Af8Yf+eHgf/v9d/8AxNG/4w/88PA//f67/wDia9AooA8O8FN8TP8AhKfGf9mReEzc/wBqL9t+0S3IQSeSmPLwuSu3HXnOa7Hf8Yf+eHgf/v8AXf8A8TR8O/8AkdfiD/2Gk/8ARCV6BQB5/v8AjD/zw8D/APf67/8AiaN/xh/54eB/+/13/wDE16BRQB5/v+MP/PDwP/3+u/8A4mjf8Yf+eHgf/v8AXf8A8TXoFFAHn+/4w/8APDwP/wB/rv8A+Jo3/GH/AJ4eB/8Av9d//E16BRQB5/v+MP8Azw8D/wDf67/+Jo3/ABh/54eB/wDv9d//ABNegUUAeHfDtviYP+Ep/saLwmf+Kju/tf2uW5GJ/k37Nq/c6Yzz1zXY7/jD/wA8PA//AH+u/wD4mj4Uf8zr/wBjbf8A/slegUAef7/jD/zw8D/9/rv/AOJo3/GH/nh4H/7/AF3/APE16BRQB5/v+MP/ADw8D/8Af67/APiaN/xh/wCeHgf/AL/Xf/xNegUUAef7/jD/AM8PA/8A3+u//iaN/wAYf+eHgf8A7/Xf/wATXoFFAHn+/wCMP/PDwP8A9/rv/wCJo3/GH/nh4H/7/Xf/AMTXoFFAHh3wwb4mDwtdf2FF4TNt/al5v+2S3IfzPObfjauNu7OO+Otdjv8AjD/zw8D/APf67/8AiaPgz/yJV7/2Gr//ANHtXoFAHn+/4w/88PA//f67/wDiaN/xh/54eB/+/wBd/wDxNegUUAef7/jD/wA8PA//AH+u/wD4mjf8Yf8Anh4H/wC/13/8TXoFFAHn+/4w/wDPDwP/AN/rv/4mjf8AGH/nh4H/AO/13/8AE16BRQB5/v8AjD/zw8D/APf67/8AiaN/xh/54eB/+/13/wDE16BRQB4d8Jm+Jg+F+k/8I9F4TbTv33km+luRN/rn3bgikfezjHbFdjv+MP8Azw8D/wDf67/+Jo+Bv/JGNC/7eP8A0okr0CgDz/f8Yf8Anh4H/wC/13/8TRv+MP8Azw8D/wDf67/+Jr0CigDz/f8AGH/nh4H/AO/13/8AE0b/AIw/88PA/wD3+u//AImvQKKAPP8Af8Yf+eHgf/v9d/8AxNG/4w/88PA//f67/wDia9AooA8/3/GH/nh4H/7/AF3/APE1V1V/i5/Y979oh8FeV9nffsmu923ac4yvXFelVR1v/kAah/16yf8AoJoA8m+GzfFAfDTQP7Eh8InT/safZzdy3Ql2dtwVcZ+ldPv+MP8Azw8D/wDf67/+Jq98Iv8Akj/hj/sHx/yrsqAPP9/xh/54eB/+/wBd/wDxNG/4w/8APDwP/wB/rv8A+Jr0CigDz/f8Yf8Anh4H/wC/13/8TRv+MP8Azw8D/wDf67/+Jr0CigDz/f8AGH/nh4H/AO/13/8AE0b/AIw/88PA/wD3+u//AImvQKKAPP8Af8Yf+eHgf/v9d/8AxNY/jB/it/wg2u/2lD4NFn/Z1x9oNvLdGTy/LbdtyuN2M4zxmvWK5/x9/wAk28S/9gm6/wDRLUAcP4Pf4rf8INoX9mw+DTZ/2db/AGc3Et0JPL8tdu7C43YxnHGa2N/xh/54eB/+/wBd/wDxNdB4B/5Jt4a/7BNr/wCiVroKAPP9/wAYf+eHgf8A7/Xf/wATRv8AjD/zw8D/APf67/8Aia9AooA8/wB/xh/54eB/+/13/wDE0b/jD/zw8D/9/rv/AOJr0CigDz/f8Yf+eHgf/v8AXf8A8TRv+MP/ADw8D/8Af67/APia9AooA8/3/GH/AJ4eB/8Av9d//E1LbP8AFr7VF9sg8F/Z9483yprvftzztyuM46Zru6KACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigArF8YeGbbxj4P1LQL1tkV9CYxJs3eU/VHxxnawBxkdK2qKAPNPhP8G7f4YXGo3T6sdXu71EiWZrbyfKjX+EfO2cnHf+EV6XRRQB53N8KfN+OMHxE/tnHkxlP7P+y9f3DRZ8zf8A7Wfu+3vXT+L/AAbovjnQn0nxFa+fAW3o6na8T4wGRux5/wAc1u0UAeGJ+zrqtjGbLRPibrdhpR62Sq+CM8j5ZVX/AMdruvh18JvD3w3ilk0pZbrULhdk19ckGRlznaoHCrnnA64GScCu5ooAwvGvheDxp4M1Lw/dS+Sl9FsWXZv8pwQyvtyM4YA4yOnWue+E/wALYfhdo9/aLqX9pzXs4lef7P5OFC4Vcbmzg7jnP8XSu+ooA8o+J/wMtfiT4qs9afWm00wwLbzRLa+Z5yq5YHdvXacMR0PavVIYY7eCOGBBHFGoREUcKAMACn0UAFcT8Vfh1/ws3wrbaN/an9meRerd+d9n87dtR027dy/385z2rtqKAPGL79nr7NMZfBPjTVfC/noBdRWu4xStjBIVZEKgnnBJA7V0/wAO/g9oPw+uZtRhln1TWLgES6hd4LDPLbR/DnueSfWvQKKACvmuPwvpfjH9rq8n0pfO0/S2S9v3XmM3CKo2gj/pptyD1KvXrHxQ+Gs/xEtdPS08Q3Ghy2Rk/eQxlxKr7cqQHX+4O9Wvht8M9I+GmiS2WlvJc3Fywe6u5gA0pA4GB0UZOBz1PNAHZUUUUAZfiPw7pvizw/daLrlv9osrpdrrnBBByGB7EEAg15Ba/s432mO9rovxH1uw0eRsvYwqylx7ssgUn32V7nRQB5NYfALR9E8YeHNZ0C/a0h0VcyQSW/mSXjksS7ybhg/Nj7pAA4rsPHvw80P4i6Kmn69HIDCxe3uYWCyQsRgkEgjB4yCMHA9BXU0UAeHR/s967BALG2+KeuRaSBs+xKrhdn93ibb/AOO16J8P/htoHw40qS00KOR5rgg3N3OQ0sxHTJAAAGTgAd/XJrraKAOA+Inwe8PfESWO9vDNp+qwgLHf2hAcgdAwPDAduhHrXGSfs6anqapaeJfiXreqaahytoytgAdMb5HUdv4a9yooAyPDHhfSPB2gw6P4ftFtbSLJxklnY9WYnkk+v4dAK5LwX8Kf+EQ+JHiLxX/bP2z+25Jn+y/ZfL8nzJvMxv3ndjp0HrXolFAFfUNPtNV0240/UYEuLS5jaKaJxw6kYINeMP8As5S6VeTSeB/H2teHYJm3NDHub8NySIT+Oa9vooA8v8FfAzSPDHiFfEOtape+I9bQhkur48I2MbgpJJb3LHHbFeoUUUAFFFFABRRRQAUUUUAFFFFAHltyl5feJtRgivJIwk8pHznAAfGP1qX+xdR/6CT/APfTf40+0/5HPVf+uk3/AKMrardLQ86UmpGF/Yuo/wDQSf8A76b/ABo/sXUf+gk//fTf41u0U7IjmZhf2LqP/QSf/vpv8aP7F1H/AKCT/wDfTf41u0UWQczML+xdR/6CT/8AfTf4019CvpEKSagXU9VYsQa36KLIOZlSyshb6alpNtkABDccHJJ/rWWDd+F9RF5YEvbscOhPBH90/wBDW/TXRZI2SRQysMEHvRa4KTTudLpWq22sWK3No2R0ZD1Q+hq7XlguZvC2srLYyho3GWhJ6r6H+hr02zuPtdnFceW8XmKG2SDDL7GsZKx30586JqKKKk1CiiigAooooAKKKKACis3XrbVbzSmt9Cv4tPuZHVWuZIvMMaZ+Yqp4346ZyM9Qa8H+FniXxAf2h9c8OjxFqetaNB9oVv7QuDKV8tgAw7Kd3HygDB6UR1ly+v4BLSPN6fifRVFfO/i3xJr2t/tUaZ4a0fW9Ss9PtpIEuLe1u5I45Aq+dJuVTg5U7Tn0r6IoWsVLuD0ly+gUUUUAFFFFAHn/AMO/+R1+IP8A2Gk/9EJXoFef/Dv/AJHX4g/9hpP/AEQlegUAFFFFABRRRQAUUUUAFFFFAHn/AMKP+Z1/7G2//wDZK9Arz/4Uf8zr/wBjbf8A/slegUAFFFFAGJ4r8Y6H4J0c6l4kvktIM7UGCzyt/dVRyT/k4FeYfDP4uaz8Qfi/f2bQPp+gppbT2lnLEu9/3iBZWbGckMeAduMdep9X1jw5o/iBrU65p1vfizk82BbhN6o+Mbtp4Jx6ivLtEAX9rrxAFAAGgIAB25hoh8dn5/kxv4Xby/NHslFFFAgooooA8/8Agz/yJV7/ANhq/wD/AEe1egV5/wDBn/kSr3/sNX//AKPavQKACiiigDy/xz458Sz+PbbwF8O47RNVe3+1XuoXg3R2kfbC9z06g/eAxzkYeveIfib8KBb6z4r1ax8V+HnmSK8MdotvNbbuNyhABjPrnJ44zmvYY9J06LVZNTi0+1TUJU2SXawqJXXj5S+MkcDjPYV418Utcf4oa5D8MvBh+0qLhJda1BBmK1RDnZnuwPJ9wF65wldNJb3/AF/JIbs029v6/U9st547q2ingbdFKgdG9QRkGpKitLaOzsoLWHPlwxrGmT2AwP5VLVO19CY3tqFFFFIZ5/8AA3/kjGhf9vH/AKUSV6BXn/wN/wCSMaF/28f+lElegUAFFFFABRRRQAUUUUAFUdb/AOQBqH/XrJ/6CavVR1v/AJAGof8AXrJ/6CaAOb+EX/JH/DH/AGD4/wCVdlXG/CL/AJI/4Y/7B8f8q7KgAooooAKKKKACiiigArn/AB9/yTbxL/2Cbr/0S1dBXP8Aj7/km3iX/sE3X/olqADwD/yTbw1/2CbX/wBErXQVz/gH/km3hr/sE2v/AKJWugoAKKKKAPG/FWu+PPEHxoufCPgPxFBo1vp+mJcXLTWkcw8wt/tITkh146cVs+H/AAz8WLPxBZ3HiDx5Y6hpscmbi1j06KNpVx0DCMEfnXOWnwz8cap8UPFurXGsTeGdM1OZVS4snR7m5iTIQIwJMQwASevQetRyah4s+DvjvRbLWvEV14l8La5cfZhNfndPayEgDLkknqD1wRu4BGaKe0b7v830/QJ7y7L8rb/qe5UUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUV4z8WtYuvGPjbSvhVoVw8QvGW41qeI8xW4+bZ9SBux3yg7mvXrCwttL023sLCFYLW2iWKGJBgIqjAA/AUAWKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKK4b4t+DH8YeCZTpxaLW9Lb7bpk8Zw6TJztB7bgMfXae1P+E3j1PiF4DttTl2rqEB+z30ajG2VQMkDsGBDD6kdqAO2ooooAKKKKACiiigAooooAKKKKACiiigAooooA8zt3VPGWqF2CjzZuScf8tK2PtEP/PWP/voVZvPAdteX09y17MrTSNIVCjjJzj9ah/4V1af8/wBN/wB8CtVJHFKjJu4z7RD/AM9Y/wDvoUfaIf8AnrH/AN9Cn/8ACurT/n+m/wC+BR/wrq0/5/pv++BT50L2Ehn2iH/nrH/30KPtEP8Az1j/AO+hT/8AhXVp/wA/03/fAo/4V1af8/03/fAo50HsJDPtEP8Az1j/AO+hR9oh/wCesf8A30Kf/wAK6tP+f6b/AL4FZ+u+C7fSdFnvY7uWRotuFZQAcsB/WjnQnRklc0FYMuVIYeoNZ+rasmnx7Ew07D5V/u+5rOt9WTT9AgRMNOwbav8Ad+Y8mt7wt4Wd5F1XWVLSMd8UT9v9pv6Cm5WRMKbk7B4W8LO8i6rrKlpGO+KJ+3+039BXaUUVi3c74xUVZBRRRSKCiiigAooooAKKKKAIb2WSCwuJYV3yRxMyKO5AyBXyz+znr+k6Pq/ifWNcu1OqTJHHbWo5uLpnZmZY06sxYLwOnfAr6srNtPDeh2GqS6lY6Np9tfzEmW6htUSWTPXLgZOfc0R0k35WCWsbedz5k+G2vWtj8fvFPiHxvNHYXluLnZas2+RpmkCiKMDl2C5UBck17rqmga3rvjCHU7/XbnT/AAkmnhjp8F1JaTm4JJLSMgVgoUjjf1HTrnpx4f0ZdZOrrpFgNTYYN6LZPOI6ffxu/WuV8TeNvAr+KpPBnjVbNStut4H1ZIvsrZJAAZzgOOeoHsaW0Yx7afn/AF8gfxSl3/4BzfwV1fxBqfiDxXFNqN5qvha2u2j0m9vHMrPh2BCynl1wBySe3qa9frxT4JQajD428WDRzc/8IOJiNLEpYxFt/wDyx3fwY3cjj7te11X2Y+i9fmL7UvX5fIKKKKQzz/4d/wDI6/EH/sNJ/wCiEr0CvP8A4d/8jr8Qf+w0n/ohK9AoAKKKKACiiigAooooAKKKKAPP/hR/zOv/AGNt/wD+yV6BXn/wo/5nX/sbb/8A9kr0CgAooooAK8c0X/k7zxB/2AU/nDXsdU00fTItYk1aPTrRNSlj8qS8WBRM6cfKXxuI4HGewoWklL1/FND+y1/W6ZcooooEFFFFAHn/AMGf+RKvf+w1f/8Ao9q9Arz/AODP/IlXv/Yav/8A0e1egUAFFFFAHhPxh+JzS+LI/h/pOuQ6BE4B1bV5Sf3KFd3lpjnJUjOPUDI5Nb3gzxh8IfAegJpWgeI7CNPvSzOSZJ3/ALztt5P6Dtiu7vvA/hPU72W81Lwvo13dTHMk9xp8UjuemSxXJqD/AIVx4I/6E3w//wCCuD/4mlG6Xn1/rsOVmzftrmG8tIbm2cSQzIskbjoykZB/I1LTIYY7eCOG3jSKKNQiRooVVUDAAA6ACn1TtfQlXtqFFFFIZ5/8Df8AkjGhf9vH/pRJXoFef/A3/kjGhf8Abx/6USV6BQAUUUUAFFFFABRRRQAVR1v/AJAGof8AXrJ/6CavVR1v/kAah/16yf8AoJoA5v4Rf8kf8Mf9g+P+VdlXG/CL/kj/AIY/7B8f8q7KgArC8SeNNA8Iy2EfiG/+yNqMvk2o8mSTzH44+RTjqOuK3ao6loek6y0DavpdlftbPvgN1bpKYm9V3A7TwOR6UAS6lqNrpGl3Wo6jL5NpaRNNNJtLbEUZJwASeB2FVPDviPSvFmhw6v4fuvtdhMWEc3lum4qSp4YA9Qe1X7m2gvbWW2vII7i3mQpJFKgZHUjBBB4IPpUWnaZYaPYpZaTZW1jaxklILWJY0XJycKoAGTzQBmaf400DVPFd/wCGrC/83V9PTfc23kyL5Y453FQp+8OhPWt2qNvoek2mrT6pa6XZQahcjbPdx26LLKOOGcDJ6Dqewq9R0XcOrCuf8ff8k28S/wDYJuv/AES1dBXP+Pv+SbeJf+wTdf8AolqADwD/AMk28Nf9gm1/9ErXQVz/AIB/5Jt4a/7BNr/6JWugoAKKKKAPJtK+MT6N461jw18UBa6LJFNu0y7WJ0huIcnBLEsM4AOeB1HBGK5/xhrlp8Y/iN4b8O+DmN9pujXgv9T1FFIiQAjCqx6kgEcdSRjoce16pomla5brBremWeowqdyx3dukqg+uGBFP03StP0a0FrpFha2FuDkQ2sKxID/uqAKI6Wv0/G2wS1vbqW6KKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigApHdY0Z3IVVGST2FLVPV45JtDvooCRK9vIqEZ4YqcdKAPCv2eXbxX4/8beN7wFpbiYQwMw+6jszFfwVIhXYftGf8kR1X/rtb/wDo5a5T9k6WM+DteiAHmrfqzHPODGMcfga6v9oz/kiOq/8AXa3/APRy0Aef+Avg9L8TvAul6/4z8QanEUt0t9LtbRlRLaGEeWhwwPJ2Z4xnOc81ufFXxfrfhWPw58MvAd1O2sXsEUTX0khaYITsX5jnDMVYlv4QOMZyPQPg7/yRzwz/ANeK/wAzXlfjJ10/9sbw3cX37uGaGIRs3QllkjX/AMf4oA1Iv2YNOubP7TrHivWbjXGXLXiOuwP64YFiM5/iB+lQfDTxh4n8GfFKX4ZeOr99Sjcf8S69kJZvu7l+Y8lWUEYJO1hjNe+V86fEN01D9rzwlb2OHmtYrYXAXqCrySHP/ACD9KAJtAT/AIQT9rrUtO/1dl4kheWIdizjzc/9/EkUfWtr9pe/ubnw1oXhPTB5l9ruoqiRA/fC4AH4u6c+1U/2j7OXRdR8JePLJCZtKvlilK9xnzEB9so4/wCBYpZruLx7+1ZpYtZBNp/h3TBdZAyrMy7gc/WaP/vmgDW/Zn1s6j8KjpsxIm0m8kg2t1Ct+8H6sw/Cuf8ADA/4T39rDWtabMlh4aiMEDDlQ6jygPfLGZh9KzPC+uJ8Kfiv8TdOn+W3+ySanaoejMvzxoPqJsf8BrsP2adAfT/hxPrl3ua71y7ednfqyISq5/4FvOf9qgDjrn7d8aPjbr/hjW/ElxpGjaPJLDBp9tKFa48t9hIB4YnBYkg4BAHFWPFfwX1v4a2UGvfCXWdcuLmCdRNYEiVpAxAyFRQGAPUFSMc54rp/HPwX8I/ErX7vVNA1+Ox1xNpujaSJOm7orPGCCpO0jIIzg8E5ritX0H4zfCLTJdWsvE66zo9phpUklMwRMgcxyjKj/cPHWgD6I8O317qfhnTr3VrJ7C+ntke5tnGDFIR8y/nmtKuX+G/jH/hPPAOneIHtxbS3Css0Q+6roxVsexIyPY11FAHiXxU8TfEvwt4Zk8UJqmnaLbxXqwRaTFbrctLGSQGeZu5xnaqjAPXIq/qnjbx74x0GZ/hjaWUAs7YNd6jcHeJbjYGeC2XDByp+Usw2k8ds1h/tO3UuoxeFPCdm37/VL8vj0IxGmfqZT+Ve1aLpFj4b8P2mlaeiwWdjAIkHQAAck+55JPqSaAOc+FF34o1D4d2d546M/wDbE8krSJcWq28kahyqgoFXHAz06EV2dUdM1zSdbWY6NqllqAgfZKbS4SXy29G2k4PsaJdb0qDWYdIn1Ozj1O4QyQ2T3CiaRefmVCdxHytyB/CfSgC9RTZJEhiaSV1SNFLM7HAUDqSewqKzvbXUbOK70+5huraZd0c0EgdHHqGHBFAE9fPnwxmPhD9pjxh4Uj+Sz1AvcRR9ArcSoAPQJIw/AV9B187KPtP7cRa1GBbw/vyP4v8AQcdvdlHPpQB9E0UUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFYfjP/AJFG9/7Z/wDoxa3KZLDHPHsmRXTIO1hkZByP1AoQmrqxxfhLwlt2ajqsfzfehgYdP9ph/IV29FFNu4oxUVZBRRRSKCiiigAooooAKKKKAOZ8SfEbwn4Q1KOw8Sa1DYXUkQmSKRXJKElQ3APdSPwrI/4Xf8OP+hqtf+/cn/xNd2yKxyyqT7ik8qP/AJ5r/wB80AcL/wALv+HH/Q1Wv/fuT/4mj/hd/wAOP+hqtf8Av3J/8TXdeVH/AM81/wC+aPKj/wCea/8AfNAHC/8AC7/hx/0NVr/37k/+Jo/4Xf8ADj/oarX/AL9yf/E13XlR/wDPNf8Avmjyo/8Anmv/AHzQBwv/AAu/4cf9DVa/9+5P/iaP+F3/AA4/6Gq1/wC/cn/xNd15Uf8AzzX/AL5o8qP/AJ5r/wB80AcL/wALv+HH/Q1Wv/fuT/4mj/hd/wAOP+hqtf8Av3J/8TXdeVH/AM81/wC+aPKj/wCea/8AfNAHifgn4r+CNM8VeM7q+8Q28MOoaos1q7I+JUEKLuGF9QRzXZf8Lv8Ahx/0NVr/AN+5P/iai+HkaHxp8QMopxrKY4/6YJXf+VH/AM81/wC+aAOF/wCF3/Dj/oarX/v3J/8AE0f8Lv8Ahx/0NVr/AN+5P/ia7ryo/wDnmv8A3zR5Uf8AzzX/AL5oA4X/AIXf8OP+hqtf+/cn/wATR/wu/wCHH/Q1Wv8A37k/+JruvKj/AOea/wDfNHlR/wDPNf8AvmgDhf8Ahd/w4/6Gq1/79yf/ABNH/C7/AIcf9DVa/wDfuT/4mu68qP8A55r/AN80eVH/AM81/wC+aAOF/wCF3/Dj/oarX/v3J/8AE0f8Lv8Ahx/0NVr/AN+5P/ia7ryo/wDnmv8A3zR5Uf8AzzX/AL5oA8T+HXxX8EaP/wAJV/aXiG3t/tviO8u7fcjnzIn2bXGF6HBrsv8Ahd/w4/6Gq1/79yf/ABNRfCiND/wmmUU48WXwHH+5Xf8AlR/881/75oA4X/hd/wAOP+hqtf8Av3J/8TR/wu/4cf8AQ1Wv/fuT/wCJruvKj/55r/3zR5Uf/PNf++aAOF/4Xf8ADj/oarX/AL9yf/E0f8Lv+HH/AENVr/37k/8Aia7ryo/+ea/980eVH/zzX/vmgDhf+F3/AA4/6Gq1/wC/cn/xNH/C7/hx/wBDVa/9+5P/AImu68qP/nmv/fNHlR/881/75oA4X/hd/wAOP+hqtf8Av3J/8TR/wu/4cf8AQ1Wv/fuT/wCJruvKj/55r/3zR5Uf/PNf++aAPE/hf8V/BGh+Fbq11XxDb20z6peTKjI5JR5mZW4XuCDXZf8AC7/hx/0NVr/37k/+JqL4NRofBd7lFP8AxOb/AKj/AKbtXf8AlR/881/75oA4X/hd/wAOP+hqtf8Av3J/8TR/wu/4cf8AQ1Wv/fuT/wCJruvKj/55r/3zR5Uf/PNf++aAOF/4Xf8ADj/oarX/AL9yf/E0f8Lv+HH/AENVr/37k/8Aia7ryo/+ea/980eVH/zzX/vmgDhf+F3/AA4/6Gq1/wC/cn/xNH/C7/hx/wBDVa/9+5P/AImu68qP/nmv/fNHlR/881/75oA4X/hd/wAOP+hqtf8Av3J/8TR/wu/4cf8AQ1Wv/fuT/wCJruvKj/55r/3zR5Uf/PNf++aAPE/hL8V/BGgfC3SNM1jxDb2t5B53mQujkrumdh0XHQg/jXZf8Lv+HH/Q1Wv/AH7k/wDiai+B0aN8GdDJRSf9I5I/6eJK7/yo/wDnmv8A3zQBwv8Awu/4cf8AQ1Wv/fuT/wCJo/4Xf8OP+hqtf+/cn/xNd15Uf/PNf++aPKj/AOea/wDfNAHC/wDC7/hx/wBDVa/9+5P/AImj/hd/w4/6Gq1/79yf/E13XlR/881/75o8qP8A55r/AN80AcL/AMLv+HH/AENVr/37k/8AiaP+F3/Dj/oarX/v3J/8TXdeVH/zzX/vmjyo/wDnmv8A3zQBwv8Awu/4cf8AQ1Wv/fuT/wCJqpqvxq+Hc+jXsMPii1aSS3kVVEcnJKkAfdr0Xyo/+ea/981S1qKP+wNQ+Rf+PWTt/smgDyv4a/FzwJo3wz0DTtT8R21vd21kkc0TI5KMOo4Wun/4Xf8ADj/oarX/AL9yf/E1Z+EcaH4P+GCUUn+z4+3tXY+VH/zzX/v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    "\n",
    "\n",
    "Ultimately, we would like to seek for representations for both sides of dyadic data (users and items) whose combination would be capable of explaining user-item affinities. To tackle this objective, latent factor or matrix factorization models are predominant in the context of CF. The latter owe their success mainly to their simplicity, efficiency, effectiveness, and extensibility. Nevertheless, this category of models is also known to suffer from a limited modeling capacity as it can\n",
    "only capture linear patterns both in the data and latent spaces."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To go beyond this limitation, there has recently been a surge of interest in using non-linear neural-based approaches. Notably, Variational Autoencoder (VAE) [3] model has been recently applied to CF with strong performance improvements over several competitive approaches. One plausible explanation for the good results achieved by VAE on the CF task is its probabilistic nature. Indeed, the key difference of this model with neural networks is that VAE does not seek to learn deterministic representations, but rather learns distributions over these representations, thereby allowing it to account for uncertainty in the latent space. That property is particularly beneficial when dealing with sparse data where few observations are available. \n",
    "\n",
    "<img alt=\"Standard VAE\" width=\"800\" style=\"display: block;margin-left: auto;margin-right: auto;\" 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    "\n",
    "Despite its remarkable performance, VAE was originally designed for vector based-data, and thus is not in complete fidelity to the two-way nature of dyadic data. Specifically, in the User-VAE, only users are explicitly represented while items are treated as features in a vector space of users, and similarly for Item-VAE. In consequence of this mismatch between VAE and the two-way nature of preference data, it is not clear how one would extend such model on the item side in a principled way, for example to represent side information such as item textual descriptions, images, etc."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.2 BiVAE Formulation\n",
    "\n",
    "As remedy to the drawback of VAE discussed earlier, Bilateral Variational Autoencoder (BiVAE) is proposed. It consists of a generative model of user-item interactions (or dyads), and a pair of inference models (user- and item-based respectively) parameterized using multilayer neural networks, all combined together in a unified framework to auto-encode dyadic preference data. As opposed to the vanilla VAE, the proposed BiVAE is “bilateral” in that it treats users and items symmetrically, making it more apt for two-way or dyadic data. In particular, BiVAE can capture uncertainty on both sides of dyadic data, which would improve its robustness and performance on sparse preference data, compared to classical one-sided variational autoencoders.\n",
    "\n",
    "<img alt=\"BiVAE\" width=\"800\" style=\"display: block;margin-left: auto;margin-right: auto;\" 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  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Notation.** The data that we seek to learn from is the user-item preference matrix, of size $U\\times I$, denoted $\\mathbf{R} = (r_{ui})$, where $r_{ui}$ is the interaction, e.g., integer rating, between user $u$ and item $i$. We use the notation $\\mathbf{r}_{u*}$ to refer to the row in $\\mathbf{R}$ corresponding to user $u$. Similarly, $\\mathbf{r}_{*i}$ refers to the $i$th column of $\\mathbf{R}$. The latent variables are the per user and item representations denoted respectively $\\mathbf{\\theta}_{u}$, $\\mathbf{\\beta}_i \\in \\mathbb{R}^{K}$.\n",
    "\n",
    "<img alt=\"Graphical Models\" width=\"600\" style=\"display: block;margin-left: auto;margin-right: auto;\" 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FFABXnXw4/wCR7+IH/YXX/wBFrXotedfDj/ke/iB/2F1/9FrQB6LRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQB538Wv9Z4P/7GG2/rXoled/Fr/WeD/wDsYbb+teiUAFFFFABRRRQB5zr4/t747eHNKb5rbRLGbVZF7GViIowfcZLCvRq878Jf6Z8bPHN6RkQQ2Vmp/u4RmYfmwr0SgAooooAK8d+NvxYu/CzW3hbwl+88Q6jhd6jJt1Y4GB/fJ6enWvXLu6isbKe7uG2xQRtI7eiqMk/kK+NvA3ivSNY+O0vi7xxfx2lsssl0hlVmG7pGgAB6DH5UlaU1F7dR/DFy69D2XUvgrpFt8JdRfWFbUPExtGupdVmctKs4G7CsTwoPGO/emfs0eN77xJ4VvtH1a4e5n0l08qWRssYmBwCe+Cp/DFanjP42eBLjwRrMGl+IYbi8ls5EhiWKQF2KkAcriuG/ZLsZB/wkl+QfLbyIQfUjcT/MVULuUu1kTKyhHvc+kqKKKQwooooAK4n4vaW+pfDHVJLcH7Vp6rf2xA5EkLBxj64I/Gu2qtqUAutJu7dhkSwOhB75UigCDQdTTWvDun6nGQVu7aObI6fMoNaFcJ8FrgzfCPRI2OWto3tj/wBs3Zf6V3dABRRRQAUUUUAFFFFABRRRQAUUUUAMmmS3t5Jpm2xxqXdj2AGSap6PruleILJbvRNQtr+Bv+WlvIHH446Ua7/yLuo/9esv/oBr8/NJ17VvD2o/bND1C4sJw334JCufr6/jQB+iVFfK/g79qPWdP8u28YWCanCODc2+I5gPUj7rfpXvXhD4o+EfG6KNC1eI3JGTZz/u5h/wE9fquRQBQ+M+oTWnw1urO0fZcatPFp0bA8jzXCk/lmtDT7GLTNNtrG2UJDbRLEijsFGB/KsL4pkXPizwHp7crJqzTuvYiOJiP1IrpqACiiigArh/FPxc8K+ENQlsNUmumu4iA0UVqx7Z4Y4U9fWu4rxj9phQfBGlMQCy3+AfQeW1TJ21KirmzefHvwhZaHaX8n2ySW6UstlEitLGucAv821c46ZzXbeFfE+n+MPDsGs6QZPs8xI2yrtZGBwQR61wHwm8HaBq3wZsoNT0q2uVvS7zs6DezbiAd3UYxxXpOjaNp/h/SodN0e2S1tIQQkads8k+5rRpJtMzTuk0XqKKKkoKKKKACmuiyIyOAVYYIPcU6igDm/grM1p4b1Tw3KxLaBqc1rED1EJO+PP4NXpFeY+BibT4zeMrMcLdW1peY9Tgpn9K9OoAKKKKAM7xF/yK+qf9ec3/AKAa534Qf8kf8M/9eEddF4i/5FfVP+vOb/0A1zvwg/5I/wCGf+vCOgDs6KKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKAPO9X/5OF0D/ALAs/wD6MFeiV53q/wDycLoH/YFn/wDRgr0SgAooooAKD0NFFAHnfwN5+F9u5++93csx9T5rV6JXnXwaP2bQtb0puG07WrqHb6DfuH869FoAKKKKAPI/2lNTew+E0kEZIN5cxxHHcck/yriPgn8LrvWPh7HrFr4u1vRPtkzloNPm8tG2naCfU8V3/wC0T4fudd+FU8llG0slhMtyUUZJUZDH8Ac1U+BHibSrP4GW9xeXkMEemtKLku4GzDE8/UEUoWSm35fcOd3yJf0zyT4+6NdeF5NL0aXxbrWuvODO8F/cb1j7KQPXrX0T8KPDz+GPhho2nTLsnEAllUjkO/zEfrXjHhLwzffGf4vXHjbWLeSLw7aTA2wkGPP2fcUeo4yT+Fd78ddX8SaB4SmvdK1v+yrcPHDbRWa/v55GPO5z9xQOgXk9z2ppuMNd2/8AhhNKU9Nl/TPW6K5CfVLvwt8IDqOr3bz3tnpYeWeQ5Z5dnUn1yaq/ByfV7z4YabfeIb2e9vLzdP5k7FmCsxKjJ9BTa1a7CT0T7nc0UUUhhXJfFRVf4U+Iw/T7DIf0rra4T403Rt/hDraRn99cpHbxL/eZ5FXH5E0AY2geK/iDH4c05LTwHHdQLbRiOc6oimRdow2McZ9K0P8AhLviP/0TqL/wbp/8TXc6VbCz0eztlGBFAiAfRQKt0Aed/wDCXfEf/onUX/g3T/4mj/hLviP/ANE6i/8ABun/AMTXolFAHnf/AAl3xH/6J1F/4N0/+Jo/4S74j/8AROov/Bun/wATXolFAHnf/CXfEf8A6J1F/wCDdP8A4mj/AIS74j/9E6i/8G6f/E16JRQB53/wl3xH/wCidRf+DdP/AImuK+IXiPxtdX3hU6l4Ljs2i1iN7dRqKP50m04TgfL9a95rzn4r/wDIT8E/9h+L/wBAagB3/CXfEf8A6J1F/wCDdP8A4mj/AIS74j/9E6i/8G6f/E16JRQB4V8WPEnje9+GGsQax4Jj0+zeNRJcjUkkMY3DnaBzXyjX3F8dDj4Ma9n/AJ5J/wChrXyj4Q+EvjHxqytpGkyR2rHm7uv3UQ/E9fwBNAHGKxVgykhgcgg9K9f+GPxW+J8F5Hp2iw3Pie3UgG2uUMhQe0vVfxJHtXp/g39l/QNK8u58XXkms3I5NvFmKBT/AOhN+YHtXtGl6Rp2iWSWekWNvZW6DCxW8YRR+AoA8o0m7v7/AONl9ca1Yf2de/2HBvtvOEvlksSQGHWu/rkdcH2H9oWycjbHqOgugb+9IkvT/vk111ABRRRQB5n8fNVOnfC+e2Q4k1C4SADuRncf5D866j4f6DF4b8B6Vp0UYjZYFeXA6uwyxNQeNvANl45k0r+0bqeGPTrjzhHFjbL04OfpXVABVAHAAwKI6J+bCWrXkYXirxK3hzT2lt9NuNRuPLeURRDaqqoyWdzwo/U1X+Hviybxv4Th1q4sBp/nSOqxiTeMKcZzgVkfGnWW0f4V6l5bYkvCtsv/AAI8/oKo3mtR/Dn4PWVnZqsupJpwMUQP3fl+aRvQDP4nApXspN9B2u4pdTf8GeNj4w1HW4orEQWumXX2aOcSbvOx1OMcVi694vlHxM0nwpqvhaxvVuJPOt7mSVZWiUZ/eBSp2nj1p3wTsY9P+HtossiG+vi17Mmfnw54JFYnh+5g1v4/+INbu5kS10iJbGB5GAXeeMD3yDV2tNRfTf5L/Mm94tr5fP8A4B6/RRRUjCgfeH1opUwHXccDPJPYUAeVaBr/AIq8PaX4zfwZ4cGtSL4huAczACIbVOQnVvoMV4N45+IXjbxRfS23iu/uoVVudPCmGNPYx8Z+rZNfVPwRUzeEdT1M/wDMR1e6mB9QHKg/+O11PibwP4b8Y2ph8RaRb3nGFkZdsif7rjDD86APz7q5o7yR65YPBH5si3MZRM43HcMDPbNfQXjL9leRPMuvA2qeYOSLG/OD9FkHB/ED6143J4P8QeEvGGm2/iLSrmxf7ZFhpE+RvnHIYcH8DQB9CfFLxH43vPhbqtvq3gmOwsmjiEl0NSSQoPNQj5QOcnA/GustvFvxGW0hCfDyJlEa4P8AaycjH+7Vn41f8kT1v/rlB/6OjrurP/jwt/8Arkv8qAOB/wCEu+I//ROov/Bun/xNH/CXfEf/AKJ1F/4N0/8Aia9EooA87/4S74j/APROov8Awbp/8TR/wl3xH/6J1F/4N0/+Jr0SigDzv/hLviP/ANE6i/8ABun/AMTR/wAJd8R/+idRf+DdP/ia9EooA87/AOEu+I//AETqL/wbp/8AE0f8Jd8R/wDonUX/AIN0/wDia9EooA87/wCEu+I//ROov/Bun/xNH/CXfEf/AKJ1F/4N0/8Aia9EooA8R8c654s1X/hHbbxL4VTR7Q65asJlvlm3MCcDAA/Ovbq88+NamPwPaX4Hy6fq1ndO391FlAJ/I16DG4liSReVZQw/GgB1FFFABWR4s1VdE8IarqTnAtrWSQH32nH61r15V+0Zrf8AZPwjuoFbbJqEyW4we2dx/lUVPhZcPiR5P+zDpTap8RtU1yYbhaW5wx/vyN/gD+dei/tQXUMXwvggkx5s18nlj6A5rz34IeL2+HmmWUmraTJHpGvXT+brDE7IQg2hcAccjkn1q/8AEZtW+Ovjyz0fwbBLJoWnfLJqLxlYdx+8+T144A71pUjzcsI/1bUiDs5Sl/XQ7b9mWS5T4TSPfSEWy3knkFzgKnGfw3ZrrbGz127+J8up23jO0u9BWHB0iIIzIexJHvznr2rZ0bw3pPhTwNFoiRI+nWdsVkEigiQAZYsO+eTXkv7OGkxXGoeKvE8NukEN1eG3tkRcKqAljgenIH4VTalUdui/4BKvGn6v/gnvNFFFQUFFFFAHnet8ftBeGSOp0e7B+m9K9Erzqb/T/wBoq3C8jS9DYt/smWTj/wBBr0WgAooooAKKKKACvOvhx/yPfxA/7C6/+i1r0WvOvhx/yPfxA/7C6/8AotaAPRaKKKACiiigAooooAKKKKACiiigAooooAKKKKAPO/i1/rPB/wD2MNt/WvRK87+LX+s8H/8AYw239a9EoAKKKKACiiigDzvwF+7+KHxBifhzeW8gH+yYRj+Rr0SvO9MP9l/tDa5buMDWdGt7uP6wsY2/9CFeiUAFFFFAHKfFGeS2+FPiWSHO8adKBj0K4P6GvFP2VtEsb638Q3d9aQXLK0MS+dGHwMMT1/CvovVtNg1nRrzTbwZgvIHgkA/uspB/nXz78NbTX/gl4k1vStc0DU9S0+92ta3em25mErLnb06ZB79DShpN36octYK3Rmj+0zf6Tofguz0WwsbOG91OcMTFAqssSck5Azy20fnXVfB3RbT4b/B+2uvENxDp7XRN5dSXDBAhYfKpz32gcVgaL8NNb+IPxGPjj4kWv2KzhIGn6M7bmVFOVD+gzyR1JPYV2Hxn/svTvhzqet39rHcXVnavDZeaSyxyS4QME+7uGeuMgZpXdODfV/0kOynNLojr9B8Q6T4n0wajoF9HfWhcoJYs43DqOaNM8RaTrN/f2Wl38Vzc6dIIruOMnML88H8j+VcJ4AksPhr8AdPv9WYQRxWZvJc9Xd/mCj3OQKo/s7afL/wgt94ivAftWv6hLdMx6lQxA/Xd+daNWnKPb8/6uZp3ipd/6/yPW6KKKkoKZKwSF2boqkn8qfWN4v1NNF8F6xqUv3LaylkP4KaAPJvhj4Ev9c8Cwahb+Mdc0qKe5uGS1s5FEajzm5AI79a67/hV2qf9FF8T/wDf5P8A4mtj4XaY+kfC3w9ZzDEq2SPJ/vMNx/nXWUAed/8ACrtU/wCii+J/+/yf/E0f8Ku1T/oovif/AL/J/wDE16JRQB53/wAKu1T/AKKL4n/7/J/8TR/wq7VP+ii+J/8Av8n/AMTXolFAHnf/AAq7VP8Aoovif/v8n/xNH/CrtU/6KL4n/wC/yf8AxNeiUUAed/8ACrtU/wCii+J/+/yf/E0f8Ku1T/oovif/AL/J/wDE16JRQB53/wAKu1T/AKKL4n/7/J/8TR/wq7VP+ii+J/8Av8n/AMTXolFAHmGq/DLU4dGvZW+IPiWQJbyMUaZMNhTwfl6V8WNw5+tfovq0L3Gi30MK7pJLeREUdyVIAr5n8Ifst6pfOtz4z1FdOhJybW0xJKR6Fvur/wCPUAeAxRSTyrFCjSSOdqogyWPoBXqfgv8AZ+8a+JHiurqD+wrXIYTXeVk9cqg5z9cV9SeEvhr4T8EwqNA0iGKbGGupR5kzfVzz+AwPauqoA8R1HwtdeDvFnw/s7/XtQ1w/a7lBPfMGKkxEhV74+pPTtXpVc18Yw1nb+F9cB+XTNbhL/wC7JmMn/wAerpT146UAFFFFABXiH7Suo2TeF9N09LuFrxb3zGgVwXVdjDJHUDkda9vrDvvBfhjU76S91Lw9pl3dSnLzT2qOzduSRUyV9Couxy3wO1Kyuvhbptrb3cMlxbhxNCrgvH8x6r1FaHxRn1Kx8G39/aaw2mWtrbM7m3X99LIeEUMeFXJ5xzW/pXhbQNCuXuNF0axsJnXYz21usZYehwK4T9oA3rfDdYLOCWWKW8jFwYlLFUGT296dR83zFTVnY3PhnLeWXwn02+1+9mup2t2u5ZrmQs20ksASeeFxWb8GL/U9b8P6prmq3lxcpqGoyNbLLIWEcY4woPQZzwK57x7rt1rHwkuF8O2d7a6LBbxwmWSBo5LluFCIp52Dqzd8YFdh8J3MfgPT7KHTri1tba3RVnuE8szyHJchDzgHuetaPWUn8v6+4haRiv6/rU7iiiioKCiiigDlfCx8z49eI2TkR6LaI313ua9OrzP4Yr/aHjrxzrI5jN9FYxN6+VH83/jxr0ygAooooAzvEX/Ir6p/15zf+gGud+EH/JH/AAz/ANeEddF4i/5FfVP+vOb/ANANc78IP+SP+Gf+vCOgDs6KKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKAPO9X/AOThdA/7As//AKMFeiV53q//ACcLoH/YFn/9GCvRKACiiigAooooA848PH+wPjf4j0p8LDrVvFqVv2yyjZIB+IB/GvR688+K1ncabFpXjXTYme58PXHmXCIPmktX4lX3wMNj2ru7C+t9T063vrKVZbe4jWWKRTkMpGQaALFFFFACMquhV1DKwwQRkEVxD/BvwHJqT3reH4N0jb3iDMImb1KZ2/pXcUUdbh5EdvbQ2lulvawpDDGNqRxqFVR6ACvEf2hb9LfXPBkOqb4tHW/8+6mCFlG0jg49q9ypkkMcyhZo1kAOQGUHB9aNbp9ncOjR89fHXxPc+IfA9k9n9osPD1zeJDFJJEyPedzJsI3CMDpkZY846V7R4Ju4rrwraCzsbi0s4Y1itjcR+W0qKAA+w8qD2zg1vPFHKAJY1cKcjcucH1p1C0TXcT1afYKKKKBhXm/xMP8Abnizwf4Ti5+0agNRucdVigGRn2LECvR3dY42d2CqoyxJ4Arzf4fA+LPGmueO5lJtZD/Z2klh/wAsIz8zj/eb+QoA9JooooAKKKKACiiigAooooAK85+K/wDyE/BP/Yfi/wDQGr0avOfiv/yE/BP/AGH4v/QGoA9GooooAiurS3vbdoLyCOeFsbo5VDKceoNSKqooVFCqowABgClooAKKKKAPNPi9GdMvPC3itPu6TqPk3BA6QzjYSfYED866fg8joeRV7xToEHijwrqOi3YHl3kDR5/ut1VvwIB/CuF+HetT6l4Z+w6plNW0iQ2N9G3UOnAb8Rg0AdZRRRQAUUUUAY3inwrpfjHQ30rW43e3Zg4KNtZWHQg1kp8MfDieF7vQxFcNDeKqz3Ek7PM4U5A3nnAx06V19FFgMXwz4T0jwlYfZNFtygON8sjl5Hx0yx5x7dBWTo/wv8M6Lr1xrEFtNNdTTGb/AEiYuiOf4gvTPPU812FFO+tw6WCiiikAVheNtZGgeB9W1HrJHbMkS/3pGG1QPfJrdrh/EKf8Jh8RtG8JQfPZ6e66nqpHQBf9VGfcnnFAHcfD3Qz4c+HujaW/+thtU8046uRlj+ZrpKAMDA6UUAFQ3VnbX0Pk3tvFcR5DbJUDDI6HB71NRQBwPxvGPgxrwHTZD/6OjruLP/jwt/8Arkv8q4f43/8AJGde/wByH/0dHXcWf/Hhb/8AXJf5UATUUUUAFFFFABRRRQAUUUUAFFFFAGD440L/AISbwJrOjgEtd2jogHd8ZX9QKp/DTXv+Ek+HOkag5/f+QIZx6Sp8jj8wa6qvNPDBHgn4rat4Zl/d6brxOp6Wf4RJ/wAtoh6c/MB6UAel0UUUAFfM/wC1frXmahoWhxtny43uXUerHaP/AEE/nX0xXPah4E8M6t4lj1/VNIt7zUYoxGkk67woByPlPGeeuKlq7RSdkyl8NtAi0f4X6Jpk8KPttUaRXUEFmGTx+NdZHGkMYSJFRB0VRgCnABVAUYA4AHaitJPmbZnFWSRznxBh1S5+H2s2+gW7XOoTWzRwxqwBJPBxn2zXLfBrQ/E2geFbHTdX0mDR7S2hO+JpRLPczMclzt4Rfbk16ZRUrRt9ynrbyCiiigAoorkfiZ4mk8NeDZvsGX1bUWFlp0Sn5nmk4BH05OfagDG+G5/tzxj4v8U9Yri9Fjat6xwjaSPYtmvR6wvBfhyLwn4O07RosE28IEr/AN+Q8s34kmt2gAooooAKKKKACvOvhx/yPfxA/wCwuv8A6LWvRa86+HH/ACPfxA/7C6/+i1oA9FooooAKKKKACiiigAooooAKKKKACiiigAooooA87+LX+s8H/wDYw239a9Erzv4tf6zwf/2MNt/WvRKACiiigAooooA84+KB/wCEf17wt42UbYdLvfsmoOO1tONhZvZW2n6mvRwcjI5FZ3iDRbXxH4dv9G1Bd1tewNC+OoyOo9weR7iuV+Fmu3U+j3PhjXnH9ueHZBZ3Ges0QH7qYD0ZcfjQB3dFFFABRRRQAVwXxk8Ean4+8AtpGiTwxXSXMc4WdiqSBc/KSAcdc/hXe0UmrjTseRa/8PfGXij4dzWetXWmf2rHapb2Nlal1toMYDOzHJZyoIBxgZOOua6v4a+F9b8LeGLSx1++tpGtrZLeK0slIhiC9W3N8zOx5J4HoK7Kiqu7t9ybaJdgooopDCvOvi9M2pado/g61Y/afEV+kLqvUW6EPMx9sAA/71ehu6RRtJIyoigszMcAAdya828ChvG3jnU/H04P9nQq2maGrD70St+9nH++3APoCKAPSIokghSKJQscahVUdgOAKfRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAc58QPD3/CVeAdX0hBmae2YwEdRIvzJj0+YCue8Da8PEngnTNSb/XvCI7hf7kqfK4/76Br0SvJEi/4QL4rXWlyfJovil2vLFjwsV4MebF7bhhgPwHegDt6KKKACiiigApCAQQRkHqDS0UAIQCMEAj0IpaKKACiiigArN8RazB4d8N3+r3ZxFZwNKR/eIHCj3JwPxrSrhfEMX/Cc+PdO8FwHfp1iyajrbDkFVOYoD/vMMkeg9qAOq+EuhT6F8N9OW/BF/fbr+8J6mWU7zn3wQPwrtKKKACiiigDO8Rf8ivqn/XnN/6Aa534Qf8AJH/DP/XhHXReIv8AkV9U/wCvOb/0A1zvwg/5I/4Z/wCvCOgDs6KKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKAPO9X/5OF0D/sCz/wDowV6JXner/wDJwugf9gWf/wBGCvRKACiiigAooooAZNDHc28kE6LJFIpR0YZDKRgg15n4PuZPh34sfwJq0jf2Tds03h+6k6bSctbE/wB5T09RXp9Yfi/wnYeMtAk0zUd8Z3CS3uYjiS3lHKyKexBoA3KK888J+Nb7StYXwd8QitvrKcWV/jbDqkY6Mp6B/Va9DoAKKKKACiiigAooooAKKK4fxr48l028Tw34SgXU/FN2MRwDmO0U/wDLWY/wqOuOpoAo/ETWrrXNSg+H3hmVhqGoru1K5j5+w2n8RJ7Mw4A967rSNKtND0e10zToxFbWsSxRqB0AGKw/A3guLwjpszXFw2oavfyefqOoSD555D/JR0A7V1FABRRRQAUUUUAFFFFABRRRQAV5z8V/+Qn4J/7D8X/oDV6NXnPxX/5Cfgn/ALD8X/oDUAejUUUUAFFFFABRRRQAV5V4/sJ/BXiqPx7pkTyadcBbfXbeNc4TolwAO69D7V6rTJoo7iF4Z0WSKRSrowyGB4II9KAOZtrmC9tIrq0lWaCZA8ciHIZT0IqWvP7u1u/g/qTfLLd+B7qQsrqC76S7Hoe5iJ79q7u2uYL21jubSZJ4JVDRyRtlWB7g0AS0UUUAFFFFABRRRQAUUVkeJPE2meFNKN/q82xSdsUSDdJO/ZEXqSaAIvFvie28J6C99MhnuHPlWdqnL3M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   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Generative Model.** Figure above depicts BiVAE generative model, as compared to VAE, in plate notations. The latent variables are drawn from prior distributions. Without loss of generality, the Gaussian priors with diagonal covariance matrices are being used. BiVAE further adopts the standard multivariate isotropic Gaussian as the prior over all user/item latent variables. That is, $p(\\bf{\\theta}_u) = \\mathcal{N}(\\bf{0},\\bf{I})$  and $p(\\bf{\\beta}_i) = \\mathcal{N}(\\bf{0},\\bf{I})$, $\\forall i,u$. \n",
    "\n",
    "Conditional on the latent variables, the observations are drawn from a univariate exponential family,\n",
    "\n",
    "$$\n",
    "p(r_{ui}|\\bf{\\theta}_u,\\bf{\\beta}_i) = \\mathrm{EXPFAM}(r_{ui}; \\eta(\\bf{\\theta}_u; \\bf{\\beta}_i;\\omega)) = h(r_{ui})\\exp\\{\\eta(\\bf{\\theta}_u;\\bf{\\beta}_i;\\omega)r_{ui} - a(\\eta(\\bf{\\theta}_u;\\bf{\\beta}_i;\\omega))\\}\n",
    "$$\n",
    "\n",
    "where $h(\\cdot)$, $\\eta(\\cdot)$ and $a(\\cdot)$ denote respectively the base measure, natural parameter and log-normalizer of the exponential family. For simplicity, $r_{ui}$ is assumed to be the sufficient statistic by itself. This form of the exponential family still encompasses many popular univariate distributions, including the Poisson, Bernoulli, Gaussian with unit variance, Gamma with fixed shape parameter, etc. Therefore, BiVAE framework can accommodate various types of preference data, such as counts, binary, continuous, etc. The conditional likelihood is further parameterized in such a way that,\n",
    "\n",
    "$$\n",
    "\\mathbb{E}(r_{ui}|\\bf{\\theta}_u,\\bf{\\beta}_i) = \\frac{d a(\\eta)}{d \\eta} = g_{\\omega}(\\bf{\\theta}_u;\\bf{\\beta}_i)\n",
    "$$\n",
    "\n",
    "where $g_\\omega(\\cdot)$ is some differentiable function (e.g., inner product, neural network, etc.) parameterized by $\\omega$, combining the latent representations to output the mean of the observation $r_{ui}$.\n",
    " \n",
    "Given some $\\bf{R}$, the goal is to find the values of the parameters $\\omega$ that would most likely have generated the observations, and to infer the posterior over the latent variables $p(\\bf{\\theta}_{1:U},\\bf{\\beta}_{1:I}|\\bf{R})$. The latter will allow us to make predictions about unknown preferences and form recommendations. However, the posterior and likelihood are intractable and thereby, exact inference and learning are infeasible.  Therefore, BiVAE relies on variational Bayes (VB), a popular and efficient approach to deal with complex probabilistic models."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Inference Model.**\n",
    "The starting point of VB is to introduce a tractable inference model $q$, governed by a set of *variational parameters* $\\nu$, which will be used as a proxy for the true but intractable posterior. A variational distribution, which breaks the coupling between $\\beta$ and $\\theta$ - a main source of intractability in our model, is chosen as:\n",
    "\n",
    "$$\n",
    "q(\\bf{\\theta}_{1:U},\\bf{\\beta}_{1:I}|\\bf{R}) = q(\\bf{\\theta}_{1:U}|\\bf{R})q(\\bf{\\beta}_{1:I}|\\bf{R})\n",
    "$$\n",
    "\n",
    "with \n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "q(\\bf{\\theta}_{1:U}|\\bf{R}) &= \\prod_{u} q(\\bf{\\theta}_u|\\bf{R}_{u*})\\nonumber\\\\\n",
    "q(\\bf{\\beta}_{1:I}|\\bf{R})  &= \\prod_{i} q(\\bf{\\beta}_i|\\bf{R}_{*i})\\nonumber\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "Without loss of generality, the following forms are adopted:\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "q(\\bf{\\theta}_u|\\bf{R}_{u*}) &= \\mathcal{N}(\\tilde{\\bf{\\mu}}_{\\tilde\\psi}(\\bf{R}_{u*}),\\tilde{\\bf\\sigma}_{\\tilde\\psi}(\\bf{R}_{u*}))\\nonumber\\\\\n",
    "q(\\bf{\\beta}_i|\\bf{R}_{*i}) &= \\mathcal{N}(\\tilde{\\bf\\mu}_{\\tilde\\phi}(\\bf{R}_{*i}),\\tilde{\\bf\\sigma}_{\\tilde\\phi}(\\bf{R}_{*i}))\\nonumber\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "where $\\nu=\\{\\tilde\\phi,\\tilde\\psi\\}$, $\\tilde{\\bf\\mu}(\\cdot)$ and $\\tilde{\\bf\\sigma}(\\cdot)$ are vector-valued functions (e.g., multilayer perceptrons) parameterized by $\\tilde\\phi$/$\\tilde\\psi$, outputting respectively the mean and covariance parameters of the variational distributions.\n",
    "\n",
    "With $q$ in place, we can proceed with approximate inference by optimizing the Evidence Lower BOund (ELBO), w.r.t. the model $\\omega$ and variational $\\nu$ parameters, given in our case by,\n",
    "\n",
    "$$\n",
    "\\mathcal{L} = \\sum_{u,i}\\mathbb{E}_{q(\\bf{\\theta}_u|\\bf{R}_{u*})}\\mathbb{E}_{q(\\bf{\\beta}_i|\\bf{R}_{*i})}[\\log p(r_{ui}|\\bf{\\theta}_u,\\bf{\\beta}_i)]\n",
    "- \\sum_{u} \\mathrm{KL}(q(\\bf{\\theta}_u|\\bf{R}_{u*})|| p(\\bf{\\theta}_u)) - \\sum_{i} \\mathrm{KL}(q(\\bf{\\beta}_i|\\bf{R}_{*i})|| p(\\bf{\\beta}_i))\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.3 Optimization\n",
    "\n",
    "In practice, stochastic optimization is used to fit BiVAE to observations. While the KL terms in the ELBO are available analytically, the expectations over the conditional log-likelihood are intractable and thereby, the direct optimization of ELBO is not possible. To overcome this difficulty, the *reparameterization trick* is used to build an unbiased Monte Carlo estimator of the ELBO:\n",
    "\n",
    "$$\n",
    "\\tilde{\\mathcal{L}} = \\sum_{u,i} \\log p(r_{ui} | \\tilde{\\bf\\theta}_u,\\tilde{\\bf\\beta}_i) - \\sum_{u} \\mathrm{KL}(q(\\bf{\\theta}_u|\\bf{r}_{u*}) ||  p(\\bf{\\theta}_u)) - \\sum_{i} \\mathrm{KL}(q(\\bf{\\beta}_i|\\bf{r}_{*i})|| p(\\bf{\\beta}_i))\n",
    "$$\n",
    "\n",
    "where \n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "\\tilde{\\bf\\theta}_u &= \\mathcal{T}(\\bf\\epsilon,\\tilde{\\bf\\psi})= \\tilde{\\bf\\mu}_{\\tilde\\psi}(\\bf{r}_{u*}) + \\tilde{\\bf\\sigma}_{\\tilde\\psi}(\\bf{r}_{u*})\\odot\\bf\\epsilon \\nonumber\\\\\n",
    "\\tilde{\\bf\\beta}_{i} &= \\mathcal{T}(\\bf\\epsilon,\\tilde{\\bf\\phi})= \\tilde{\\bf\\mu}_{\\tilde\\phi}(\\bf{r}_{*i}) + \\tilde{\\bf\\sigma}_{\\tilde\\phi}(\\bf{r}_{*i})\\odot\\bf\\epsilon \\nonumber\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "with $\\bf\\epsilon \\sim \\mathcal{N}(\\bf{0},\\bf{I})$.\n",
    "\n",
    "Now all the quantities involved are tractable. However, performing unbiased stochastic optimization over the above objective is not convenient, due to the mixing between $r_{ui}$, $\\bf{r}_{u*}$ and $\\bf{r}_{*i}$. To overcome this difficulty and ease subsampling of observations, the two-way nature of BiVAE model is exploited to perform alternate optimization in a Gauss-Seidel fashion. Precisely, the parameters are organized into two blocks consisting of user-related and item-related parameters respectively, then alternate the optimization of each block while holding the other one fixed.  For more details on the optimization procedure, please refer to the original paper [1]."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2 Cornac implementation of BiVAE\n",
    "\n",
    "BiVAE is implemented in the Cornac framework as part of the [model collections](https://github.com/PreferredAI/cornac#models).\n",
    "* Detailed documentations of the BiVAE model in Cornac can be found [here](https://cornac.readthedocs.io/en/latest/models.html#module-cornac.models.bivaecf.recom_bivaecf).\n",
    "* Source codes of the BiVAE implementation is available on [Cornac](https://github.com/PreferredAI/cornac/tree/master/cornac/models/bivaecf).\n",
    "* For all experiments related to BiVAE, please refer to [this repository](https://github.com/PreferredAI/bi-vae).\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3 Experiments on MovieLens\n",
    "\n",
    "\n",
    "### 3.1 Load and split data\n",
    "\n",
    "To evaluate the performance of item recommendation, we adopted the provided `python_random_split` tool for the consistency.  Data is randomly split into training and test sets with the ratio of 75/25.\n",
    "\n",
    "\n",
    "Note that Cornac also cover different [built-in schemes](https://cornac.readthedocs.io/en/latest/eval_methods.html) for model evaluation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 4.81k/4.81k [00:01<00:00, 2.42kKB/s]\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\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>itemID</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>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>186</td>\n",
       "      <td>302</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>22</td>\n",
       "      <td>377</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>244</td>\n",
       "      <td>51</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>166</td>\n",
       "      <td>346</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   userID  itemID  rating\n",
       "0     196     242     3.0\n",
       "1     186     302     3.0\n",
       "2      22     377     1.0\n",
       "3     244      51     2.0\n",
       "4     166     346     1.0"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = movielens.load_pandas_df(\n",
    "    size=MOVIELENS_DATA_SIZE,\n",
    "    header=[\"userID\", \"itemID\", \"rating\"]\n",
    ")\n",
    "\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "train, test = python_random_split(data, 0.75)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.2 Cornac Dataset\n",
    "\n",
    "To work with models implemented in Cornac, we need to construct an object from [Dataset](https://cornac.readthedocs.io/en/latest/data.html#module-cornac.data.dataset) class.\n",
    "\n",
    "Dataset Class in Cornac serves as the main object that the models will interact with.  In addition to data transformations, Dataset provides a bunch of useful iterators for looping through the data, as well as supporting different negative sampling techniques."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of users: 943\n",
      "Number of items: 1642\n"
     ]
    }
   ],
   "source": [
    "train_set = cornac.data.Dataset.from_uir(train.itertuples(index=False), seed=SEED)\n",
    "\n",
    "print('Number of users: {}'.format(train_set.num_users))\n",
    "print('Number of items: {}'.format(train_set.num_items))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.3 Train the BiVAE model\n",
    "\n",
    "The BiVAE has a few important parameters that we need to consider:\n",
    "\n",
    "- `k`: dimension of the latent space (i.e. the size of $\\bf{\\theta}_u$  and  $\\bf{\\beta}_i$ ).\n",
    "- `encoder_structure`: dimension(s) of hidden layer(s) of the user and item encoders.\n",
    "- `act_fn`: non-linear activation function used in the encoders.\n",
    "- `likelihood`: choice of the likelihood function being optimized.\n",
    "- `n_epochs`: number of passes through training data.\n",
    "- `batch_size`: size of mini-batches of data during training.\n",
    "- `learning_rate`: step size in the gradient update rules.\n",
    "\n",
    "To train the model, we simply need to call the `fit()` method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "132fcc4256dc43a8bc010c9d535d046c",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/500 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Took 69.1472 seconds for training.\n"
     ]
    }
   ],
   "source": [
    "bivae = cornac.models.BiVAECF(\n",
    "    k=LATENT_DIM,\n",
    "    encoder_structure=ENCODER_DIMS,\n",
    "    act_fn=ACT_FUNC,\n",
    "    likelihood=LIKELIHOOD,\n",
    "    n_epochs=NUM_EPOCHS,\n",
    "    batch_size=BATCH_SIZE,\n",
    "    learning_rate=LEARNING_RATE,\n",
    "    seed=SEED,\n",
    "    use_gpu=torch.cuda.is_available(),\n",
    "    verbose=True\n",
    ")\n",
    "\n",
    "with Timer() as t:\n",
    "    bivae.fit(train_set)\n",
    "print(\"Took {} seconds for training.\".format(t))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.4 Prediction and Evaluation\n",
    "\n",
    "Now that our model is trained, we can produce the ranked lists for recommendation.  Every recommender models in Cornac provide `rate()` and `rank()` methods for predicting item rated value as well as item ranked list for a given user.  To make use of the current evaluation schemes, we will through `predict()` and `predict_ranking()` functions inside `cornac_utils` to produce the predictions.\n",
    "\n",
    "Let's measure recommendation performance of the model using top-K ranking metrics."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Took 1.7215 seconds for prediction.\n"
     ]
    }
   ],
   "source": [
    "with Timer() as t:\n",
    "    all_predictions = predict_ranking(bivae, train, usercol='userID', itemcol='itemID', remove_seen=True)\n",
    "print(\"Took {} seconds for prediction.\".format(t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MAP:\t0.146552\n",
      "NDCG:\t0.474124\n",
      "Precision@K:\t0.412527\n",
      "Recall@K:\t0.225064\n"
     ]
    }
   ],
   "source": [
    "eval_map = map_at_k(test, all_predictions, col_prediction='prediction', k=TOP_K)\n",
    "eval_ndcg = ndcg_at_k(test, all_predictions, col_prediction='prediction', k=TOP_K)\n",
    "eval_precision = precision_at_k(test, all_predictions, col_prediction='prediction', k=TOP_K)\n",
    "eval_recall = recall_at_k(test, all_predictions, col_prediction='prediction', k=TOP_K)\n",
    "\n",
    "print(\"MAP:\\t%f\" % eval_map,\n",
    "      \"NDCG:\\t%f\" % eval_ndcg,\n",
    "      \"Precision@K:\\t%f\" % eval_precision,\n",
    "      \"Recall@K:\\t%f\" % eval_recall, sep='\\n')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/scrapbook.scrap.json+json": {
       "data": 0.14655205218191958,
       "encoder": "json",
       "name": "map",
       "version": 1
      }
     },
     "metadata": {
      "scrapbook": {
       "data": true,
       "display": false,
       "name": "map"
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "application/scrapbook.scrap.json+json": {
       "data": 0.4741242642717392,
       "encoder": "json",
       "name": "ndcg",
       "version": 1
      }
     },
     "metadata": {
      "scrapbook": {
       "data": true,
       "display": false,
       "name": "ndcg"
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "application/scrapbook.scrap.json+json": {
       "data": 0.41252653927813165,
       "encoder": "json",
       "name": "precision",
       "version": 1
      }
     },
     "metadata": {
      "scrapbook": {
       "data": true,
       "display": false,
       "name": "precision"
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "application/scrapbook.scrap.json+json": {
       "data": 0.22506395891693493,
       "encoder": "json",
       "name": "recall",
       "version": 1
      }
     },
     "metadata": {
      "scrapbook": {
       "data": true,
       "display": false,
       "name": "recall"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Record results with papermill for tests\n",
    "sb.glue(\"map\", eval_map)\n",
    "sb.glue(\"ndcg\", eval_ndcg)\n",
    "sb.glue(\"precision\", eval_precision)\n",
    "sb.glue(\"recall\", eval_recall)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4 Discussion\n",
    "\n",
    "BiVAE is a new variational autoencoder tailored for dyadic data, where observations consist of measurements associated with two sets of objects, e.g., users, items and corresponding ratings.  The model is symmetric, which makes it easier to extend axiliary data from both sides of users and items.  In addition to preference data, the model can be applied to other types of dyadic data such as documentword matrices, and other tasks such as co-clustering.  \n",
    "\n",
    "In the paper, there is also a discussion on Constrained Adaptive Priors (CAP), a proposed method to build informative priors to mitigate the well-known posterior collapse problem. We have left out that part purposely, not to distract the audiences.  Nevertheless, it is very interesting and worth taking a look.  \n",
    "\n",
    "[This repository](https://github.com/PreferredAI/bi-vae) will provide you a more comprehensive set of experiments related to BiVAE."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "1. Quoc-Tuan Truong, Salah, Aghiles, and Hady W. Lauw. \"Bilateral Variational Autoencoder for Collaborative Filtering.\" Proceedings of the 14th ACM International Conference on Web Search and Data Mining. 2021. https://dl.acm.org/doi/pdf/10.1145/3437963.3441759\n",
    "2. Salah, Aghiles, Quoc-Tuan Truong, and Hady W. Lauw. \"Cornac: A Comparative Framework for Multimodal Recommender Systems.\" Journal of Machine Learning Research 21.95 (2020): 1-5. https://cornac.preferred.ai\n",
    "3. Liang, Dawen, et al. \"Variational autoencoders for collaborative filtering.\" Proceedings of the 2018 World Wide Web Conference. 2018."
   ]
  }
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