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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xLXWx4uhqtYJ"
      },
      "source": [
        "<table class=\"tfo-notebook-buttons\" align=\"left\">\n",
        "  <td>\n",
        "    <a target=\"_blank\" href=\"https://colab.research.google.com/github/PreferredAI/tutorials/blob/master/recommender-systems/09_deep_learning.ipynb\"><img src=\"https://www.tensorflow.org/images/colab_logo_32px.png\" />Run in Google Colab</a>\n",
        "  </td>\n",
        "  <td>\n",
        "    <a target=\"_blank\" href=\"https://github.com/PreferredAI/tutorials/blob/master/recommender-systems/09_deep_learning.ipynb\"><img src=\"https://www.tensorflow.org/images/GitHub-Mark-32px.png\" />View source on GitHub</a>\n",
        "  </td>\n",
        "</table>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wzPrmZOMtXt1"
      },
      "source": [
        "# Deep Learning"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Bh3gYub8f6qZ"
      },
      "source": [
        "Recently deep learning has produced significant advancements on various machine learning tasks. To develop an appreciation of how deep learning has an effect on recommender systems, in this tutorial we look into example models from two broad categories. One models collaborative filtering or user-item interaction data, while the other models content associated with items (or users)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MqktDa7H2hKz"
      },
      "source": [
        "## 1. Setup"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "41oWCMUG2eC_"
      },
      "source": [
        "!pip install --quiet cornac==1.15.4"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YqKrDcGH2k7E",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "7f9ecda3-c025-4f77-8234-29f6edf20511"
      },
      "source": [
        "import os\n",
        "import sys\n",
        "\n",
        "import cornac\n",
        "from cornac.data import Reader\n",
        "from cornac.datasets import movielens, citeulike\n",
        "from cornac.eval_methods import RatioSplit\n",
        "from cornac.models import GMF, MLP, NeuMF, VAECF, CDL, ConvMF, WMF, CTR \n",
        "from cornac.data import TextModality\n",
        "from cornac.data.text import BaseTokenizer\n",
        "\n",
        "import tensorflow as tf\n",
        "\n",
        "print(f\"System version: {sys.version}\")\n",
        "print(f\"Cornac version: {cornac.__version__}\")\n",
        "print(f\"Tensorflow version: {tf.__version__}\")\n",
        "\n",
        "SEED = 42\n",
        "VERBOSE = True"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "System version: 3.10.11 (main, Apr  5 2023, 14:15:10) [GCC 9.4.0]\n",
            "Cornac version: 1.15.4\n",
            "Tensorflow version: 2.12.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "r76coF3ZyWxb"
      },
      "source": [
        "## 2. Deep Learning for Collaborative Filtering\n",
        "\n",
        "In this section, we study two frameworks of deep learning, and how they can be used to model user-item interactions.  Neural collaborative filtering is based on multi-layer perceptrons, while as suggested by its name, variational autoencoder for collaborative filtering is based on VAE.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0GePqE99j5nr"
      },
      "source": [
        "### Neural Collaborative Filtering\n",
        "\n",
        "Neural collaborative filtering consists of a family of models developed based on neural networks to tackle the problem of collaborative filtering based on implicit feedback.  The final model NeuMF is a combination of two components, namely Generalized Matrix Factorization (GMF) and Multi-Layer Perceptrons (MLP), which are also independent models respectively.\n",
        "\n",
        "- GMF projects element-wise product between user and item embedding vectors through *Sigmoid* function to out the prediction:\n",
        "<!-- \\begin{equation}\n",
        "\\hat{y}_{ij} = \\sigma \\big(\\mathbf{w}^T (\\mathbf{u}_i \\odot \\mathbf{v}_j)\\big) = \\sigma \\big(\\sum_{k=1}^{K} w_k . u_{ik} . v_{jk}\\big)\n",
        "\\end{equation} -->\n",
        "<p align=\"center\">\n",
        "  <img src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAWAAAAA5CAYAAAAIl/HHAAAS7ElEQVR4Ae3dBdA1v1UG8Ad3dy3F3aVAcXd3+Bd3d7dCkeJug9PiVqBAcXd3KVrcvfj8mE0b8u3u3fu+e189Z+bO7s1ms8mzycmxZJOiQqAQuAkIvFWSByd5QJK7ugY9WZKHJPmiJC/SpddpIVAIFAKFwE4IPEKSv0zycl15j5rknZPco0ur00KgECgECoGdEXjuJA9N8phTuXdP8k5JHmfn51RxhUAhUAgUAgMC75bkh6e0eyV5v+F6/S0ECoFCoBA4EQLfkOQzkmDEX5bk+0/0nCq2ECgECoFCoEOg2X/vk+SRk3C8/UuSe3Z56rQQKAQKgULgBAiw//5bksfoyiYNP7D7X6eFQCFQCBQCJ0CA2eEHh3KfemLKLzik199CoBAoBAqBHRB4xMnm+5NJHpTk1bsyXzXJbyf5oSQv3aXXaSFQCBQChUAhUAgUAoVAIVAIFAKFQCFQCBQChUAhUAgUAoVAIVAIFAKFQCFQCBQChUAhUAgUApeDgNjepz/hr/aKuJz3Wk8tBAqBa4DAeyb5n+73+0l+94jfnyf5++7+viznli0XFQJXBoF+NdF5K/VGSd5+5ddvHXjeZ92m+9uOXzepzY+UxPaRIz1Wkl/rGOiHjRk2/tevrZh76yRfmuTvpjKtoLN0ueh0CNzE/noStF4vyZvvVPLdktgg5RmSPPZU7u8kefQkjzat0/+snZ5124p5lWkBwk1pNzPAZ69sHfk8Sf51Ypj/sdMeD/rkRyb59yRnZeo3Bf9Tt+M9krzSqR9y3ct/8SSfu2Mj3jXJ43flGWCf1/23acq7d//H00dJ4ndb6ZDU8BFJ3vQGgGMjna9P8kwH2vIunRT8h0me8ED+rZdfLMmvLkjfW8uofIcR+Kokz3842//PoXPcBiIN/NTAMM/b7hceCtDJ37hLw2Ces/vfn2Lcn3jLBwWGs/YJHZOTd/Z0PXDX8Nym6R+yod7G4jd1TPgbN9yzNYtlyzdhMtva3svI9xRJfmbYMGm1HuxR35zkTVZz3YyLn5Dk40/YlCdN8t9JnnLDM6zvZ6N74g15b3IWOHAQPc1KI98iyVevXL/ql/QLTrIn2FhRUi/ptznSfG5oLxoFhr3KrXIejsAnJ3n/h/9dPuMQsJ0dkflDk7zBctZrf4UkahCsDfTzNpIz7tc3FkIi4igpSp5qkvqWsCAk/M0UorWU5yqns70yTR1DL5HkPycmzIH2vMfcXHkvFYFnSfIXW0yLGIDYw0Zvl8Q3pm4ivcO0Y9Qp2/Y5G+3LPNW/MjnpTlmfpbJfLclHJWFfNfF+dJJ3PEZtWir4HOlfcsCBQUpW1+tGhJw/TvIyZ6i499Ok4N9acd6doei65cQI/FISJp+iCYFvPbH5wWNIv739dwn8t7mAusw9m7njU5K81MxF0Rzs0S86c+0ikjiJ2D6XyOfY2devG71AEhEN/A/HEvPM93ZM2Cfni64HAiwLX7lWVWFSt4U4Nv4qyWvNNBjjoQUwTThiUmx1zp92Oj75dB+HkPR2Tx/P+eyT/XeLs+jbk7zyTF0871mTGLTUmEZsys88pT9XSzzyKATq05OIN12j90mytrm3cnq8nAu3a6QNDZ9jmA4sxawu1Y/tkjT4RO1B1+RogcXPnqOuzDM+Q98k4VM70bbwBVL9HrTlWXs8Zyxj7rmilfYkGrfFNLPEqUGiMLv2g0Tn/rEphnX2xiuUKLKAWkoqGlcMcSr2hHnpwJjbSF832Wtcf/AUdypG2KCR9qdJPma6yWD40Sn9JyZG42WK//uA7id+dYlINf+w4JDBmP9xKv/zuwK+cJpA1MeG3GehDz+Ced13+ubY3HPEOfoQpLr42SS8x1WoFUfkLyR5hbkCVtJ+IMnSohWMWbmXvem4SVhYoS8Tj/3O/7F+909yv5U2b7lEldV2eOsf+vPeRADxhWUhmm87FE4zac47iznY419jyHPsX05/JlAbyfdhnPiRPvV4xxa4Ib/xq40EEQunGr1+kr8d6tGunfUo3NU7u6Md1M8G5p8Mtqm7kvzRWZ84c5+O0jOmLefPN1POmMTZZbEDVZ7KLLLhn6bAddLjkww3GBQ679JKIAPKdZNPI8D54CFvdD/jK//bWqYzHEnIpPEl+tSpLj0DlrfV8SwMmNT6QUsPnEknAb/OTHqf1CYijL2n50iCkZ6FRIWwRS+RpbYkiy1kcG/pby2PeO5DBMcfScJebaJoX6PgYNMvCAUm2J58QmiPhTifOfUL/fSnTxC62Lz2/ECYYiP91TObZkdT+fEkW/BqZYzHeyTBoNDvDbbS154k/lOExr7v9EwTjP7bSGw2oehQjHbLv+X4jBNujdc+7B4zAHqhJA8dpCId6yum6+2wpBIeCqB3vw6rYx7zOxR4zhvMwzg6CzkpvLw5svJNJ+pV5T4fkwNmK4/VSMis/M9T2mtOaQ5fkIQT66zE1ukTMktE+lSPkQELRZI+x4C1a02Fwiju6AiTtG9gj7O0zs8BtEawVh+TSd9H9KE158NavxG+MzL0vg6cWY1R9Olz50w4x/Q7E8chIt1/2pCJNvlzQ1r/95c7DapPP/bcO/YcmPsJqdyLtL31adojIaARoWxUpbX5ZacMvkmHsfUSZbt36dh4EHPafw1hm55tZelI+nc/fknQ+iiT1xZ6tu5TTt8y8x7xvd6k2Mrs+yueo+5v2S6uHAl73tMdWmB7CIfLKMmZjUiVjVT6F9uf7miAkpSbbbS7dPJTDOjeM09hMliSnrRJKM8aMWcATCQD8gFEA04a0wB63Cl6oZeIp0ubDy9/wCZ4FgZMzX3dlRqQasbYZLZbbfNjpxxpjRHKqw8w/7i/xanqdD8/IwX2ZVPT2YjnSLgW9XCJfmOK2Fi6fsr0l5y0LEJFTyaih/QJw7lxQsreg5h6aHowx7jO6g8Y64K5kdwJHcZJ74jl+KOZ9KQ/9Vqm9h2zurTxINE339cXPE0yxt5InMe91G3SJ7X25ovxnv5/a6MxrI3j4p82KfT3wIGpqaeP3ehAVz/vaXFcUuH7/RCaqmFPg56WJKul9P7evc8xEXaVUVrBEHXMpXXYZnEddk2toRIBzEv1kjB0AfSkDvfCZ+tqprV2C0ey6coSnYUBH3oXTDa9U8+z2a61kT2PpDjSIQYsP1UOZmzn3sHHTb6Fsaz+/1pd75Pkk/rMwzlJbKsEPNx67r80n6+ZKeWDB3V2zAKbPcPnmFZg/h0HtJ6xHlv+8wuZMPpxQrMcJT6rF3siAOhjx5IJHDNvhJmKfZ6bWMZ+Y+2C/nsscWISNPs2KntJgh+fC/c5B/pYD5q893SHBCxjc0r1kgjw2TsbmenHQesakRxAfQPaPePRwP7aI39LThhlY14Y5EjUIWaJOe+mvE1d7h2OYxn+UxeBRhrWqVBT/Tni2N4sNTwPwe7PVgpYYsDvNdVtNEF4lyaMNWKP8n7naLRZymPi6aWNufukUQlJfzBTvjC8pXfQdumae14rn/axtlz3rwcNrd03d6SiH9P3DklwJCHvYCQ24TkNouWjQe5pLjBJYVyj2ag97zxHki6Hb6OmRovwaYQhEUR64ktq4wJP6aXjPl9/znSh3/QOXF97ZtLCWzjM2h4pVP8x+sW7IBUjfWsUyqZLdxyM7S8fUjHUcbsA7en5o1u0ncDStCBa5JLJtAm0s/tCcMTxpvZMVMxaq5iZiNPHpjK9CK1QHn8z4J6dasBj8S+TCDvgSN95YGACwcv20teI6iOfXwucx9xI135MEuclqgkVaJxZW7kYkOf3A8E1E4L0ngG/4eQMovYfIpJl/77X8rPpbTUvfeBUL21yPkdwf+9J2lkzMdj3YGk1JsZtR68lO//cc/dMEy3Tm+eUTWsy6WAASyT+nPS8B5FEMbuRMexRtjK+e3iHVHAaZzMZyCP6odeSMVCmIe9H/e41OSr7OuEbo62WD0qf6c15fAAPnG4UDqlMEUUYpIVLfV52XGGltt70TLbrXgOWl5mhv0fRyqe19KRv9mQiwPcsf+9j5pUnQsPYpf2R3vGeOeJLMl5n3xUJh4OpcXLLHm2DR71BnFakG52nbxQbK1CYLswkF00YiBCoNtv5zx48ZxPu66YtguHXpGv5SRVwYZ7pmRU7GDDZb/cgUtFSrC0PMZMHTzNpkhRAumz2aA48ndI16hQto4/eWKqfSWiLVCtfs+kuldWnm6DE767Z40Qu6LT6Fal0iai/sx128lB7B6PzdamsvdO9+z6cjObBfkm7WCM2Q5EQ5yU2aDjrH6cippJ+XJtQaZatjWLkR1XduyW8SSe4CWfznnvCPEfBCe8R1dIkef2YliFiRJ9vEQt4DdMjU04jPIikjEk2Z6B8/b4qxob+MppPmMn63Qox0n5yMK6kIQy4FwiYvzjHtZk2DRfMeo6YZEjL6jpLBrHwLbO6AW6mM1M1IoIbEE0NaOmOpLNWyT79Is4NeCFVXrijyWMLWRq4piq2Mqg2vdQvnSlGm3um3PKf5Uh7WKuLQSa0iURoeztRGKQt9icMTIdvZgcddgtjVU/Si449905dJ2kYhMe2U4f0O0RWB805WNxnEHhHSyRWcxzES3lPlS5SwHuDN6npkElLPTAjppPzEIkTI9yyyvI8z8EsMBkSovfkuQQFkR+kvTebYSg0MxOMPr20X4V6N+Gurx/m6T4Tvr7HdCEKgvTbO9fUh+mlkVBVpi8RN7TxUcqVD9PG30ZNjrbCnGgc4GG9NN/Kb0fP6J3Xxt/3THWhja+RZzxgKQMJsq80L+Z3DZkxN5ESKtCDIRsprM2Kw21X9i+nEmZ2FYj0tIdUpDNZKMIO1dvp1tpoMiEFkG4wdhMxm560Foq0dv95rmGwcw4WZeqDzF5LpEOPIZJLea9SOpMTc9/aQF+rL9snR9hlOR/X6uZas/+yoTbn8ta+eKhs1wkDNFIxuq1cQlILBxShpB/T6nsJeEvZa3kw2NYe+Zr9l+BDGLIQC7U6TX8fdlAvE8kd9IqTaN6MzpjrH8xsIky9IomZnXoxGkPunXV3POCKJhgAVJ4lJ9FFV5u9fQyFObYO7FNsWrSVUWo/VBbpjZ2KnU/nPTVhJKS4vi+1Z5LI2daaSayl90dqLDX8OhKNZS7M6VBb2F6Nwy8+lPGSrpvMf3N6Ng3G6kdCQR/ZcN6qYbwmbn2DrRex/zZfAAmcmZQGtufYJpS0kFTPFEdvX2pEiLBYhfmk1Wm69H8HTNrKutmFX7h3WxVlAYLGzC0rJA2RSJq9tT2AraU561radTmS8o9lVKdqG6bJpjjHkLY+U0QKk4F3cqzZYOsz9spHFefImiMq/dp7YR/c4micK/sqpBlzx9bf+8S4qbxLJqNj26a/bDVXbSmbA6x3THLQU+tJ/XsRTZ1jmgmjOa5pQ22yJkia3GC8Jwk55ORuRFhq+3B4N0wY6tQvDml5YcI8skgYLhsqBjvLpYc7zSwtnMKMM7epzXDLlfzLdkR1uCrMigR7VVXLPV6gzol5IlLcnA3TO2kCwZT1jgPGvZcD9I7CLyiBPf8YE49VXlTgrZu4b2mGSJgW3bMl/23LI1qHJI/fcfqNptcteJgwfBGj96dtuW81D4YrRAXTFi95VRjYaqUXLvpA4ZxDYCH7yZPNrP1yx5M/8AIfQDWkqnHyiiTp/Q6tGocYAkeN5dLXnTiD2P3XQtZaGzm7fDxAnOkeRHJk48dUrvPY3QOLtTL0Uasx8bizLCxRNoGq1wrWnrf5mpfGFLEUIrS5oCuQkcovLnPJGXQFqnijqsBJcdbQMf4GjrctTOs6gGayXYuD1oZ7TuFme6jUJDlhVOznQrIO7e9xHTA8ZR1pbKI+Wmjcsc/yfsUyFx1AgERwSPI6UERdvgAEDIY5G9sFPPpkj2ByWfLWcxTb+9dqSKabrT/x7Uw0mC0br/ArCwTEDWO8fm05/ckaVgXvbocuSAuBQuCCEGDrtaquMcy9j/b+LioECoFCoBCYQUBIoFjoU/2ox0WFQCFQCBQChUAhUAgUAoVAIVAIFAKFQCFQCBQChUAhUAgUAoVAIVAIFAKFwK1EwP4PYqcrTv1Wvv5qdCFQCFwmArYGsPXp2r7JW+onfhoj9921cU/cLfdXnkKgECgEbiUC9oI+ZlP8OZAwX5uF+8zQWXZimyuz0gqBQqAQuPEI+OYbBroH2bC/GPAeSFYZhUAhcOMRsDezjXjsv2I/CF98IBEjexTYoGftN27sVAx4Aq8OhUAhUAgcQsB+Dr7/Z8tYm4DbD6JtDM6kcGilnM18eioG3KNR54VAIVAIrCCAYdo20jfZ9vjCQzHgFbDrUiFQCBQCPQK2jrQvxF1JHjRdaF9/8Cl3EvLab/xYZDHgHt06LwQKgUJgAQH2X9/NY//1RQW7oyF2YIS52nZy7Td+iYH9uJxwE4B1KAQKgUJgCQGfqGof4PQdOJ9i8p21s3yB3Cb4vqXmm3I+j+5LDT77XnQJCPwvsO00UrFyq/4AAAAASUVORK5CYII=\" />\n",
        "</p>\n",
        "where $\\odot$ is element-wise product, $\\mathbf{u}_i$ and $\\mathbf{v}_j$ are user and item embeddings, $\\mathbf{w}$ are the projection weights, and $\\sigma$ is the *Sigmoid* function.\n",
        "\n",
        "- MLP projects concatenation of user and item embeddings through multiple layers:\n",
        "<!-- \\begin{align*}\n",
        "\\mathbf{z}_1 & = \\phi_1 (\\mathbf{u}_i, \\mathbf{v}_j) = \\begin{bmatrix} \\mathbf{u}_i\\\\ \\mathbf{v}_j \\end{bmatrix} \\\\\n",
        "\\mathbf{z}_2 & = \\phi_2 (\\mathbf{w}_2^T \\mathbf{z}_1 + b_2) \\\\\n",
        "\\vdots & \\\\\n",
        "\\mathbf{z}_L & = \\phi_L (\\mathbf{w}_L^T \\mathbf{z}_{L-1} + b_L) \\\\\n",
        "\\hat{y}_{ij} & = \\sigma (\\mathbf{w}_{L+1}^T \\mathbf{z}_L) \n",
        "\\end{align*} -->\n",
        "<p align=\"center\">\n",
        "<img 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\" />\n",
        "</p>\n",
        "where $\\phi$ is a non-linear activation function (could be *Tanh* as recommended by the authors).\n",
        "\n",
        "- NeuMF is a fusion of GMF and MLP:\n",
        "<!-- \\begin{equation}\n",
        "\\hat{y}_{ij} = \\sigma \\bigg(\\mathbf{w}^T \\begin{bmatrix} \\mathbf{u}_i \\odot \\mathbf{v}_j \\\\ \\mathbf{z}_L \\end{bmatrix} \\bigg)\n",
        "\\end{equation} -->\n",
        "<p align=\"center\">\n",
        "<img src=\"data:image/png;base64,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\" />\n",
        "</p>\n",
        "\n",
        "The models are learned by minimizing log-loss function:\n",
        "<!-- \\begin{align*}\n",
        "\\mathcal{L}  & = - \\sum_{(u,i) \\in \\mathbf{R}^+} \\log \\hat{y}_{ui} - \\sum_{(u,i) \\in \\mathbf{R}^-} \\log (1 - \\hat{y}_{ui}) \\\\\n",
        "& = - \\sum_{(u,i) \\in \\mathbf{R}^+ \\cup \\mathbf{R}^- } y_{ui} \\log \\hat{y}_{ui} + (1 - y_{ui}) \\log (1 - \\hat{y}_{ui})\n",
        "\\end{align*} -->\n",
        "<p align=\"center\">\n",
        "<img 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\" />\n",
        "</p>\n",
        "\n",
        "Let's try the models all together! "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "p2iyzuFFs1Fq",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000,
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            "a734ef0aef5740ae894f1b6706fff496",
            "d9e6c3e264794560a33a9e07f4259e3c",
            "af897a93e1ae4f5fac9fbc7b83041545",
            "37a6af0a47614431a15ee5ad4031494d",
            "43444cf1a658409e8a5de9ac22650553",
            "1d7ce82df394429386f79b87f4049e3a",
            "167422d36fc048ae881289894eae12af",
            "7d4b03a5511d4b76bac5875790f250f9",
            "e10bfea60e2a4de5a67d33795302b247"
          ]
        },
        "outputId": "2b6cadc8-7667-4621-cf2e-ec6333d8d1a1"
      },
      "source": [
        "GMF_FACTORS = 8  # @param\n",
        "MLP_LAYERS = [32, 16, 8]  # @param\n",
        "ACTIVATION = \"tanh\"  # @param [\"tanh\", \"sigmoid\", \"relu\", \"leaky_relu\"]\n",
        "NEG_SAMPLES = 3  # @param\n",
        "NUM_EPOCHS = 10  # @param \n",
        "BATCH_SIZE = 256  # @param\n",
        "LEARNING_RATE = 0.001  # @param\n",
        "\n",
        "gmf = GMF(num_factors=GMF_FACTORS, num_epochs=NUM_EPOCHS, batch_size=BATCH_SIZE, \n",
        "          num_neg=NEG_SAMPLES, lr=LEARNING_RATE, seed=SEED, verbose=VERBOSE)\n",
        "mlp = MLP(layers=MLP_LAYERS, act_fn=ACTIVATION, num_epochs=NUM_EPOCHS, batch_size=BATCH_SIZE, \n",
        "          num_neg=NEG_SAMPLES, lr=LEARNING_RATE, seed=SEED, verbose=VERBOSE)\n",
        "neumf = NeuMF(num_factors=GMF_FACTORS, layers=MLP_LAYERS, act_fn=ACTIVATION, num_epochs=NUM_EPOCHS,\n",
        "              num_neg=NEG_SAMPLES, batch_size=BATCH_SIZE, lr=LEARNING_RATE, seed=SEED, verbose=VERBOSE)\n",
        "\n",
        "wmf = WMF(k=GMF_FACTORS, max_iter=200, learning_rate=0.001, seed=SEED, verbose=VERBOSE)\n",
        "\n",
        "ml_100k = movielens.load_feedback(variant=\"100K\", reader=Reader(bin_threshold=4.0))\n",
        "ratio_split = RatioSplit(\n",
        "  data=ml_100k, test_size=0.2, exclude_unknowns=True, seed=SEED, verbose=VERBOSE\n",
        ")\n",
        "ndcg_50 = cornac.metrics.NDCG(k=50)\n",
        "rec_50 = cornac.metrics.Recall(k=50)\n",
        "\n",
        "cornac.Experiment(\n",
        "  eval_method=ratio_split,\n",
        "  models=[gmf, mlp, neumf, wmf],\n",
        "  metrics=[ndcg_50, rec_50],\n",
        ").run()"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Data from http://files.grouplens.org/datasets/movielens/ml-100k/u.data\n",
            "will be cached into /root/.cornac/ml-100k/u.data\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "0.00B [00:00, ?B/s]"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "4bba239abb5d43a4a2403dfe4086497f"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "File cached!\n",
            "rating_threshold = 1.0\n",
            "exclude_unknowns = True\n",
            "---\n",
            "Training data:\n",
            "Number of users = 942\n",
            "Number of items = 1420\n",
            "Number of ratings = 44300\n",
            "Max rating = 1.0\n",
            "Min rating = 1.0\n",
            "Global mean = 1.0\n",
            "---\n",
            "Test data:\n",
            "Number of users = 921\n",
            "Number of items = 1067\n",
            "Number of ratings = 11044\n",
            "Number of unknown users = 0\n",
            "Number of unknown items = 0\n",
            "---\n",
            "Total users = 942\n",
            "Total items = 1420\n",
            "\n",
            "[GMF] Training started!\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
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            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "8c4cb7e84ad84498b14f7230deb18e0b"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "[GMF] Evaluation started!\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Ranking:   0%|          | 0/921 [00:00<?, ?it/s]"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "64f9d7c6a38047ef97b36ff82e50caf0"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "[MLP] Training started!\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "  0%|          | 0/10 [00:00<?, ?it/s]"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "a8ddf9ffa0014339b387e59bdfe64083"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "[MLP] Evaluation started!\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Ranking:   0%|          | 0/921 [00:00<?, ?it/s]"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "404b36a0aefc44a49d3804ab397ead21"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "[NeuMF] Training started!\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
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            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "60e7115082a9415fb0ad19554e5f07a0"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "[NeuMF] Evaluation started!\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Ranking:   0%|          | 0/921 [00:00<?, ?it/s]"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "856a051cc2e14a4ebd3a52fc743478e3"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "[WMF] Training started!\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
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            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "7bc239d35c8d461abea878d762f6d25f"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Learning completed!\n",
            "\n",
            "[WMF] Evaluation started!\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Ranking:   0%|          | 0/921 [00:00<?, ?it/s]"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "6e33306739b444b3b5fb07521908413a"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "TEST:\n",
            "...\n",
            "      | NDCG@50 | Recall@50 | Train (s) | Test (s)\n",
            "----- + ------- + --------- + --------- + --------\n",
            "GMF   |  0.1609 |    0.2778 |   33.4836 |   1.2062\n",
            "MLP   |  0.1630 |    0.2807 |   24.3624 |   1.2698\n",
            "NeuMF |  0.2412 |    0.4268 |   24.6304 |   1.3844\n",
            "WMF   |  0.1976 |    0.3753 |    8.4846 |   0.5714\n",
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QUFnKYm-uWLh"
      },
      "source": [
        "### Variational Autoencoder for Collaborative Filtering (VAECF)\n",
        "\n",
        "\n",
        "Variational Autoencoders (VAE) is a type of autoencoders which is a neural network with auto-associative mapping of inputs.  Normal autoencoders learns a determinisic latent representation of an input, while VAE learns a distribution of that representation.  VAECF model extends VAE for the collaborative filtering problem with implicit feedback data.\n",
        "\n",
        "Let the data for user $i$ (e.g., history clicks) be a vector $\\mathbf{x}_i \\in \\mathbb{N}^M$ where M is the number of items.  The generative model of VAECF can be described as follows:\n",
        "\n",
        "- User latent representation is sampled from standard Gaussion prior: $\\mathbf{u}_i \\sim \\mathcal{N}(0, \\mathbf{I}_K)$\n",
        "\n",
        "- $\\mathbf{z}_i$ is transformed via a non-linear function $f_{\\theta}$ to produce a probability distribution over items (normalized using *softmax*): $\\pi(\\mathbf{u}_i) \\propto \\exp \\{ f_{\\theta}(\\mathbf{u}_i) \\}$\n",
        "\n",
        "- User data $\\mathbf{x}_i$ is assumed to have been drawn from the multinomial distribution: $\\mathbf{x}_i \\sim \\mathrm{Mult}(N_i, \\pi(\\mathbf{u}_i))$\n",
        "\n",
        "The Multinomial (*mult*) log-likelihood for user $i$ conditioned on the latent representation is:\n",
        "<!-- \\begin{equation}\n",
        "\\log p_{\\theta} (\\mathbf{x}_i | \\mathbf{u}_i) = \\mathcal{L}_{mult} = \\sum_{i=1}^{N} \\sum_{j=1}^{M} x_{ij} \\log \\pi_j(\\mathbf{u}_i)\n",
        "\\end{equation} -->\n",
        "<p align=\"center\">\n",
        "<img src=\"data:image/png;base64,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\" />\n",
        "</p>\n",
        "\n",
        "Other choices of likelihood including Bernoulli (*bern*), Gaussian (*gaus*), or Poisson (*pois*) can be used:\n",
        "<!-- \\begin{align*}\n",
        "\\mathcal{L}_{bern} &= \\sum_{i=1}^{N} \\sum_{j=1}^{M} x_{ij} \\log \\sigma(f_{\\theta}(\\mathbf{u}_i)_j) + (1 - x_{ij}) \\log (1 - \\sigma(f_{\\theta}(\\mathbf{u}_i)_j)) \\\\\n",
        "\\mathcal{L}_{gaus} &= \\sum_{i=1}^{N} \\sum_{j=1}^{M} - (x_{ij} - \\sigma(f_{\\theta}(\\mathbf{u}_i)_j))^2  \\\\\n",
        "\\mathcal{L}_{pois} &= \\sum_{i=1}^{N} \\sum_{j=1}^{M} x_{ij} \\log \\sigma(f_{\\theta}(\\mathbf{u}_i)_j) - \\sigma(f_{\\theta}(\\mathbf{u}_i)_j)\n",
        "\\end{align*} -->\n",
        "<p align=\"center\">\n",
        "<img 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\" />\n",
        "</p>\n",
        "\n",
        "\n",
        "\n",
        "The encoder-decoder architecture is due to the use of amortized inference, a technique of variational inference, for learning the generative model (**decoder**) $f_{\\theta}$.  Amortized inference learns an inference model (**encoder**) $g_{\\phi} (\\mathbf{x}_i) \\equiv [\\mu_{\\phi}(\\mathbf{x}_i), \\sigma_{\\phi}(\\mathbf{x}_i)]$, which makes use of the observed data $\\mathbf{x}_i$ to approximate the true intractable posterior $p(\\mathbf{u}_i | \\mathbf{x}_i)$ with a simpler variational distribution:\n",
        "<!-- \\begin{equation}\n",
        "q_{\\phi}(\\mathbf{u}_i | \\mathbf{x}_i) = \\mathcal{N} (\\mu_{\\phi}(\\mathbf{x}_i), \\mathrm{diag}\\{\\sigma_{\\phi}^2(\\mathbf{x}_i)\\}) \n",
        "\\end{equation} -->\n",
        "<p align=\"center\">\n",
        "  <img src=\"data:image/png;base64,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\">\n",
        "</p>\n",
        "\n",
        "Learning the model parameters $\\{\\theta, \\phi\\}$ is done via maximizing the evidence lower bound (ELBO):\n",
        "<!-- \\begin{equation}\n",
        "\\mathcal{L}_{\\beta} = \\mathbb{E}_{q_{\\phi} (\\mathbf{u}_i | \\mathbf{x}_i)} [\\log p_{\\theta} (\\mathbf{x}_i | \\mathbf{u}_i)] - \\beta . \\mathrm{KL}(q_{\\phi} (\\mathbf{u}_i | \\mathbf{x}_i) || p(\\mathbf{u}_i))\n",
        "\\end{equation} -->\n",
        "<p align=\"center\">\n",
        "  <img src=\"data:image/png;base64,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\">\n",
        "</p>\n",
        "\n",
        "where $\\beta$ is a hyper-parameter to control the strength of regularization introduced by enforcing small Kullback-Leibler (KL) divergence between posterior $q_{\\phi} (\\mathbf{u}_i | \\mathbf{x}_i)$ and the prior $p(\\mathbf{u}_i)$.\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ndiIw1WJ8Ghv",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 806,
          "referenced_widgets": [
            "319134fdc8ec45cea0f8fa0c8d6780bb",
            "0d583ef88e4a4809a36fcb168f634050",
            "0ec30aaf54da4824ab89d7cbc856eee9",
            "3bc4ca3086654512a7d0c53cb8f2c58f",
            "601c514dfcf5468d8110093f42402959",
            "deb67cbe260e496b8dc82a3dfe2729f2",
            "371718af5c4f4356b5f9b0ee0a2aacdc",
            "4e093a7919374967bc78ff2ece02caa2",
            "9d8e2109e61e49fab0507545645d2ceb",
            "2eefe0a51b3043a691fffd0696e7ae57",
            "77482fd8bcb641e9b207802602e6ca06",
            "f33393dcf81f4bdbb8108e18976584d0",
            "9f51d3c656604cb4ad226aedd1369f29",
            "7a41b55314654c62a4ee4cc4d4f90f43",
            "e64ec1556cfd4a4ab30f7d83a872fa4e",
            "c23123c3bb4c406ca7b9517fe7382b7d",
            "086a971b71654656ae8c84f62661de41",
            "f40def6fb7b94b8e8f391cb4801a5668",
            "f1365aa3ce9a44a794d16c5bf42a9fd6",
            "a324a8c35bdc46acb2a20163a266e49b",
            "fd29302811d54b6c95002be0ecbb2b36",
            "ea53ccbdf53b4f82a4db6ede3e23aabe",
            "8493eecb8c664044af739987951c37db",
            "cdccb5a2ab2541f1b1a1c3db1bb19cf1",
            "ec7049093acf412c99e9fa041d925597",
            "4d33fff7b486490984ffc5ff868565e5",
            "156050b745214942ad739028fdbfa761",
            "cf16caa13e564b9c98e3c0ff9e5707b7",
            "949e76d4dde0449f922e040cc81bb420",
            "52a3ca6e126b4fa69ea3104efa6d1fd9",
            "a2fddcd5302c448d8b1012ec51a8d3c2",
            "764c9d413c774cd99e70c77efd212818",
            "20a9ae89f96241f7955f96684a53894e",
            "40b0443a36984a6697b00d5f52fa2b67",
            "089e9e95fd0945c1b93e15e12e6ffdae",
            "f733577cfd114f5399746f877102b7eb",
            "d27e3f42a3e94be1b4e7cd71e80e323b",
            "6db59f42cd54439aaf0b21d7fb56eedf",
            "70471d7cc6f44832b3330c792c8362f3",
            "9ff286dafad84df5a2b62d704ac15024",
            "0dcd080c786c478eb9ef06b216ff7cbd",
            "5c9446fcf98246e880c72bcf236e537b",
            "19b39d38278b4f359a25107b20a3904d",
            "a31ca0ed2f7745c892fe9aebefc5c272"
          ]
        },
        "outputId": "c8f88fed-5401-44a1-ae60-4d37161d96b3"
      },
      "source": [
        "NUM_FACTORS = 25  # @param\n",
        "AE_LAYERS = [100, 50]  # @param\n",
        "ACTIVATION = \"tanh\"  # @param [\"tanh\", \"sigmoid\", \"relu\", \"leaky_relu\"]\n",
        "LIKELIHOOD = \"bern\"  # @param [\"bern\", \"mult\", \"gaus\", \"pois\"]\n",
        "NUM_EPOCHS = 600  # @param \n",
        "BATCH_SIZE = 256  # @param\n",
        "LEARNING_RATE = 0.001  # @param\n",
        "\n",
        "vaecf = VAECF(k=NUM_FACTORS, autoencoder_structure=AE_LAYERS, act_fn=ACTIVATION,\n",
        "              likelihood=LIKELIHOOD, n_epochs=NUM_EPOCHS, batch_size=BATCH_SIZE,\n",
        "              learning_rate=LEARNING_RATE, seed=SEED, verbose=VERBOSE, use_gpu=True)\n",
        "\n",
        "wmf = WMF(k=NUM_FACTORS, max_iter=200, learning_rate=0.001, seed=SEED, verbose=VERBOSE)\n",
        "\n",
        "ml_100k = movielens.load_feedback(variant=\"100K\", reader=Reader(bin_threshold=4.0))\n",
        "ratio_split = RatioSplit(\n",
        "  data=ml_100k, test_size=0.2, exclude_unknowns=True, seed=SEED, verbose=VERBOSE\n",
        ")\n",
        "\n",
        "cornac.Experiment(\n",
        "  eval_method=ratio_split, models=[vaecf, wmf], metrics=[rec_50, ndcg_50],\n",
        ").run()"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "rating_threshold = 1.0\n",
            "exclude_unknowns = True\n",
            "---\n",
            "Training data:\n",
            "Number of users = 942\n",
            "Number of items = 1420\n",
            "Number of ratings = 44300\n",
            "Max rating = 1.0\n",
            "Min rating = 1.0\n",
            "Global mean = 1.0\n",
            "---\n",
            "Test data:\n",
            "Number of users = 921\n",
            "Number of items = 1067\n",
            "Number of ratings = 11044\n",
            "Number of unknown users = 0\n",
            "Number of unknown items = 0\n",
            "---\n",
            "Total users = 942\n",
            "Total items = 1420\n",
            "\n",
            "[VAECF] Training started!\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "  0%|          | 0/600 [00:00<?, ?it/s]"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "319134fdc8ec45cea0f8fa0c8d6780bb"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "[VAECF] Evaluation started!\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Ranking:   0%|          | 0/921 [00:00<?, ?it/s]"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "f33393dcf81f4bdbb8108e18976584d0"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "[WMF] Training started!\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "  0%|          | 0/200 [00:00<?, ?it/s]"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "8493eecb8c664044af739987951c37db"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Learning completed!\n",
            "\n",
            "[WMF] Evaluation started!\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Ranking:   0%|          | 0/921 [00:00<?, ?it/s]"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "40b0443a36984a6697b00d5f52fa2b67"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "TEST:\n",
            "...\n",
            "      | NDCG@50 | Recall@50 | Train (s) | Test (s)\n",
            "----- + ------- + --------- + --------- + --------\n",
            "VAECF |  0.2405 |    0.4250 |   20.3484 |   1.4547\n",
            "WMF   |  0.2045 |    0.3958 |    8.1604 |   0.6233\n",
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-8iXcfuKsVa8"
      },
      "source": [
        "## 3. Deep Learning for Content-Based Filtering\n",
        "\n",
        "A different way to use deep learning is to model the content of items (or users).  The key idea is to derive low-dimensional representations from this content, originally in the form of text, images, etc., and to use these representations to enhance recommender systems in a similar way to content-based methods.  In the following, we illustrate two examples based on autoencoder and convolutional neural networks respectively."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "742yJ53Fj1Zz"
      },
      "source": [
        "### Collaborative Deep Learning (CDL)\n",
        "\n",
        "CDL makes use of Stacked-Denoising Autoencoders (SDAE) to model item text content, with the objective of improving upon Collaborative Topic Regression (CTR) model making use of topic model for the similar purpose.  CDL is a hierarchical Bayesian model, the generative process is as follows:\n",
        "\n",
        "- For each user $i$\n",
        "  - Draw latent vector $\\mathbf{u}_i \\sim \\mathcal{N}(0, \\lambda^{-1} \\mathbf{I})$\n",
        "- For each item $j$\n",
        "  - Put its corrupted content $\\mathbf{x}_j^{0}$ through SDAE\n",
        "  - Draw clean content $\\mathbf{x}_j \\sim \\mathcal{N}(\\mathbf{x}_L, \\lambda^{-1}\\mathbf{I})$\n",
        "    - User middle representation $\\mathbf{x}_j^{L/2}$\n",
        "  - Draw item offset $\\mathbf{\\epsilon}_j \\sim \\mathcal{N}(0, \\lambda^{-1} \\mathbf{I})$\n",
        "  - Set item latent vector $\\mathbf{v}_j$ to be: $\\mathbf{v}_j = \\mathbf{\\epsilon}_j + \\mathbf{x}_j^{L/2}$\n",
        "- For each user-item pair $(i, j)$\n",
        "  - Draw rating $r_{ij} \\sim \\mathcal{N}(\\mathbf{u}_i^T \\mathbf{v}_j, c_{ij}^{-1})$\n",
        "\n",
        "The confidence parameter $c_{ij}$ is defined similar to that for CTR:\n",
        "<!-- \\begin{equation}\n",
        "c_{i,j} = \n",
        "\\begin{cases} \n",
        "a & \\mbox{if } r_{i,j} > 0 \\\\\n",
        "b & \\mbox{otherwise }\n",
        "\\end{cases}\n",
        "\\end{equation} -->\n",
        "<p align=\"center\">\n",
        "  <img src=\"data:image/png;base64,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\">\n",
        "</p>\n",
        "\n",
        "Learning CDL model is done via minimizing the loss function:\n",
        "<!-- \\begin{align*}\n",
        "\\mathcal{L} = & \\frac{\\lambda_u}{2} \\sum_{i} || \\mathbf{u}_i ||_2^2 + \\frac{\\lambda_w}{2} \\sum_{l} (||\\mathbf{W}_l||_F^2 + ||\\mathbf{b}_l||^2) \\\\\n",
        "& + \\frac{\\lambda_v}{2} \\sum_{j} || \\mathbf{v}_j - \\mathbf{x}^{\\frac{L}{2}}_{j} ||_2^2 \\\\\n",
        "& + \\frac{\\lambda_n}{2} \\sum_{j} || \\mathbf{x}^{L}_{j} - \\mathbf{x}^{c}_{j} ||_2^2 \\\\\n",
        "& +  \\sum_{i,j} \\frac{c_{ij}}{2} (r_{ij} - \\mathbf{u}_i^T \\mathbf{v}_j)^2\n",
        "\\end{align*} -->\n",
        "<p align=\"center\">\n",
        "  <img 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\">\n",
        "</p>\n",
        "\n",
        "Let's do a comparison between CDL and CTR models."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NZ2Al6omrlEP",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 927,
          "referenced_widgets": [
            "d75b686ff2574c48b0835c5a1840f17b",
            "789d4f19efe04a35912ea89da0fd8363",
            "c1a3b74947a743f5ad270bd5efe4972b",
            "49cc99d5d4594f05aa8f9b48ddbd399f",
            "b47a23df34184761bce8d3ab5beec4ab",
            "c26694d591cd4da5b710d169b398b9e1",
            "3a225d7fc72545aa99a2e2eb096f3f99",
            "ed7f72a45ae14438b62d62cb507ab869",
            "dad3be7f8bf04279bfd593e01aa15d48",
            "7d9419e2eacc4df2bb153b75f03e913f",
            "00def7b7596542b0b636e481c5fd4d14",
            "245477ff98774e6ca9c3651c6ff935ef",
            "d706206ec60f45ac80b2e38696e15a6b",
            "42c773ab09414863a0645a8b168ec460",
            "c8ad41e44fc64db0a1d9bb2463eb2d86",
            "95d9dfbf5e2f4ed5bb88263fc80a9bdf",
            "2b32ec13cf084dadb9de743a863f1f1e",
            "d4e4a04aab3941c8941e8bfd128b4d2b",
            "bfef356c10c64effaeee5880f316bb27",
            "6a8fb6d2066744d2a7293d640500431b",
            "0f1e9bb71f34473c913ba5b5a8d796f4",
            "4b060e17a64143da9dcf1800febda7a3",
            "d713fb790ce4429a9213b46cf33d01b9",
            "3cd7d3ee21e545caafd501dfb5978e1b",
            "4be13d6cd37b417b950abf857bb7b687",
            "3d9e7d40026e4762ac6f40d0ccd7a500",
            "5e4dd968cdef4d8eac1e4d915ae5bb2e",
            "1dd38e9d73d247969052bc2a2f4e88a7",
            "17337c2aba814946aaac8cb025bb6250",
            "27123d05dcab4c53a628196bdd2f514f",
            "acfd5800ce0a4e11b4f245253c088c65",
            "1086eb98e11845e1a725c1b4d2204463",
            "711697d1e7bd46e290dcdfe1b3157bdc",
            "20b67be5fa2c4a0b8ef7555da0947640",
            "f350b3e3c3ef4d3d9ce69c14d35d8a5a",
            "f78f6dbd60a743fe8e08a64f2d782712",
            "57d87b4b9de14b9d9ef96358a7ba20b3",
            "08656b78739c45ad81238a29e670dd4f",
            "679dc6d212a04b258d1808611d522051",
            "893e453d8fc8461a9f696a1bed3e3c3e",
            "74bf9514b07c4effa41c2acd64c8864f",
            "61ac999dd50b4831b6b4ac2144ee429e",
            "fa8a1b19fa984a35a3cbf5314ba6f9a3",
            "dbca3f6208024ab9894d342ab226d811",
            "ba578c31743b4ef688a8599983416976",
            "cf33b6e3f7674fa28c120d0b899de985",
            "3a0ac8c2d1704f89ad79a157d4d8fbbf",
            "e8b698415d304a81a935bd8cbb0aabfa",
            "9370a30e4df14c25a82d4e0df003dbb8",
            "f0ce909c37c5497e91d41293348410f4",
            "b26734b6aa36491b913936499c872219",
            "957e7b346f1648389ec6ad8baf3b16d9",
            "7a4170422520462e84b16789ab52bf20",
            "7db363974d8b42738e5ce9a35b6f3977",
            "9f63a8285964446da8b8368ce42239b0"
          ]
        },
        "outputId": "c09be3ad-e750-40b2-f08a-404728367a74"
      },
      "source": [
        "VOCAB_SIZE = 2000  # @param\n",
        "NUM_FACTORS = 50  # @param\n",
        "AE_LAYERS = [500, 100]  # @param\n",
        "ACTIVATION = \"tanh\"  # @param [\"tanh\", \"sigmoid\", \"relu\", \"leaky_relu\"]\n",
        "A = 1.0  # @param\n",
        "B = 0.01  # @param\n",
        "LAMBDA_U = 0.1  # @param\n",
        "LAMBDA_V = 0.1  # @param\n",
        "LAMBDA_W = 0.1  # @param\n",
        "LAMBDA_N = 10.0  # @param\n",
        "CORRUPTION_RATE = 0.3  # @param\n",
        "DROPOUT_RATE = 0.1  # @param\n",
        "NUM_EPOCHS = 100  # @param \n",
        "BATCH_SIZE = 100  # @param\n",
        "LEARNING_RATE = 0.001  # @param\n",
        "\n",
        "cdl = CDL(k=NUM_FACTORS, autoencoder_structure=AE_LAYERS, act_fn=ACTIVATION, a=A, b=B,\n",
        "          lambda_u=LAMBDA_U, lambda_v=LAMBDA_V, lambda_w=LAMBDA_W, lambda_n=LAMBDA_N,\n",
        "          corruption_rate=CORRUPTION_RATE, dropout_rate=DROPOUT_RATE, vocab_size=VOCAB_SIZE,\n",
        "          max_iter=NUM_EPOCHS, batch_size=BATCH_SIZE, seed=SEED, verbose=VERBOSE)\n",
        "\n",
        "ctr = CTR(k=NUM_FACTORS, max_iter=NUM_EPOCHS, a=A, b=B, lambda_u=LAMBDA_U, lambda_v=LAMBDA_V, seed=SEED, verbose=VERBOSE)\n",
        "\n",
        "plots, movie_ids = movielens.load_plot()\n",
        "feedback = movielens.load_feedback(variant=\"100k\", reader=Reader(item_set=movie_ids, bin_threshold=4.0))\n",
        "item_text_modality = TextModality(\n",
        "  corpus=plots, ids=movie_ids, tokenizer=BaseTokenizer(sep=\"\\t\", stop_words=\"english\"), max_vocab=VOCAB_SIZE,\n",
        ")\n",
        "\n",
        "ratio_split = RatioSplit(\n",
        "  data=feedback, \n",
        "  test_size=0.2, \n",
        "  exclude_unknowns=True, \n",
        "  item_text=item_text_modality, \n",
        "  seed=SEED, verbose=VERBOSE,\n",
        ")\n",
        "\n",
        "cornac.Experiment(eval_method=ratio_split, models=[cdl, ctr], metrics=[rec_50, ndcg_50]).run()"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Data from https://static.preferred.ai/cornac/datasets/movielens/ml_plot.zip\n",
            "will be cached into /root/.cornac/movielens/ml_plot.dat\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "0.00B [00:00, ?B/s]"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "d75b686ff2574c48b0835c5a1840f17b"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Unzipping ...\n",
            "File cached!\n",
            "rating_threshold = 1.0\n",
            "exclude_unknowns = True\n",
            "---\n",
            "Training data:\n",
            "Number of users = 942\n",
            "Number of items = 1299\n",
            "Number of ratings = 42303\n",
            "Max rating = 1.0\n",
            "Min rating = 1.0\n",
            "Global mean = 1.0\n",
            "---\n",
            "Test data:\n",
            "Number of users = 921\n",
            "Number of items = 978\n",
            "Number of ratings = 10536\n",
            "Number of unknown users = 0\n",
            "Number of unknown items = 0\n",
            "---\n",
            "Total users = 942\n",
            "Total items = 1299\n",
            "\n",
            "[CDL] Training started!\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "  0%|          | 0/100 [00:00<?, ?it/s]"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "245477ff98774e6ca9c3651c6ff935ef"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Learning completed!\n",
            "\n",
            "[CDL] Evaluation started!\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Ranking:   0%|          | 0/921 [00:00<?, ?it/s]"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "d713fb790ce4429a9213b46cf33d01b9"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "[CTR] Training started!\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "  0%|          | 0/100 [00:00<?, ?it/s]"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "20b67be5fa2c4a0b8ef7555da0947640"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Learning completed!\n",
            "\n",
            "[CTR] Evaluation started!\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Ranking:   0%|          | 0/921 [00:00<?, ?it/s]"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "ba578c31743b4ef688a8599983416976"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "TEST:\n",
            "...\n",
            "    | NDCG@50 | Recall@50 | Train (s) | Test (s)\n",
            "--- + ------- + --------- + --------- + --------\n",
            "CDL |  0.2063 |    0.4067 |   18.6602 |   0.6654\n",
            "CTR |  0.1865 |    0.3344 |   89.2309 |   0.6498\n",
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "r-8mCmABFe8e"
      },
      "source": [
        "### Convolutional Matrix Factorization (ConvMF)\n",
        "\n",
        "ConvMF model integrates convolutional neural network (CNN) into probabilistic matrix factorization (PMF).  The model captures contextual information of item documents (e.g., reviews, abstracts, or synopses) and further enhances the rating prediction accuracy.  The generative process is as follows:\n",
        "\n",
        "- For each user $i$\n",
        "  - Draw latent vector $\\mathbf{u}_i \\sim \\mathcal{N}(0, \\lambda^{-1} \\mathbf{I})$\n",
        "- For each item $j$\n",
        "  - Put its content $\\mathbf{x}_j$ through CNN parameterized by $\\mathbf{W}$\n",
        "  - Draw item offset $\\mathbf{\\epsilon}_j \\sim \\mathcal{N}(0, \\lambda^{-1} \\mathbf{I})$\n",
        "  - Set item latent vector $\\mathbf{v}_j$ to be: $\\mathbf{v}_j = \\mathbf{\\epsilon}_j + \\mathrm{CNN}(\\mathbf{W}, \\mathbf{x}_j)$\n",
        "- For each user-item pair $(i, j)$\n",
        "  - Draw rating $r_{ij} \\sim \\mathcal{N}(\\mathbf{u}_i^T \\mathbf{v}_j, \\sigma^2)$\n",
        "\n",
        "Learning ConvMF model is done via minimizing the following negative log-likelihood function:\n",
        "<!-- \\begin{equation}\n",
        "\\mathcal{L} = \\sum_{(i,j)\\in \\mathbf{R}} (r_{ij} - \\mathbf{u}_i^T \\mathbf{v}_j)^2 + \\lambda_u \\sum_{i}^{N} || \\mathbf{u}_i ||^2 + \\lambda_v \\sum_{j}^{M} || \\mathbf{v}_j - \\mathrm{CNN}(\\mathbf{W}, \\mathbf{x}_j)||^2 +\\lambda_\\mathbf{W} \\sum_{w_l \\in \\mathbf{W}} ||w_k||^2 \n",
        "\\end{equation} -->\n",
        "<p align=\"center\">\n",
        "  <img src=\"data:image/png;base64,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\">\n",
        "</p>\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
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          "height": 973,
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          ]
        },
        "outputId": "92520009-3b20-4241-afac-52a318decc68"
      },
      "source": [
        "VOCAB_SIZE = 2000  # @param\n",
        "NUM_FACTORS = 5  # @param\n",
        "HIDDEN_DIM = 50  # @param\n",
        "CNN_FILTER_SIZES = [2, 3, 4, 5]  # @param\n",
        "CNN_NUM_FILTERS = 128  # @param\n",
        "WORD_EMB_DIM = 32  # @param\n",
        "SEQ_MAX_LENGTH = 50  # @param\n",
        "DROPOUT_RATE = 0.2  # @param\n",
        "LAMBDA_U = 0.1  # @param\n",
        "LAMBDA_V = 0.1  # @param\n",
        "NUM_EPOCHS = 5  # @param\n",
        "CNN_EPOCHS = 3  # @param\n",
        "CNN_BATCH_SIZE = 256  # @param\n",
        "CNN_LEARNING_RATE = 0.001  # @param\n",
        "\n",
        "convmf = ConvMF(k=NUM_FACTORS, n_epochs=NUM_EPOCHS, cnn_epochs=CNN_EPOCHS, cnn_bs=CNN_BATCH_SIZE,\n",
        "                cnn_lr=CNN_LEARNING_RATE, emb_dim=WORD_EMB_DIM, max_len=SEQ_MAX_LENGTH,\n",
        "                filter_sizes=CNN_FILTER_SIZES, num_filters=CNN_NUM_FILTERS, hidden_dim=HIDDEN_DIM, \n",
        "                dropout_rate=DROPOUT_RATE, lambda_u=LAMBDA_U, lambda_v=LAMBDA_V,\n",
        "                seed=SEED, verbose=VERBOSE)\n",
        "\n",
        "plots, movie_ids = movielens.load_plot()\n",
        "feedback = movielens.load_feedback(variant=\"100k\", reader=Reader(item_set=movie_ids))\n",
        "item_text_modality = TextModality(\n",
        "  corpus=plots, ids=movie_ids, tokenizer=BaseTokenizer(sep=\"\\t\", stop_words=\"english\"), max_vocab=VOCAB_SIZE,\n",
        ")\n",
        "\n",
        "ratio_split = RatioSplit(\n",
        "  data=feedback, \n",
        "  test_size=0.2, \n",
        "  rating_threshold=4.0, \n",
        "  exclude_unknowns=True, \n",
        "  item_text=item_text_modality, \n",
        "  seed=SEED, \n",
        "  verbose=VERBOSE\n",
        ")\n",
        "\n",
        "rmse = cornac.metrics.RMSE()\n",
        "\n",
        "cornac.Experiment(\n",
        "  eval_method=ratio_split, models=[convmf], metrics=[rmse, rec_50], user_based=False\n",
        ").run()"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "rating_threshold = 4.0\n",
            "exclude_unknowns = True\n",
            "---\n",
            "Training data:\n",
            "Number of users = 943\n",
            "Number of items = 1518\n",
            "Number of ratings = 75846\n",
            "Max rating = 5.0\n",
            "Min rating = 1.0\n",
            "Global mean = 3.5\n",
            "---\n",
            "Test data:\n",
            "Number of users = 942\n",
            "Number of items = 1279\n",
            "Number of ratings = 18933\n",
            "Number of unknown users = 0\n",
            "Number of unknown items = 0\n",
            "---\n",
            "Total users = 943\n",
            "Total items = 1518\n",
            "\n",
            "[ConvMF] Training started!\n",
            "Epoch: 1/5\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Optimizing CNN:   0%|          | 0/3 [00:00<?, ?it/s]"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "3aebc9d2855049a0ad000d2db544bb70"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Loss: 321274.83751 Elapsed: 4.9209s Converge: 32127483751194401103607414434072424368948078599515144192.000000 \n",
            "Epoch: 2/5\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Optimizing CNN:   0%|          | 0/3 [00:00<?, ?it/s]"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "3830ace7961244d8bc765f380d04f112"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Loss: 67855.77857 Elapsed: 0.5862s Converge: 0.788792 \n",
            "Epoch: 3/5\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Optimizing CNN:   0%|          | 0/3 [00:00<?, ?it/s]"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "2e8faf1370ea4c96a13afbc97ad6b5e4"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Loss: 65870.73165 Elapsed: 0.5541s Converge: 0.029254 \n",
            "Epoch: 4/5\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Optimizing CNN:   0%|          | 0/3 [00:00<?, ?it/s]"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "0e1cc1698f3341f0a0f497ed00cd8b75"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Loss: 68643.34711 Elapsed: 0.5607s Converge: 0.042092 \n",
            "Epoch: 5/5\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Optimizing CNN:   0%|          | 0/3 [00:00<?, ?it/s]"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "ff23d82b24b74c72aaf39cb0938b6dda"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Loss: 71814.57446 Elapsed: 0.4816s Converge: 0.046199 \n",
            "\n",
            "[ConvMF] Evaluation started!\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Rating:   0%|          | 0/18933 [00:00<?, ?it/s]"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "4d6ecc31b3304a3aa489c8d92d10cfba"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Ranking:   0%|          | 0/942 [00:00<?, ?it/s]"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "479eb46445fa4f828e10cde34428e011"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "TEST:\n",
            "...\n",
            "       |   RMSE | Recall@50 | Train (s) | Test (s)\n",
            "------ + ------ + --------- + --------- + --------\n",
            "ConvMF | 0.9806 |    0.0083 |   12.3871 |   0.8335\n",
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0FmiuTYiP_pB"
      },
      "source": [
        "## References\n",
        "\n",
        "1.   He, X., Liao, L., Zhang, H., Nie, L., Hu, X., & Chua, T. S. (2017, April). Neural collaborative filtering. In Proceedings of the 26th international conference on world wide web (pp. 173-182).\n",
        "2.   Liang, D., Krishnan, R. G., Hoffman, M. D., & Jebara, T. (2018, April). Variational autoencoders for collaborative filtering. In Proceedings of the 2018 World Wide Web Conference (pp. 689-698).\n",
        "3.   Wang, H., Wang, N., & Yeung, D. Y. (2015, August). Collaborative deep learning for recommender systems. In Proceedings of the 21th ACM SIGKDD international conference on knowledge discovery and data mining (pp. 1235-1244).\n",
        "4.   Kim, D., Park, C., Oh, J., Lee, S., & Yu, H. (2016, September). Convolutional matrix factorization for document context-aware recommendation. In Proceedings of the 10th ACM conference on recommender systems (pp. 233-240).\n",
        "5.   Cornac - A Comparative Framework for Multimodal Recommender Systems (https://cornac.preferred.ai/)"
      ]
    }
  ]
}