9_Mult_VAE.ipynb

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  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/ivoryRabbit/RecSys/blob/master/9_Mult_VAE.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "viikY8IQdVTY"
      },
      "source": [
        "# Mult-VAE\n",
        "\n",
        "- [Variational Autoencoders for Collaborative Filtering](https://arxiv.org/pdf/1802.05814.pdf)\n",
        "\n",
        "## Experiment"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "M8FDcw4rVboe"
      },
      "source": [
        "import glob\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "from typing import Callable, Tuple, List\n",
        "from tqdm.notebook import tqdm\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline\n",
        "plt.style.use('ggplot')\n",
        "\n",
        "from sklearn.model_selection import train_test_split\n",
        "\n",
        "import tensorflow as tf\n",
        "import tensorflow.keras.backend as K\n",
        "\n",
        "from tensorflow.keras.layers import Layer, Input, Dense, Dropout, Reshape\n",
        "from tensorflow.keras.models import Model, load_model\n",
        "from tensorflow.keras.callbacks import ModelCheckpoint, EarlyStopping\n",
        "from tensorflow.keras.optimizers import Adam\n",
        "from tensorflow.keras.regularizers import l2\n",
        "\n",
        "from tensorflow.keras.utils import get_file\n",
        "import zipfile\n",
        "\n",
        "np.random.seed(777)\n",
        "tf.random.set_seed(777)"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sdjqodyYVf9I"
      },
      "source": [
        "def load_data(data_size : str) -> pd.DataFrame:\n",
        "    ''' load Movie Lens data '''\n",
        "\n",
        "    if data_size == '1m':\n",
        "        fname = 'ml-1m.zip'\n",
        "        data = 'ml-1m/ratings.dat'\n",
        "    elif data_size == '10m':\n",
        "        fname = 'ml-10m.zip'\n",
        "        data = 'ml-10M100K/ratings.dat'\n",
        "    elif data_size == '20m':\n",
        "        fname = 'ml-20m.zip'\n",
        "        data = 'ml-20m/ratings.csv'\n",
        "    elif data_size == '25m':\n",
        "        fname = 'ml-25m.zip'\n",
        "        data = 'ml-25m/ratings.csv'\n",
        "    if not glob.glob(data):\n",
        "        origin = f'http://files.grouplens.org/datasets/movielens/{fname}'\n",
        "        file = get_file(fname, origin)\n",
        "        zip_ref = zipfile.ZipFile(file, 'r')\n",
        "        zip_ref.extractall()\n",
        "\n",
        "    col_names = ['user_id', 'movie_id', 'rating', 'timestamp']\n",
        "    if data_size in ['20m', '25m']:\n",
        "        ratings = pd.read_csv(data, names = col_names, engine = 'python')\n",
        "    else:\n",
        "        ratings = pd.read_csv(data, sep = '|', delimiter = '::', names = col_names, engine = 'python')\n",
        "    print(ratings.shape)\n",
        "    return ratings"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RZf8Gzf0VhYV",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 248
        },
        "outputId": "8342bf94-8865-4d24-e5f3-d98f521ecc18"
      },
      "source": [
        "ratings = load_data('1m')\n",
        "ratings.head()"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Downloading data from http://files.grouplens.org/datasets/movielens/ml-1m.zip\n",
            "5922816/5917549 [==============================] - 0s 0us/step\n",
            "(1000209, 4)\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
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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>user_id</th>\n",
              "      <th>movie_id</th>\n",
              "      <th>rating</th>\n",
              "      <th>timestamp</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
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              "      <td>1193</td>\n",
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              "      <th>1</th>\n",
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              "      <td>3</td>\n",
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              "    <tr>\n",
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              "      <td>914</td>\n",
              "      <td>3</td>\n",
              "      <td>978301968</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>1</td>\n",
              "      <td>3408</td>\n",
              "      <td>4</td>\n",
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              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>1</td>\n",
              "      <td>2355</td>\n",
              "      <td>5</td>\n",
              "      <td>978824291</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   user_id  movie_id  rating  timestamp\n",
              "0        1      1193       5  978300760\n",
              "1        1       661       3  978302109\n",
              "2        1       914       3  978301968\n",
              "3        1      3408       4  978300275\n",
              "4        1      2355       5  978824291"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 3
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KJ_TaXgGIZlL",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "e5e878ca-cfad-4b4f-fca5-82176daf0a79"
      },
      "source": [
        "user_list = ratings.user_id.unique()\n",
        "user_idx_map = {e: i for i, e in enumerate(user_list)}\n",
        "n_user = len(user_list)\n",
        "print(f'# of user = {n_user}')\n",
        "\n",
        "item_list = ratings.movie_id.unique()\n",
        "item_idx_map = {e: i for i, e in enumerate(item_list)}\n",
        "n_item = len(item_list)\n",
        "print(f'# of item = {n_item}')"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "# of user = 6040\n",
            "# of item = 3706\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 195
        },
        "id": "OZBgXqzfz5_k",
        "outputId": "42b74ff4-fad8-4241-ec51-d049c21b6cc7"
      },
      "source": [
        "ratings = ratings.assign(\r\n",
        "    user_id = ratings.user_id.map(user_idx_map),\r\n",
        "    movie_id = ratings.movie_id.map(item_idx_map)\r\n",
        ")\r\n",
        "ratings.head()"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
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              "    }\n",
              "\n",
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              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>user_id</th>\n",
              "      <th>movie_id</th>\n",
              "      <th>rating</th>\n",
              "      <th>timestamp</th>\n",
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              "  </thead>\n",
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              "      <th>1</th>\n",
              "      <td>0</td>\n",
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              "      <td>978302109</td>\n",
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              "      <td>3</td>\n",
              "      <td>978301968</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
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              "    </tr>\n",
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              "      <td>0</td>\n",
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              "      <td>5</td>\n",
              "      <td>978824291</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   user_id  movie_id  rating  timestamp\n",
              "0        0         0       5  978300760\n",
              "1        0         1       3  978302109\n",
              "2        0         2       3  978301968\n",
              "3        0         3       4  978300275\n",
              "4        0         4       5  978824291"
            ]
          },
          "metadata": {
            "tags": []
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        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dmXavvj5IbOY"
      },
      "source": [
        "def binarizer(df: pd.DataFrame, threshold = 4) -> pd.DataFrame:\n",
        "    df = df.assign(rating = np.where(df.rating >= threshold, 1, 0))\n",
        "    return df[df.rating > 0.0].reset_index(drop = True)\n",
        "\n",
        "def make_warm(df: pd.DataFrame, threshold = 5) -> pd.DataFrame: # remove cold starters\n",
        "    positive = df.groupby('user_id')['movie_id'].count()\n",
        "    positive = positive.index[positive >= threshold]\n",
        "    return df[df.user_id.isin(positive)].reset_index(drop = True)\n",
        "\n",
        "def train_valid_test_split(df: pd.DataFrame, size: float) -> pd.DataFrame:\n",
        "    train_user, test_user = train_test_split(df.user_id.unique(), test_size = 2 * size, random_state = 777)\n",
        "    valid_user, test_user = train_test_split(test_user, test_size = 0.5, random_state = 777)\n",
        "    train, valid, test = map(lambda x: df[df.user_id.isin(x)], (train_user, valid_user, test_user))\n",
        "    train, valid, test = map(lambda df: df.reset_index(drop = True), (train, valid, test))\n",
        "    return train, valid, test\n",
        "\n",
        "def query_relev_split(df: pd.DataFrame, size: float) -> pd.DataFrame:\n",
        "    timeorder = df.groupby('user_id')['timestamp'].rank(method = 'first', ascending = True)\n",
        "    seen_cnts = df.groupby('user_id')['movie_id'].transform('count')\n",
        "    df = df.assign(seen_cnts = seen_cnts, timeorder = timeorder)\n",
        "    query = df[df.timeorder < df.seen_cnts * (1-size)]\n",
        "    relev = df[df.timeorder >= df.seen_cnts * (1-size)]\n",
        "    relev = relev[relev.user_id.isin(query.user_id.unique())]\n",
        "    query, relev = map(lambda df: df.drop(columns = ['timeorder', 'seen_cnts']), (query, relev))\n",
        "    query, relev = map(lambda df: df.reset_index(drop = True), (query, relev))\n",
        "    return query, relev\n",
        "\n",
        "def list_agg(df: pd.DataFrame) -> pd.DataFrame:\n",
        "    return df.groupby('user_id', as_index = False)[['movie_id']].agg(list)"
      ],
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Q61otQWA3tFe",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 195
        },
        "outputId": "deb08fc7-0890-4745-a25f-1139d0e59ca9"
      },
      "source": [
        "data = binarizer(ratings)\n",
        "data = make_warm(data)\n",
        "data.head()"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
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              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>user_id</th>\n",
              "      <th>movie_id</th>\n",
              "      <th>rating</th>\n",
              "      <th>timestamp</th>\n",
              "    </tr>\n",
              "  </thead>\n",
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              "      <th>0</th>\n",
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              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>0</td>\n",
              "      <td>6</td>\n",
              "      <td>1</td>\n",
              "      <td>978302039</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>0</td>\n",
              "      <td>7</td>\n",
              "      <td>1</td>\n",
              "      <td>978300719</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   user_id  movie_id  rating  timestamp\n",
              "0        0         0       1  978300760\n",
              "1        0         3       1  978300275\n",
              "2        0         4       1  978824291\n",
              "3        0         6       1  978302039\n",
              "4        0         7       1  978300719"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QJvVnvKX3uNv"
      },
      "source": [
        "train, valid, test = train_valid_test_split(data, size = 0.1)\n",
        "valid_q, valid_r = query_relev_split(valid, size = 0.2)\n",
        "test_q, test_r = query_relev_split(test, size = 0.2)"
      ],
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Sf7jGLD1bpQT"
      },
      "source": [
        "def train_generator(train: pd.DataFrame, \r\n",
        "                    n_item: int,\r\n",
        "                    batch_size: int) -> np.ndarray:\r\n",
        "\r\n",
        "    train = list_agg(train)\r\n",
        "    \r\n",
        "    n_data = train.index.size\r\n",
        "    ids = np.arange(n_data)\r\n",
        "    profile = train['movie_id']\r\n",
        "\r\n",
        "    n_batch = int(np.ceil(n_data / batch_size))\r\n",
        "    while True:\r\n",
        "        np.random.shuffle(ids)\r\n",
        "        for batch_step in range(n_batch):     \r\n",
        "            lower = batch_size * batch_step\r\n",
        "            upper = batch_size + lower\r\n",
        "            \r\n",
        "            batch_id = ids[lower: upper]\r\n",
        "            batch = np.zeros(shape = (batch_id.size, n_item), dtype = np.float32)\r\n",
        "            for i, idx in enumerate(batch_id):\r\n",
        "                batch[i, profile[idx]] = 1.0\r\n",
        "            \r\n",
        "            yield batch"
      ],
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Us8c86FLTv93"
      },
      "source": [
        "def valid_generator(query: pd.DataFrame,\n",
        "                    relev: pd.DataFrame,\n",
        "                    n_item: int,\n",
        "                    batch_size: int) -> Tuple[np.ndarray]:\n",
        "\n",
        "    query = list_agg(query)\n",
        "    relev = list_agg(relev)\n",
        "\n",
        "    n_data = query.index.size\n",
        "    ids = np.arange(n_data)\n",
        "    profile_q = query['movie_id']\n",
        "    profile_r = relev['movie_id']\n",
        "\n",
        "    n_batch = int(np.ceil(n_data / batch_size))\n",
        "    while True:\n",
        "        np.random.shuffle(ids)\n",
        "        for batch_step in range(n_batch):\n",
        "            lower = batch_size * batch_step\n",
        "            upper = batch_size + lower\n",
        "            \n",
        "            batch_id = ids[lower: upper]\n",
        "            batch_q = np.zeros(shape = (batch_id.size, n_item), dtype = np.float32)\n",
        "            batch_r = np.zeros(shape = (batch_id.size, n_item), dtype = np.float32)\n",
        "            for i, idx in enumerate(batch_id):\n",
        "                batch_q[i, profile_q[idx]] = 1.0 # seen\n",
        "                batch_r[i, profile_r[idx]] = 1.0 # unseen\n",
        "\n",
        "            yield batch_q, batch_r"
      ],
      "execution_count": 10,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rHgipqQH0UKF"
      },
      "source": [
        "def rmse(true: tf.Tensor, pred: tf.Tensor) -> tf.Tensor:\n",
        "    rmse = K.sqrt(K.mean(K.square(true - pred), axis = 1))\n",
        "    return K.mean(rmse, axis = 0)\n",
        "\n",
        "def binary_cross_entropy(true: tf.Tensor, pred: tf.Tensor) -> tf.Tensor:\n",
        "    ce = K.sum(K.binary_crossentropy(true, pred), axis = 1)\n",
        "    return K.mean(ce, axis = 0)\n",
        "\n",
        "def multinomial(true: tf.Tensor, pred: tf.Tensor) -> tf.Tensor:\n",
        "    ll = -K.sum(true * K.log(pred), axis = 1)\n",
        "    return K.mean(ll, axis = 0)\n",
        "\n",
        "def batch_ndcg(query: tf.Tensor, \n",
        "               relev: tf.Tensor,\n",
        "               pred: tf.Tensor, \n",
        "               weight: tf.Tensor,\n",
        "               k = 100) -> tf.Tensor: # only for validation\n",
        "\n",
        "    rec = tf.where(query == 1.0, -1.0, pred) # leave only unseen-data\n",
        "    rec = tf.argsort(rec, axis = 1, direction = 'DESCENDING')[:, :k]\n",
        "    shape = tf.shape(rec)\n",
        "\n",
        "    row = tf.repeat(tf.range(shape[0]), shape[1])\n",
        "    row = tf.expand_dims(row, axis = 1)\n",
        "    col = tf.reshape(rec, shape = [-1])\n",
        "    col = tf.expand_dims(col, axis = 1)\n",
        "    loc = tf.concat([row, col], axis = 1)\n",
        "\n",
        "    top_k = tf.reshape(tf.gather_nd(relev, loc), shape = shape)\n",
        "    ideal = tf.sort(relev, axis = 1, direction = 'DESCENDING')[:, :k]\n",
        "    weight = weight[:shape[1]]\n",
        "\n",
        "    dcg = tf.reduce_sum(top_k * weight, axis = 1)\n",
        "    idcg = tf.reduce_sum(ideal * weight, axis = 1)\n",
        "    return tf.reduce_mean(dcg / idcg, axis = 0)"
      ],
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VqB87z-wDm2E"
      },
      "source": [
        "class Encoder(tf.keras.layers.Layer):\r\n",
        "    def __init__(self, units):\r\n",
        "        super(Encoder, self).__init__()\r\n",
        "        self.units = units\r\n",
        "\r\n",
        "    def build(self, input_shape):\r\n",
        "        self.encoder_layer = Dense(2 * self.units,\r\n",
        "                                   activation = 'tanh',\r\n",
        "                                   kernel_initializer = 'glorot_uniform',\r\n",
        "                                   bias_initializer = 'zeros',\r\n",
        "                                   kernel_regularizer = l2(1e-3),\r\n",
        "                                   name = 'mean')\r\n",
        "        self.reshape_layer = Reshape((2, self.units))\r\n",
        "   \r\n",
        "    def call(self, inputs):\r\n",
        "        x = self.encoder_layer(inputs)\r\n",
        "        x = self.reshape_layer(x)\r\n",
        "        return x[:, 0], x[:, 1]"
      ],
      "execution_count": 12,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7WtWaOpiEPlz"
      },
      "source": [
        "class Sampling(tf.keras.layers.Layer):\r\n",
        "    def call(self, inputs, training = False):\r\n",
        "        mean, log_var = inputs\r\n",
        "        if training:\r\n",
        "            return mean + K.exp(0.5 * log_var) * K.random_normal(tf.shape(mean))\r\n",
        "        return mean"
      ],
      "execution_count": 13,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "g5O9BLOKDoSB"
      },
      "source": [
        "class Decoder(tf.keras.layers.Layer):\r\n",
        "    def __init__(self, units, likelihood):\r\n",
        "        super(Decoder, self).__init__()\r\n",
        "        self.units = units\r\n",
        "        self.likelihood = likelihood\r\n",
        "        \r\n",
        "        dist_map = {'multinomial': 'softmax', 'logistic': 'sigmoid', 'gaussian': 'linear'}\r\n",
        "        self.last_activation = dist_map[self.likelihood]\r\n",
        "\r\n",
        "    def build(self, input_shape):\r\n",
        "        self.decoder_layer = Dense(self.units,\r\n",
        "                                   activation = self.last_activation, \r\n",
        "                                   kernel_initializer = 'glorot_uniform',\r\n",
        "                                   bias_initializer = 'zeros',\r\n",
        "                                   kernel_regularizer = l2(1e-3),\r\n",
        "                                   name = 'decoder')\r\n",
        "\r\n",
        "    def call(self, inputs):\r\n",
        "        return self.decoder_layer(inputs)"
      ],
      "execution_count": 14,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "l20MXSwhqATy"
      },
      "source": [
        "class VAE(tf.keras.models.Model):\r\n",
        "    def __init__(self, input_dim, latent_dim, dropout_rate, anneal_rate, likelihood = 'multinomial'):\r\n",
        "        super(VAE, self).__init__()\r\n",
        "        self.input_dim = input_dim\r\n",
        "        self.latent_dim = latent_dim\r\n",
        "        self.dropout_rate = dropout_rate\r\n",
        "        self.anneal_rate = anneal_rate\r\n",
        "        self.likelihood = likelihood\r\n",
        "\r\n",
        "        self.dropout= Dropout(self.dropout_rate)\r\n",
        "        self.encoder = Encoder(self.latent_dim)\r\n",
        "        self.sampler = Sampling()\r\n",
        "        self.decoder = Decoder(self.input_dim, self.likelihood)\r\n",
        "\r\n",
        "        _ = self.call(Input(shape = (self.input_dim, )), training = True)\r\n",
        "        self.build(input_shape = (None, self.input_dim))\r\n",
        "\r\n",
        "    def call(self, inputs, training = False):\r\n",
        "        x = self.dropout(inputs) if training else inputs\r\n",
        "        mean, log_var = self.encoder(x)\r\n",
        "        z = self.sampler([mean, log_var], training)\r\n",
        "        if training:\r\n",
        "            return self.decoder(z), mean, log_var\r\n",
        "        return self.decoder(z)\r\n",
        "\r\n",
        "    def kld_loss(self, mean, log_var):\r\n",
        "        kl = -0.5 * K.sum(1 + log_var - K.exp(log_var) - K.square(mean), axis = 1)\r\n",
        "        return K.mean(kl, axis = 0)\r\n",
        "        \r\n",
        "    def train_step(self, inputs):\r\n",
        "        with tf.GradientTape() as tape:\r\n",
        "            outputs, mean, log_var = self(inputs, training = True)\r\n",
        "            ll_loss = self.loss(inputs, outputs)\r\n",
        "            kl_loss = self.anneal_rate * self.kld_loss(mean, log_var)\r\n",
        "            loss = ll_loss + kl_loss\r\n",
        "        grads = tape.gradient(loss, self.trainable_variables)\r\n",
        "        self.optimizer.apply_gradients(zip(grads, self.trainable_variables))\r\n",
        "        return {'loss': loss}\r\n",
        "\r\n",
        "    def test_step(self, data):\r\n",
        "        query, relev = data\r\n",
        "        pred = self(query)\r\n",
        "\r\n",
        "        weight = tf.range(2, self.input_dim, dtype = 'float32')\r\n",
        "        weight = tf.math.reciprocal(tf.math.log(weight))\r\n",
        "        ndcg = batch_ndcg(query, relev, pred, weight)\r\n",
        "        return {'ndcg': ndcg}"
      ],
      "execution_count": 15,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Vc70c_-V0PfB"
      },
      "source": [
        "def show_history(hist, loss: str, metric: str) -> None:\r\n",
        "    fig, (ax1, ax2) = plt.subplots(2, 1, figsize = (8, 6))\r\n",
        "\r\n",
        "    ax1.plot(hist.history[f'{loss}'])\r\n",
        "    ax1.set_title(loss, fontsize = 20)\r\n",
        "    ax1.set_ylabel(loss)\r\n",
        "    ax1.set_xlabel('epoch')\r\n",
        "\r\n",
        "    ax2.plot(hist.history[f'val_{metric}'])\r\n",
        "    ax2.set_title(metric, fontsize = 20)\r\n",
        "    ax2.set_ylabel(metric)\r\n",
        "    ax2.set_xlabel('epoch')\r\n",
        "    plt.tight_layout()"
      ],
      "execution_count": 16,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NHoctUBox1Z4"
      },
      "source": [
        "def test_predictor(query: pd.DataFrame, \n",
        "                   model: Callable,\n",
        "                   n_item: int, \n",
        "                   batch_size: int, \n",
        "                   N = 100) -> float:\n",
        "\n",
        "    query = list_agg(query)\n",
        "\n",
        "    n_data = query.index.size\n",
        "    ids = np.arange(n_data)\n",
        "    profile = query['movie_id']\n",
        "\n",
        "    pred = []\n",
        "    n_batch = int(np.ceil(n_data / batch_size))\n",
        "    for batch_step in range(n_batch):\n",
        "        lower = batch_size * batch_step\n",
        "        upper = batch_size + lower\n",
        "\n",
        "        batch_id = ids[lower: upper]\n",
        "        batch = np.zeros(shape = (batch_id.size, n_item))\n",
        "        for i, idx in enumerate(batch_id):\n",
        "            batch[i, profile[idx]] = 1.0\n",
        "\n",
        "        pred_batch = model.predict(batch, verbose = 0)\n",
        "        \n",
        "        rec = np.argsort(np.where(batch == 1.0, -1.0, pred_batch), axis = 1)[:, :-N-1:-1]\n",
        "        pred.append(rec)\n",
        "    pred = np.concatenate(pred)\n",
        "    pred = [{'user_id': query.at[i, 'user_id'], 'movie_id': pred[i]} for i in range(n_data)]\n",
        "    return pd.DataFrame(pred)"
      ],
      "execution_count": 17,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "G05LGp9eAfE0"
      },
      "source": [
        "class evaluate:\n",
        "    def __init__(self, true: pd.DataFrame, pred: pd.DataFrame):\n",
        "        self.true = true\n",
        "        self.pred = pred\n",
        "        self.max_K = 10000\n",
        "        self.idcg = np.cumsum([1.0 / np.log(i+2) for i in range(self.max_K)])\n",
        "\n",
        "    def _recall(self, gt: List, rec: List, K = None) -> float:\n",
        "        K = K if K else self.max_K\n",
        "        res = [r for r in rec[:K] if r in gt]\n",
        "        return len(res) / np.min([K, len(gt)])\n",
        "    \n",
        "    def _precision(self, gt: List, rec: List, K = None) -> float:\n",
        "        K = K if K else self.max_K\n",
        "        res = [r for r in rec[:K] if r in gt]\n",
        "        return len(res) / len(rec[:K])\n",
        "\n",
        "    def _AP(self, gt: List, rec: List, K = None) -> float: # Average Precision\n",
        "        K = K if K else self.max_K\n",
        "        res = 0.0\n",
        "        for i, r in enumerate(rec[:K]):\n",
        "            if r in gt:\n",
        "                res += self._precision(gt, rec[:K], i+1)\n",
        "        return res / np.min([K, len(gt)])\n",
        "\n",
        "    def _RR(self, gt: List, rec: List, K = None) -> float: # Reciprocal Rank\n",
        "        K = K if K else self.max_K\n",
        "        for i, r in enumerate(rec[:K]):\n",
        "            if r in gt:\n",
        "                return  1.0 / (i+1)\n",
        "        return 0\n",
        "\n",
        "    def _nDCG(self, gt: List, rec: List, K = None) -> float: # normalized Discounted Cumulative Gain\n",
        "        K = K if K else self.max_K\n",
        "        dcg = 0.0\n",
        "        for i, r in enumerate(rec[:K]):\n",
        "            if r in gt:\n",
        "                dcg += 1.0 / np.log(i+2)\n",
        "        idcg = self.idcg[min([len(gt), K])-1]\n",
        "        return dcg / idcg\n",
        "    \n",
        "    def __call__(self, K = None):\n",
        "        self.K = K\n",
        "        self.recall = 0\n",
        "        self.precision = 0\n",
        "        self.MAP = 0\n",
        "        self.MRR = 0\n",
        "        self.nDCG = 0\n",
        "        n = self.true.index.size\n",
        "        for gt, rec in zip(tqdm(self.true.movie_id), self.pred.movie_id):\n",
        "            self.recall += self._recall(gt, rec, K) / n\n",
        "            self.precision += self._precision(gt, rec, K) / n\n",
        "            self.MAP += self._AP(gt, rec, K) / n\n",
        "            self.MRR += self._RR(gt, rec, K) / n\n",
        "            self.nDCG += self._nDCG(gt, rec, K) / n\n",
        "\n",
        "    def print_all(self):\n",
        "        K = '@' + str(self.K) if self.K else ''\n",
        "        print(f'{\"Recall\":>12}{K} : {self.recall:.5f}',\n",
        "              f'\\n{\"Precision\":>12}{K} : {self.precision:.5f}',\n",
        "              f'\\n{\"MAP\":>12}{K} : {self.MAP:.5f}',\n",
        "              f'\\n{\"MRR\":>12}{K} : {self.MRR:.5f}',\n",
        "              f'\\n{\"nDCG\":>12}{K} : {self.nDCG:.5f}')"
      ],
      "execution_count": 18,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FqV0G-jz0HbN"
      },
      "source": [
        "epochs = 100\r\n",
        "batch_size = 128\r\n",
        "\r\n",
        "train_gen = train_generator(train, n_item, batch_size)\r\n",
        "valid_gen = valid_generator(valid_q, valid_r, n_item, batch_size)\r\n",
        "\r\n",
        "steps_per_epoch = train.user_id.nunique() // batch_size + 1\r\n",
        "validation_steps = valid.user_id.nunique() // batch_size + 1"
      ],
      "execution_count": 19,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JiZzjtRaFhlg"
      },
      "source": [
        "## 1. Multinomial"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "EfDSYBod6ZuU",
        "outputId": "0f97ab73-f035-47e1-e816-26a55dad9c0e"
      },
      "source": [
        "model = VAE(n_item, latent_dim = 256, dropout_rate = 0.5, anneal_rate = 0.2)\r\n",
        "model.compile(optimizer = Adam(lr = 1e-4), loss = multinomial)\r\n",
        "\r\n",
        "model.summary()"
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Model: \"vae\"\n",
            "_________________________________________________________________\n",
            "Layer (type)                 Output Shape              Param #   \n",
            "=================================================================\n",
            "dropout (Dropout)            (None, 3706)              0         \n",
            "_________________________________________________________________\n",
            "encoder (Encoder)            ((None, 256), (None, 256) 1897984   \n",
            "_________________________________________________________________\n",
            "sampling (Sampling)          (None, 256)               0         \n",
            "_________________________________________________________________\n",
            "decoder (Decoder)            (None, 3706)              952442    \n",
            "=================================================================\n",
            "Total params: 2,850,426\n",
            "Trainable params: 2,850,426\n",
            "Non-trainable params: 0\n",
            "_________________________________________________________________\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "aOSh_Etb0Ldx",
        "outputId": "9078b947-3f4d-4edd-c5f8-d59225817515"
      },
      "source": [
        "%%time\r\n",
        "early_stopping = EarlyStopping(monitor = 'val_ndcg', mode = 'max', verbose = 1, patience = epochs // 5)\r\n",
        "model_checkpoint = ModelCheckpoint('mult-VAE.h5', monitor = 'val_ndcg', mode = 'max', save_best_only = True)\r\n",
        "\r\n",
        "hist = model.fit(x = train_gen, validation_data = valid_gen, epochs = epochs,\r\n",
        "                 steps_per_epoch = steps_per_epoch, validation_steps = validation_steps, \r\n",
        "                 verbose = 1, callbacks = [early_stopping, model_checkpoint])\r\n",
        "show_history(hist, 'loss', 'ndcg')"
      ],
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Epoch 1/100\n",
            "38/38 [==============================] - 3s 20ms/step - loss: 790.2711 - val_ndcg: 0.0615\n",
            "Epoch 2/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 764.9847 - val_ndcg: 0.1262\n",
            "Epoch 3/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 734.9812 - val_ndcg: 0.1369\n",
            "Epoch 4/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 720.2128 - val_ndcg: 0.1490\n",
            "Epoch 5/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 717.7779 - val_ndcg: 0.1494\n",
            "Epoch 6/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 711.3165 - val_ndcg: 0.1639\n",
            "Epoch 7/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 715.9703 - val_ndcg: 0.1487\n",
            "Epoch 8/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 710.7153 - val_ndcg: 0.1709\n",
            "Epoch 9/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 705.2137 - val_ndcg: 0.1631\n",
            "Epoch 10/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 704.1770 - val_ndcg: 0.1733\n",
            "Epoch 11/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 705.8942 - val_ndcg: 0.1743\n",
            "Epoch 12/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 698.1043 - val_ndcg: 0.1862\n",
            "Epoch 13/100\n",
            "38/38 [==============================] - 0s 9ms/step - loss: 695.4157 - val_ndcg: 0.1679\n",
            "Epoch 14/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 696.7531 - val_ndcg: 0.1679\n",
            "Epoch 15/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 696.6508 - val_ndcg: 0.1703\n",
            "Epoch 16/100\n",
            "38/38 [==============================] - 0s 9ms/step - loss: 692.6747 - val_ndcg: 0.1900\n",
            "Epoch 17/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 687.8589 - val_ndcg: 0.1582\n",
            "Epoch 18/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 689.5685 - val_ndcg: 0.2004\n",
            "Epoch 19/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 685.3638 - val_ndcg: 0.1827\n",
            "Epoch 20/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 683.7685 - val_ndcg: 0.1833\n",
            "Epoch 21/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 684.4359 - val_ndcg: 0.1670\n",
            "Epoch 22/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 682.3496 - val_ndcg: 0.2141\n",
            "Epoch 23/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 682.9136 - val_ndcg: 0.1833\n",
            "Epoch 24/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 682.1420 - val_ndcg: 0.2142\n",
            "Epoch 25/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 677.0250 - val_ndcg: 0.2071\n",
            "Epoch 26/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 676.5534 - val_ndcg: 0.2117\n",
            "Epoch 27/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 674.1814 - val_ndcg: 0.2094\n",
            "Epoch 28/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 677.0584 - val_ndcg: 0.2199\n",
            "Epoch 29/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 671.2233 - val_ndcg: 0.1802\n",
            "Epoch 30/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 672.5855 - val_ndcg: 0.2242\n",
            "Epoch 31/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 674.9824 - val_ndcg: 0.2172\n",
            "Epoch 32/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 672.1902 - val_ndcg: 0.1929\n",
            "Epoch 33/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 668.4472 - val_ndcg: 0.1901\n",
            "Epoch 34/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 667.5925 - val_ndcg: 0.2071\n",
            "Epoch 35/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 665.7378 - val_ndcg: 0.2126\n",
            "Epoch 36/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 669.2565 - val_ndcg: 0.1866\n",
            "Epoch 37/100\n",
            "38/38 [==============================] - 0s 7ms/step - loss: 666.4213 - val_ndcg: 0.2130\n",
            "Epoch 38/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 664.7935 - val_ndcg: 0.2138\n",
            "Epoch 39/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 666.0225 - val_ndcg: 0.2050\n",
            "Epoch 40/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 662.4913 - val_ndcg: 0.1838\n",
            "Epoch 41/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 665.4812 - val_ndcg: 0.1917\n",
            "Epoch 42/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 666.1038 - val_ndcg: 0.2003\n",
            "Epoch 43/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 664.0577 - val_ndcg: 0.2061\n",
            "Epoch 44/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 661.5553 - val_ndcg: 0.2031\n",
            "Epoch 45/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 663.5983 - val_ndcg: 0.2066\n",
            "Epoch 46/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 666.5452 - val_ndcg: 0.2110\n",
            "Epoch 47/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 666.3806 - val_ndcg: 0.2213\n",
            "Epoch 48/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 661.1912 - val_ndcg: 0.2121\n",
            "Epoch 49/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 658.4014 - val_ndcg: 0.2238\n",
            "Epoch 50/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 659.8701 - val_ndcg: 0.1913\n",
            "Epoch 00050: early stopping\n",
            "CPU times: user 21.5 s, sys: 2.09 s, total: 23.6 s\n",
            "Wall time: 18.5 s\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 576x432 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 195
        },
        "id": "-4tP0-a-zSxv",
        "outputId": "ae05a50d-b21c-4b89-a49e-b8ce14998a9c"
      },
      "source": [
        "true = list_agg(test_r)\r\n",
        "true.head(5)"
      ],
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "execute_result",
          "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>user_id</th>\n",
              "      <th>movie_id</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>2</td>\n",
              "      <td>[177, 179, 183, 84, 4, 198, 199, 207]</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>8</td>\n",
              "      <td>[59, 438, 93, 123, 463, 525, 30, 288, 534, 322...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>41</td>\n",
              "      <td>[175, 182, 563, 184, 1176, 116, 128, 1037, 104...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>78</td>\n",
              "      <td>[1258, 305, 500, 2230]</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>91</td>\n",
              "      <td>[558, 1176, 195, 587, 592, 74, 1904, 186, 647,...</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   user_id                                           movie_id\n",
              "0        2              [177, 179, 183, 84, 4, 198, 199, 207]\n",
              "1        8  [59, 438, 93, 123, 463, 525, 30, 288, 534, 322...\n",
              "2       41  [175, 182, 563, 184, 1176, 116, 128, 1037, 104...\n",
              "3       78                             [1258, 305, 500, 2230]\n",
              "4       91  [558, 1176, 195, 587, 592, 74, 1904, 186, 647,..."
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 22
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fgw83iYFysnj",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 195
        },
        "outputId": "7758b53a-b075-43b5-f234-00906a7daca4"
      },
      "source": [
        "pred = test_predictor(test_q, model, n_item, batch_size, N = 100)\n",
        "pred.head(5)"
      ],
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>user_id</th>\n",
              "      <th>movie_id</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>2</td>\n",
              "      <td>[48, 92, 22, 97, 132, 217, 210, 151, 171, 23, ...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>8</td>\n",
              "      <td>[244, 184, 134, 92, 68, 171, 315, 44, 124, 97,...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>41</td>\n",
              "      <td>[132, 62, 160, 189, 155, 856, 758, 775, 86, 72...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>78</td>\n",
              "      <td>[104, 38, 68, 128, 48, 184, 44, 97, 132, 92, 5...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>91</td>\n",
              "      <td>[44, 64, 124, 9, 8, 612, 741, 596, 733, 104, 6...</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   user_id                                           movie_id\n",
              "0        2  [48, 92, 22, 97, 132, 217, 210, 151, 171, 23, ...\n",
              "1        8  [244, 184, 134, 92, 68, 171, 315, 44, 124, 97,...\n",
              "2       41  [132, 62, 160, 189, 155, 856, 758, 775, 86, 72...\n",
              "3       78  [104, 38, 68, 128, 48, 184, 44, 97, 132, 92, 5...\n",
              "4       91  [44, 64, 124, 9, 8, 612, 741, 596, 733, 104, 6..."
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 23
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jKQgNhpY0Bjl",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 292,
          "referenced_widgets": [
            "ca23871c2a014b90af0ce28ffe091b68",
            "8611ca1639fa49e5a3327e91915c9d1a",
            "68109c3e2de747acbd90b0d29599583f",
            "a7cbd31015cd448ebdf1f6873abfa534",
            "3dde720576e04e0fb12e75a5efb25e42",
            "46fcef68c03c4ac9bb77142f63b71c8a",
            "468fa0e1aa5346c587289772b25ad68e",
            "932eaaf431164a99a4bf39ef67bc9d60",
            "2e9272bd654b4c28801c2372fa78a728",
            "476fc25914a74c38879fdc12911a283e",
            "10ffdbe5f7c9439084b9118daa154f91",
            "7bb59b398efc4b0eadc9b281f7eeef7d",
            "2f9e7f56327c48ab87c27ddbe9f5acfc",
            "2e443ced276f4f13b8bcff3d2e636769",
            "916d38f7b18a4e0fbfc935e2efb8b40c",
            "544e0f6d39b34b1084b9227e769c9ce0"
          ]
        },
        "outputId": "2de933a7-5c34-495d-b465-9485bfe9501e"
      },
      "source": [
        "scores = evaluate(true, pred)\n",
        "\n",
        "scores(K = 20)\n",
        "scores.print_all()\n",
        "\n",
        "scores(K = 100)\n",
        "scores.print_all()"
      ],
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "ca23871c2a014b90af0ce28ffe091b68",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(FloatProgress(value=0.0, max=604.0), HTML(value='')))"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "      Recall@20 : 0.13176 \n",
            "   Precision@20 : 0.07980 \n",
            "         MAP@20 : 0.04657 \n",
            "         MRR@20 : 0.23441 \n",
            "        nDCG@20 : 0.11709\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "2e9272bd654b4c28801c2372fa78a728",
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            ]
          },
          "metadata": {
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          }
        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "      Recall@100 : 0.36462 \n",
            "   Precision@100 : 0.05621 \n",
            "         MAP@100 : 0.05923 \n",
            "         MRR@100 : 0.24296 \n",
            "        nDCG@100 : 0.20713\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rGSWMi2K3_8s"
      },
      "source": [
        "## 2. Logistic"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "75Jaa7PCFo4h",
        "outputId": "653d30e0-e2b2-42aa-b6ac-1ae12fa8e11c"
      },
      "source": [
        "model = VAE(n_item, latent_dim = 256, dropout_rate = 0.5, anneal_rate = 0.2, likelihood = 'logistic')\r\n",
        "model.compile(optimizer = Adam(lr = 1e-4), loss = binary_cross_entropy)\r\n",
        "\r\n",
        "model.summary()"
      ],
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Model: \"vae_1\"\n",
            "_________________________________________________________________\n",
            "Layer (type)                 Output Shape              Param #   \n",
            "=================================================================\n",
            "dropout_1 (Dropout)          (None, 3706)              0         \n",
            "_________________________________________________________________\n",
            "encoder_1 (Encoder)          ((None, 256), (None, 256) 1897984   \n",
            "_________________________________________________________________\n",
            "sampling_1 (Sampling)        (None, 256)               0         \n",
            "_________________________________________________________________\n",
            "decoder_1 (Decoder)          (None, 3706)              952442    \n",
            "=================================================================\n",
            "Total params: 2,850,426\n",
            "Trainable params: 2,850,426\n",
            "Non-trainable params: 0\n",
            "_________________________________________________________________\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "BZbS8YbmFo4i",
        "outputId": "ea93b1d9-2f75-4470-e459-1e535155804e"
      },
      "source": [
        "%%time\r\n",
        "early_stopping = EarlyStopping(monitor = 'val_ndcg', mode = 'max', verbose = 1, patience = epochs // 5)\r\n",
        "model_checkpoint = ModelCheckpoint('logi-VAE.h5', monitor = 'val_ndcg', mode = 'max', save_best_only = True)\r\n",
        "\r\n",
        "hist = model.fit(x = train_gen, validation_data = valid_gen, epochs = epochs,\r\n",
        "                 steps_per_epoch = steps_per_epoch, validation_steps = validation_steps, \r\n",
        "                 verbose = 1, callbacks = [early_stopping, model_checkpoint])\r\n",
        "show_history(hist, 'loss', 'ndcg')"
      ],
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Epoch 1/100\n",
            "38/38 [==============================] - 1s 12ms/step - loss: 2530.8128 - val_ndcg: 0.0475\n",
            "Epoch 2/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 1972.0025 - val_ndcg: 0.1144\n",
            "Epoch 3/100\n",
            "38/38 [==============================] - 0s 9ms/step - loss: 1326.2715 - val_ndcg: 0.1343\n",
            "Epoch 4/100\n",
            "38/38 [==============================] - 0s 12ms/step - loss: 983.5166 - val_ndcg: 0.1625\n",
            "Epoch 5/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 800.4059 - val_ndcg: 0.1572\n",
            "Epoch 6/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 701.9360 - val_ndcg: 0.1473\n",
            "Epoch 7/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 638.6970 - val_ndcg: 0.1465\n",
            "Epoch 8/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 597.4224 - val_ndcg: 0.1437\n",
            "Epoch 9/100\n",
            "38/38 [==============================] - 0s 9ms/step - loss: 564.9872 - val_ndcg: 0.1531\n",
            "Epoch 10/100\n",
            "38/38 [==============================] - 0s 9ms/step - loss: 547.2012 - val_ndcg: 0.1455\n",
            "Epoch 11/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 528.9292 - val_ndcg: 0.1309\n",
            "Epoch 12/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 512.5093 - val_ndcg: 0.1281\n",
            "Epoch 13/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 505.1934 - val_ndcg: 0.1512\n",
            "Epoch 14/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 492.1157 - val_ndcg: 0.1376\n",
            "Epoch 15/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 485.0523 - val_ndcg: 0.1593\n",
            "Epoch 16/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 479.5702 - val_ndcg: 0.1375\n",
            "Epoch 17/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 473.1795 - val_ndcg: 0.1606\n",
            "Epoch 18/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 469.8881 - val_ndcg: 0.1474\n",
            "Epoch 19/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 462.3114 - val_ndcg: 0.1462\n",
            "Epoch 20/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 462.4916 - val_ndcg: 0.1508\n",
            "Epoch 21/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 458.3724 - val_ndcg: 0.1533\n",
            "Epoch 22/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 450.9294 - val_ndcg: 0.1525\n",
            "Epoch 23/100\n",
            "38/38 [==============================] - 0s 11ms/step - loss: 454.3284 - val_ndcg: 0.1574\n",
            "Epoch 24/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 447.0410 - val_ndcg: 0.1495\n",
            "Epoch 00024: early stopping\n",
            "CPU times: user 10.9 s, sys: 878 ms, total: 11.8 s\n",
            "Wall time: 8.44 s\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 576x432 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 195
        },
        "id": "IgoF0-JiFo4k",
        "outputId": "36c2bcf0-2369-4bef-9635-042c84ca7ed4"
      },
      "source": [
        "true = list_agg(test_r)\r\n",
        "true.head(5)"
      ],
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>user_id</th>\n",
              "      <th>movie_id</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>2</td>\n",
              "      <td>[177, 179, 183, 84, 4, 198, 199, 207]</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>8</td>\n",
              "      <td>[59, 438, 93, 123, 463, 525, 30, 288, 534, 322...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>41</td>\n",
              "      <td>[175, 182, 563, 184, 1176, 116, 128, 1037, 104...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>78</td>\n",
              "      <td>[1258, 305, 500, 2230]</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>91</td>\n",
              "      <td>[558, 1176, 195, 587, 592, 74, 1904, 186, 647,...</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   user_id                                           movie_id\n",
              "0        2              [177, 179, 183, 84, 4, 198, 199, 207]\n",
              "1        8  [59, 438, 93, 123, 463, 525, 30, 288, 534, 322...\n",
              "2       41  [175, 182, 563, 184, 1176, 116, 128, 1037, 104...\n",
              "3       78                             [1258, 305, 500, 2230]\n",
              "4       91  [558, 1176, 195, 587, 592, 74, 1904, 186, 647,..."
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 27
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 195
        },
        "id": "SNvbNQ3KFo4k",
        "outputId": "ed98795b-3ba9-4e58-8e0a-c730418b00e4"
      },
      "source": [
        "pred = test_predictor(test_q, model, n_item, batch_size, N = 100)\n",
        "pred.head(5)"
      ],
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
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              "        text-align: right;\n",
              "    }\n",
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              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>user_id</th>\n",
              "      <th>movie_id</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>2</td>\n",
              "      <td>[48, 128, 38, 132, 23, 51, 167, 97, 669, 92, 2...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>8</td>\n",
              "      <td>[44, 124, 127, 97, 669, 5, 22, 92, 134, 244, 1...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>41</td>\n",
              "      <td>[104, 48, 128, 38, 132, 51, 23, 167, 669, 92, ...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>78</td>\n",
              "      <td>[104, 44, 124, 127, 38, 48, 128, 132, 64, 51, ...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>91</td>\n",
              "      <td>[104, 44, 124, 127, 48, 51, 64, 23, 97, 669, 2...</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   user_id                                           movie_id\n",
              "0        2  [48, 128, 38, 132, 23, 51, 167, 97, 669, 92, 2...\n",
              "1        8  [44, 124, 127, 97, 669, 5, 22, 92, 134, 244, 1...\n",
              "2       41  [104, 48, 128, 38, 132, 51, 23, 167, 669, 92, ...\n",
              "3       78  [104, 44, 124, 127, 38, 48, 128, 132, 64, 51, ...\n",
              "4       91  [104, 44, 124, 127, 48, 51, 64, 23, 97, 669, 2..."
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 28
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 292,
          "referenced_widgets": [
            "297d8422d55b465ab08e2dbf868371f2",
            "93a20313ae8e4c9a8e990fe114029fe7",
            "8b2a241c604b480b8ad0801c0bd9b30c",
            "f658d25976d048fe8170652b2285c7e0",
            "3ab229355d4f432a8f1ff63f00e98465",
            "870ac261693c4dbf8d30898910ff5bb7",
            "7ac2e5298a474f91bf85aeb72795c6e5",
            "a1333214a6154ffc92f4bb5d26a23402",
            "b88f9669289f45c5a9578182a85ad58a",
            "64bd0c8f1a0346199eb71a5994d77fc8",
            "4583bd2759044ca2adfeb0c5bc5614a9",
            "551ecacb918e4856afb9277e56146ede",
            "b46810ef39f140d0be91767d46d30bc4",
            "8a6ed954a8874d738d7c5f319c6bf0cb",
            "6048c9c95db54f59a29fb4a5fad64bea",
            "e4e1818bd7e3430fb117e8dd56f53811"
          ]
        },
        "id": "xDwoXc5MFo4k",
        "outputId": "5b749a78-bb49-43b5-a834-9dc2df285e08"
      },
      "source": [
        "scores = evaluate(true, pred)\n",
        "\n",
        "scores(K = 20)\n",
        "scores.print_all()\n",
        "\n",
        "scores(K = 100)\n",
        "scores.print_all()"
      ],
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "297d8422d55b465ab08e2dbf868371f2",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(FloatProgress(value=0.0, max=604.0), HTML(value='')))"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "      Recall@20 : 0.10474 \n",
            "   Precision@20 : 0.06548 \n",
            "         MAP@20 : 0.03201 \n",
            "         MRR@20 : 0.17679 \n",
            "        nDCG@20 : 0.08946\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "b88f9669289f45c5a9578182a85ad58a",
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          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "      Recall@100 : 0.25740 \n",
            "   Precision@100 : 0.04270 \n",
            "         MAP@100 : 0.03874 \n",
            "         MRR@100 : 0.18404 \n",
            "        nDCG@100 : 0.14888\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3RQJclIQcbyM"
      },
      "source": [
        "### 3. Mult-DAE"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9csYp1DyJ3uQ"
      },
      "source": [
        "class DAE(tf.keras.models.Model):\r\n",
        "    def __init__(self, input_dim, latent_dim, dropout_rate):\r\n",
        "        super(DAE, self).__init__()\r\n",
        "        self.input_dim = input_dim\r\n",
        "        self.latent_dim = latent_dim\r\n",
        "        self.dropout_rate = dropout_rate\r\n",
        "\r\n",
        "        self.dropout = Dropout(self.dropout_rate)\r\n",
        "        self.encoder = Dense(self.latent_dim, \r\n",
        "                             activation = 'selu',\r\n",
        "                             kernel_initializer = 'glorot_uniform',\r\n",
        "                             bias_initializer = 'zeros',\r\n",
        "                             kernel_regularizer = l2(1e-3),\r\n",
        "                             name = 'encoder')\r\n",
        "        self.decoder = Dense(self.input_dim,\r\n",
        "                             activation = 'softmax',\r\n",
        "                             kernel_initializer = 'glorot_uniform',\r\n",
        "                             bias_initializer = 'zeros',\r\n",
        "                             kernel_regularizer = l2(1e-3),\r\n",
        "                             name = 'decoder')\r\n",
        "\r\n",
        "        _ = self.call(Input(shape = (self.input_dim, )), training = True)\r\n",
        "        self.build(input_shape = (None, self.input_dim))\r\n",
        "\r\n",
        "    def call(self, inputs, training = False):\r\n",
        "        x = self.dropout(inputs) if training else inputs\r\n",
        "        h = self.encoder(x)\r\n",
        "        return self.decoder(h)\r\n",
        "\r\n",
        "    def train_step(self, inputs):\r\n",
        "        with tf.GradientTape() as tape:\r\n",
        "            outputs = self(inputs, training = True)\r\n",
        "            loss = self.loss(inputs, outputs)\r\n",
        "        grads = tape.gradient(loss, self.trainable_variables)\r\n",
        "        self.optimizer.apply_gradients(zip(grads, self.trainable_variables))\r\n",
        "        return {'loss': loss}\r\n",
        "\r\n",
        "    def test_step(self, data):\r\n",
        "        query, relev = data\r\n",
        "        pred = self(query)\r\n",
        "\r\n",
        "        weight = tf.range(2, self.input_dim, dtype = 'float32')\r\n",
        "        weight = tf.math.reciprocal(tf.math.log(weight))\r\n",
        "        ndcg = batch_ndcg(query, relev, pred, weight)\r\n",
        "        return {'ndcg': ndcg}"
      ],
      "execution_count": 30,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "N8ln-SLNGDc9",
        "outputId": "e6feed7e-e426-4e52-8fd2-84680c996a74"
      },
      "source": [
        "model = DAE(n_item, latent_dim = 256, dropout_rate = 0.5)\r\n",
        "model.compile(optimizer = Adam(lr = 1e-4), loss = multinomial)\r\n",
        "\r\n",
        "model.summary()"
      ],
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Model: \"dae\"\n",
            "_________________________________________________________________\n",
            "Layer (type)                 Output Shape              Param #   \n",
            "=================================================================\n",
            "dropout_2 (Dropout)          (None, 3706)              0         \n",
            "_________________________________________________________________\n",
            "encoder (Dense)              (None, 256)               948992    \n",
            "_________________________________________________________________\n",
            "decoder (Dense)              (None, 3706)              952442    \n",
            "=================================================================\n",
            "Total params: 1,901,434\n",
            "Trainable params: 1,901,434\n",
            "Non-trainable params: 0\n",
            "_________________________________________________________________\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "mdtrxboMGDc-",
        "outputId": "17c9da8d-20c6-44f7-9c48-ff6a5161c8da"
      },
      "source": [
        "%%time\r\n",
        "early_stopping = EarlyStopping(monitor = 'val_ndcg', mode = 'max', verbose = 1, patience = epochs // 5)\r\n",
        "model_checkpoint = ModelCheckpoint('mult-DAE.h5', monitor = 'val_ndcg', mode = 'max', save_best_only = True)\r\n",
        "\r\n",
        "hist = model.fit(x = train_gen, validation_data = valid_gen, epochs = epochs,\r\n",
        "                 steps_per_epoch = steps_per_epoch, validation_steps = validation_steps, \r\n",
        "                 verbose = 1, callbacks = [early_stopping, model_checkpoint])\r\n",
        "show_history(hist, 'loss', 'ndcg')"
      ],
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Epoch 1/100\n",
            "38/38 [==============================] - 1s 12ms/step - loss: 772.4105 - val_ndcg: 0.1051\n",
            "Epoch 2/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 730.0532 - val_ndcg: 0.1180\n",
            "Epoch 3/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 714.9914 - val_ndcg: 0.1324\n",
            "Epoch 4/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 703.2492 - val_ndcg: 0.1622\n",
            "Epoch 5/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 697.0266 - val_ndcg: 0.1621\n",
            "Epoch 6/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 701.2551 - val_ndcg: 0.1359\n",
            "Epoch 7/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 686.6201 - val_ndcg: 0.1643\n",
            "Epoch 8/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 685.6510 - val_ndcg: 0.1862\n",
            "Epoch 9/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 674.1777 - val_ndcg: 0.1852\n",
            "Epoch 10/100\n",
            "38/38 [==============================] - 0s 7ms/step - loss: 681.4982 - val_ndcg: 0.1851\n",
            "Epoch 11/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 674.6839 - val_ndcg: 0.1780\n",
            "Epoch 12/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 665.8164 - val_ndcg: 0.2119\n",
            "Epoch 13/100\n",
            "38/38 [==============================] - 0s 11ms/step - loss: 673.7491 - val_ndcg: 0.2020\n",
            "Epoch 14/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 659.8020 - val_ndcg: 0.1930\n",
            "Epoch 15/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 665.3139 - val_ndcg: 0.2065\n",
            "Epoch 16/100\n",
            "38/38 [==============================] - 0s 7ms/step - loss: 657.3636 - val_ndcg: 0.1859\n",
            "Epoch 17/100\n",
            "38/38 [==============================] - 0s 7ms/step - loss: 660.3803 - val_ndcg: 0.2114\n",
            "Epoch 18/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 659.1074 - val_ndcg: 0.2066\n",
            "Epoch 19/100\n",
            "38/38 [==============================] - 0s 7ms/step - loss: 663.1113 - val_ndcg: 0.1917\n",
            "Epoch 20/100\n",
            "38/38 [==============================] - 0s 9ms/step - loss: 660.4189 - val_ndcg: 0.1971\n",
            "Epoch 21/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 644.9914 - val_ndcg: 0.2099\n",
            "Epoch 22/100\n",
            "38/38 [==============================] - 0s 7ms/step - loss: 655.0488 - val_ndcg: 0.2075\n",
            "Epoch 23/100\n",
            "38/38 [==============================] - 0s 7ms/step - loss: 651.2641 - val_ndcg: 0.1736\n",
            "Epoch 24/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 654.9747 - val_ndcg: 0.1668\n",
            "Epoch 25/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 644.7142 - val_ndcg: 0.1924\n",
            "Epoch 26/100\n",
            "38/38 [==============================] - 0s 7ms/step - loss: 649.7966 - val_ndcg: 0.2118\n",
            "Epoch 27/100\n",
            "38/38 [==============================] - 0s 7ms/step - loss: 651.6177 - val_ndcg: 0.1953\n",
            "Epoch 28/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 644.4928 - val_ndcg: 0.2142\n",
            "Epoch 29/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 641.9962 - val_ndcg: 0.2156\n",
            "Epoch 30/100\n",
            "38/38 [==============================] - 0s 7ms/step - loss: 648.3295 - val_ndcg: 0.1715\n",
            "Epoch 31/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 639.9325 - val_ndcg: 0.2131\n",
            "Epoch 32/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 642.8477 - val_ndcg: 0.2026\n",
            "Epoch 33/100\n",
            "38/38 [==============================] - 0s 11ms/step - loss: 647.4785 - val_ndcg: 0.1841\n",
            "Epoch 34/100\n",
            "38/38 [==============================] - 0s 7ms/step - loss: 639.5083 - val_ndcg: 0.2039\n",
            "Epoch 35/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 651.0295 - val_ndcg: 0.2001\n",
            "Epoch 36/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 628.0166 - val_ndcg: 0.2053\n",
            "Epoch 37/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 643.5605 - val_ndcg: 0.2080\n",
            "Epoch 38/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 638.7460 - val_ndcg: 0.2223\n",
            "Epoch 39/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 643.0311 - val_ndcg: 0.2178\n",
            "Epoch 40/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 634.4687 - val_ndcg: 0.2100\n",
            "Epoch 41/100\n",
            "38/38 [==============================] - 0s 7ms/step - loss: 643.0926 - val_ndcg: 0.2207\n",
            "Epoch 42/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 634.7544 - val_ndcg: 0.2071\n",
            "Epoch 43/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 636.2664 - val_ndcg: 0.2090\n",
            "Epoch 44/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 636.7904 - val_ndcg: 0.2195\n",
            "Epoch 45/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 631.1347 - val_ndcg: 0.2188\n",
            "Epoch 46/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 636.4452 - val_ndcg: 0.2054\n",
            "Epoch 47/100\n",
            "38/38 [==============================] - 0s 7ms/step - loss: 636.1499 - val_ndcg: 0.2183\n",
            "Epoch 48/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 634.7068 - val_ndcg: 0.2115\n",
            "Epoch 49/100\n",
            "38/38 [==============================] - 0s 7ms/step - loss: 635.7214 - val_ndcg: 0.2071\n",
            "Epoch 50/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 622.4114 - val_ndcg: 0.2060\n",
            "Epoch 51/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 632.0474 - val_ndcg: 0.2160\n",
            "Epoch 52/100\n",
            "38/38 [==============================] - 0s 10ms/step - loss: 625.9836 - val_ndcg: 0.2063\n",
            "Epoch 53/100\n",
            "38/38 [==============================] - 0s 7ms/step - loss: 631.3829 - val_ndcg: 0.2033\n",
            "Epoch 54/100\n",
            "38/38 [==============================] - 0s 7ms/step - loss: 630.0374 - val_ndcg: 0.2211\n",
            "Epoch 55/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 621.6865 - val_ndcg: 0.2089\n",
            "Epoch 56/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 637.0302 - val_ndcg: 0.2234\n",
            "Epoch 57/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 629.5379 - val_ndcg: 0.2202\n",
            "Epoch 58/100\n",
            "38/38 [==============================] - 0s 7ms/step - loss: 632.0799 - val_ndcg: 0.2444\n",
            "Epoch 59/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 621.8542 - val_ndcg: 0.2003\n",
            "Epoch 60/100\n",
            "38/38 [==============================] - 0s 7ms/step - loss: 623.8458 - val_ndcg: 0.2298\n",
            "Epoch 61/100\n",
            "38/38 [==============================] - 0s 7ms/step - loss: 630.7802 - val_ndcg: 0.2102\n",
            "Epoch 62/100\n",
            "38/38 [==============================] - 0s 7ms/step - loss: 624.2194 - val_ndcg: 0.2414\n",
            "Epoch 63/100\n",
            "38/38 [==============================] - 0s 7ms/step - loss: 625.0933 - val_ndcg: 0.2296\n",
            "Epoch 64/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 623.8410 - val_ndcg: 0.2117\n",
            "Epoch 65/100\n",
            "38/38 [==============================] - 0s 7ms/step - loss: 626.2993 - val_ndcg: 0.2109\n",
            "Epoch 66/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 618.1666 - val_ndcg: 0.2223\n",
            "Epoch 67/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 624.4247 - val_ndcg: 0.2161\n",
            "Epoch 68/100\n",
            "38/38 [==============================] - 0s 7ms/step - loss: 629.7680 - val_ndcg: 0.2123\n",
            "Epoch 69/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 614.5058 - val_ndcg: 0.2266\n",
            "Epoch 70/100\n",
            "38/38 [==============================] - 0s 7ms/step - loss: 623.0621 - val_ndcg: 0.2156\n",
            "Epoch 71/100\n",
            "38/38 [==============================] - 0s 10ms/step - loss: 620.1717 - val_ndcg: 0.2096\n",
            "Epoch 72/100\n",
            "38/38 [==============================] - 0s 7ms/step - loss: 618.7310 - val_ndcg: 0.1814\n",
            "Epoch 73/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 626.3555 - val_ndcg: 0.2111\n",
            "Epoch 74/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 616.7596 - val_ndcg: 0.2014\n",
            "Epoch 75/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 619.4399 - val_ndcg: 0.2337\n",
            "Epoch 76/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 620.5179 - val_ndcg: 0.2208\n",
            "Epoch 77/100\n",
            "38/38 [==============================] - 0s 7ms/step - loss: 608.2394 - val_ndcg: 0.2433\n",
            "Epoch 78/100\n",
            "38/38 [==============================] - 0s 8ms/step - loss: 623.8816 - val_ndcg: 0.2407\n",
            "Epoch 00078: early stopping\n",
            "CPU times: user 29.6 s, sys: 2.81 s, total: 32.4 s\n",
            "Wall time: 24 s\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 576x432 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 195
        },
        "id": "ICJbY26XGDdC",
        "outputId": "e9ce24e3-fd16-4d17-c078-acd61820a265"
      },
      "source": [
        "true = list_agg(test_r)\r\n",
        "true.head(5)"
      ],
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>user_id</th>\n",
              "      <th>movie_id</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>2</td>\n",
              "      <td>[177, 179, 183, 84, 4, 198, 199, 207]</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>8</td>\n",
              "      <td>[59, 438, 93, 123, 463, 525, 30, 288, 534, 322...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>41</td>\n",
              "      <td>[175, 182, 563, 184, 1176, 116, 128, 1037, 104...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>78</td>\n",
              "      <td>[1258, 305, 500, 2230]</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>91</td>\n",
              "      <td>[558, 1176, 195, 587, 592, 74, 1904, 186, 647,...</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   user_id                                           movie_id\n",
              "0        2              [177, 179, 183, 84, 4, 198, 199, 207]\n",
              "1        8  [59, 438, 93, 123, 463, 525, 30, 288, 534, 322...\n",
              "2       41  [175, 182, 563, 184, 1176, 116, 128, 1037, 104...\n",
              "3       78                             [1258, 305, 500, 2230]\n",
              "4       91  [558, 1176, 195, 587, 592, 74, 1904, 186, 647,..."
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 33
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 195
        },
        "id": "Kd8zN0U4GDdC",
        "outputId": "ae49c7b6-225f-4aef-d849-1b233f3c6e4f"
      },
      "source": [
        "pred = test_predictor(test_q, model, n_item, batch_size, N = 100)\n",
        "pred.head(5)"
      ],
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>user_id</th>\n",
              "      <th>movie_id</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>2</td>\n",
              "      <td>[92, 22, 48, 132, 60, 97, 171, 189, 23, 151, 2...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>8</td>\n",
              "      <td>[244, 184, 134, 381, 315, 171, 5, 256, 92, 124...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>41</td>\n",
              "      <td>[856, 62, 155, 132, 160, 112, 189, 775, 666, 2...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>78</td>\n",
              "      <td>[104, 68, 406, 92, 531, 38, 1712, 97, 831, 113...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>91</td>\n",
              "      <td>[9, 8, 612, 741, 596, 44, 64, 1523, 116, 682, ...</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   user_id                                           movie_id\n",
              "0        2  [92, 22, 48, 132, 60, 97, 171, 189, 23, 151, 2...\n",
              "1        8  [244, 184, 134, 381, 315, 171, 5, 256, 92, 124...\n",
              "2       41  [856, 62, 155, 132, 160, 112, 189, 775, 666, 2...\n",
              "3       78  [104, 68, 406, 92, 531, 38, 1712, 97, 831, 113...\n",
              "4       91  [9, 8, 612, 741, 596, 44, 64, 1523, 116, 682, ..."
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 34
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 292,
          "referenced_widgets": [
            "8884c0a35bd04c2a9967df8a38a09af5",
            "462990ddb17d4dc5bf7ecd674cf357cf",
            "c0c740d8130d44ee9e97693033ac7bc7",
            "d0e98f49a2b040e2bdb479c8fee6c763",
            "a87ab1f507dc41edbd6b3501b3600ca9",
            "20fb858674044312b9c5d2d3cdc99925",
            "2140931047584f01a221cf6fe69be7b5",
            "873052c8ef3b4bd1a9a3bc9f55755f6b",
            "769681b057dd407b9da653f4c83609d5",
            "c162444dd8aa4186b60a0b2dddc9102f",
            "6543e3f38d2a4a0dbff7e35b687e0911",
            "5e1e66d04afd4c4aa90fc2646e4eb6be",
            "c4d051fba0eb4893927a86598852c812",
            "8d4cfe308db94dc494a22a70fb8089f7",
            "defb16a32b72454c8eb894f0800dc77a",
            "1c2d5ab8c7a04655b843a0ac3eaeb770"
          ]
        },
        "id": "bSd7eLpQGDdC",
        "outputId": "69f3bc9c-ba68-4c21-b67b-c3d4adb4c5b8"
      },
      "source": [
        "scores = evaluate(true, pred)\n",
        "\n",
        "scores(K = 20)\n",
        "scores.print_all()\n",
        "\n",
        "scores(K = 100)\n",
        "scores.print_all()"
      ],
      "execution_count": 35,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "8884c0a35bd04c2a9967df8a38a09af5",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(FloatProgress(value=0.0, max=604.0), HTML(value='')))"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "      Recall@20 : 0.14089 \n",
            "   Precision@20 : 0.08104 \n",
            "         MAP@20 : 0.04800 \n",
            "         MRR@20 : 0.23517 \n",
            "        nDCG@20 : 0.12145\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "769681b057dd407b9da653f4c83609d5",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(FloatProgress(value=0.0, max=604.0), HTML(value='')))"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "      Recall@100 : 0.39001 \n",
            "   Precision@100 : 0.05684 \n",
            "         MAP@100 : 0.06267 \n",
            "         MRR@100 : 0.24279 \n",
            "        nDCG@100 : 0.21694\n"
          ],
          "name": "stdout"
        }
      ]
    }
  ]
}