time_series_with_rnn.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using TensorFlow backend.\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from sklearn.preprocessing import MinMaxScaler\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from keras.models import Sequential\n",
    "from keras.layers import LSTM, Dense\n",
    "\n",
    "from matplotlib import pyplot\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Introduction\n",
    "\n",
    "This is an experiment in time series forecasting, using recurrent neural network (RNN). Time series data is a set of access log entries, containing timestamps. One can solve the problem with other methods, such as manual feature engineering + xgboost, etc.\n",
    "\n",
    "After looking at data, I will formulate the problem I want to solve and will translorm data to fit the problem. I will then provide 2 solutions: a simple baseline solution and RNN solution. After evaluating the RNN solution, I will end up with short discussion on ways to improve it."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Raw data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>10</th>\n",
       "      <th>11</th>\n",
       "      <th>12</th>\n",
       "      <th>13</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>147.214.18.128</td>\n",
       "      <td>-</td>\n",
       "      <td>-</td>\n",
       "      <td>2016-11-27</td>\n",
       "      <td>03:16:03</td>\n",
       "      <td>100</td>\n",
       "      <td>GET /rawdata-dispatcher/progress/count?executi...</td>\n",
       "      <td>rc:200</td>\n",
       "      <td>22</td>\n",
       "      <td>-</td>\n",
       "      <td>Apache-HttpClient/4.3.3 (java 1.5)</td>\n",
       "      <td>in:244</td>\n",
       "      <td>out:223</td>\n",
       "      <td>us:2545</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>147.214.18.128</td>\n",
       "      <td>-</td>\n",
       "      <td>-</td>\n",
       "      <td>2016-11-27</td>\n",
       "      <td>03:16:05</td>\n",
       "      <td>100</td>\n",
       "      <td>GET /rawdata-dispatcher/progress/count?executi...</td>\n",
       "      <td>rc:200</td>\n",
       "      <td>21</td>\n",
       "      <td>-</td>\n",
       "      <td>Apache-HttpClient/4.3.3 (java 1.5)</td>\n",
       "      <td>in:244</td>\n",
       "      <td>out:222</td>\n",
       "      <td>us:2187</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>localhost</td>\n",
       "      <td>-</td>\n",
       "      <td>-</td>\n",
       "      <td>2016-11-27</td>\n",
       "      <td>03:16:07</td>\n",
       "      <td>100</td>\n",
       "      <td>GET /server-status?auto HTTP/1.1</td>\n",
       "      <td>rc:200</td>\n",
       "      <td>387</td>\n",
       "      <td>-</td>\n",
       "      <td>collectd/5.5.1</td>\n",
       "      <td>in:94</td>\n",
       "      <td>out:585</td>\n",
       "      <td>us:475</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>147.214.18.128</td>\n",
       "      <td>-</td>\n",
       "      <td>-</td>\n",
       "      <td>2016-11-27</td>\n",
       "      <td>03:16:08</td>\n",
       "      <td>100</td>\n",
       "      <td>GET /rawdata-dispatcher/progress/count?executi...</td>\n",
       "      <td>rc:200</td>\n",
       "      <td>22</td>\n",
       "      <td>-</td>\n",
       "      <td>Apache-HttpClient/4.3.3 (java 1.5)</td>\n",
       "      <td>in:244</td>\n",
       "      <td>out:223</td>\n",
       "      <td>us:1835</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>147.214.18.128</td>\n",
       "      <td>-</td>\n",
       "      <td>-</td>\n",
       "      <td>2016-11-27</td>\n",
       "      <td>03:16:08</td>\n",
       "      <td>100</td>\n",
       "      <td>GET /rawdata-dispatcher/progress/list?executio...</td>\n",
       "      <td>rc:200</td>\n",
       "      <td>4554</td>\n",
       "      <td>-</td>\n",
       "      <td>Apache-HttpClient/4.3.3 (java 1.5)</td>\n",
       "      <td>in:259</td>\n",
       "      <td>out:4757</td>\n",
       "      <td>us:3021</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               0  1  2           3         4    5   \\\n",
       "0  147.214.18.128  -  -  2016-11-27  03:16:03  100   \n",
       "1  147.214.18.128  -  -  2016-11-27  03:16:05  100   \n",
       "2       localhost  -  -  2016-11-27  03:16:07  100   \n",
       "3  147.214.18.128  -  -  2016-11-27  03:16:08  100   \n",
       "4  147.214.18.128  -  -  2016-11-27  03:16:08  100   \n",
       "\n",
       "                                                  6       7     8  9   \\\n",
       "0  GET /rawdata-dispatcher/progress/count?executi...  rc:200    22  -   \n",
       "1  GET /rawdata-dispatcher/progress/count?executi...  rc:200    21  -   \n",
       "2                   GET /server-status?auto HTTP/1.1  rc:200   387  -   \n",
       "3  GET /rawdata-dispatcher/progress/count?executi...  rc:200    22  -   \n",
       "4  GET /rawdata-dispatcher/progress/list?executio...  rc:200  4554  -   \n",
       "\n",
       "                                   10      11        12       13  \n",
       "0  Apache-HttpClient/4.3.3 (java 1.5)  in:244   out:223  us:2545  \n",
       "1  Apache-HttpClient/4.3.3 (java 1.5)  in:244   out:222  us:2187  \n",
       "2                      collectd/5.5.1   in:94   out:585   us:475  \n",
       "3  Apache-HttpClient/4.3.3 (java 1.5)  in:244   out:223  us:1835  \n",
       "4  Apache-HttpClient/4.3.3 (java 1.5)  in:259  out:4757  us:3021  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv('access_logs_201612.txt', sep=' ', header=None)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is a typical access log entry, showing what requests are made to a server, along with request info such as the origin of a request (column 0), the time it is made (columns 3 and 4), etc.\n",
    "\n",
    "In such system one might want to know how many requests per time unit are expected in the near future (e.g in the coming 24 hours). Knowing this can be used for tasks such as resource optimization, where one uses various number of servers to respond well to request spikes.\n",
    "\n",
    "For training efficiency, I will transform log data to requests per hour, so there is less data to work with."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Transformed data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def load_logfile():\n",
    "    df = pd.read_csv(\n",
    "        'access_logs_201612.txt', \n",
    "        sep=' ', \n",
    "        header=None, \n",
    "        parse_dates={'timestamp': [3, 4]}, \n",
    "        date_parser=lambda x: pd.datetime.strptime(x, '%Y-%m-%d %H:%M:%S')\n",
    "    )\n",
    "    df['dayofyear'] = df.timestamp.dt.dayofyear\n",
    "    df['hour'] = df.timestamp.dt.hour\n",
    "    data = pd.DataFrame(df.groupby(['dayofyear', 'hour'])\n",
    "                        .count()\n",
    "                        .reset_index()\n",
    "                       ).rename(columns={'timestamp': 'requests_per_hour'})\n",
    "    return data['requests_per_hour']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "requests_per_hour = load_logfile()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    5163\n",
       "1    7129\n",
       "2    7593\n",
       "3    8951\n",
       "4    5429\n",
       "Name: requests_per_hour, dtype: int64"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "requests_per_hour.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f8104ea4240>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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+Of937tpl6u9zaINN3ToH+8/xOYc0vZXsWx2WK+eQ1jnYwicnkl2fUoSVfKKi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\nipKHioOiKIqSh4qDoiiKksf/ByOU3TEeqbogAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8104ea4ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "requests_per_hour.plot(title='requests per hour', color='blue')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that in the first hour there were 5163 requests, followed by 7129 requests in the second hour, etc. The graph above shows all request counts."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "394"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(requests_per_hour)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_test = 24"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are 394 data entries. I will try to predict the counts for the last 24 (num_test) hours in this sequence."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Baseline\n",
    "\n",
    "Since I want to evaluate the performance of the RNN model, I need a baseline model to evaluate against. One possible prediction/model of the number of requests in the next hour is to say that there will be as many as in the current hour. This is obviously quite an naive approach but it makes a good baseline. That is, if RNN does not perform better than baseline, RNN would not be a good approach to solve this problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y = requests_per_hour[-num_test:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "Preds = Y.shift().values\n",
    "Preds[0] = requests_per_hour[len(requests_per_hour)-num_test-1]\n",
    "Y = Y.values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f810e391710>]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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lvJz/9xH/fRenkP3Lv0SvP9Aqb4lDdjbXpURbre/fz9fTaqGVlHDm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\nDoIgCEIEIg6CIAhCBP8fz5yeFLgecrEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f810e3917b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pyplot.plot(Y, color='blue')\n",
    "pyplot.plot(Preds, color='red')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6064985.166666667"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "baseline_mse = mean_squared_error(Y, Preds)\n",
    "baseline_mse"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I measure mean squared error (mse) because it is the metric I use in the RNN model below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### RNN model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "def scale(X):\n",
    "    scaler = MinMaxScaler(feature_range=[-1, 1])\n",
    "    X = X.astype('float64')\n",
    "    X = scaler.fit_transform(X.values.reshape(-1, 1))\n",
    "    return scaler, pd.Series(X.flatten())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "scaler, X = scale(requests_per_hour)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I scale data in the range [1-, 1] since it is the range used by the LSTM activation function in the RNN model below. Then I split data into train and test parts.\n",
    "\n",
    "I train the model with x_train, y_train. Then I make predictions on x_test and compare them with y_test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_xy(X):\n",
    "    Y = X\n",
    "    X = X.shift()\n",
    "    X[0] = 0\n",
    "    assert len(X) == len(Y)\n",
    "    return X, Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "X, Y = get_xy(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_train_test(X, Y, num_test=int(0.2*len(X))):\n",
    "    return X[:-num_test], Y[:-num_test], X[-num_test:], Y[-num_test:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_train, y_train, x_test, y_test = get_train_test(X, Y, num_test=num_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(370, 370, 24, 24)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(x_train), len(y_train), len(x_test), len(y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Create model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_model(units=1, batch_input_shape=(1, 1, 1)):\n",
    "    model = Sequential([\n",
    "        LSTM(units=units, stateful=True, batch_input_shape=batch_input_shape),\n",
    "        Dense(1, activation='linear')\n",
    "    ])\n",
    "    model.compile(optimizer='adam', loss='mse')\n",
    "    return model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Simple stateful model with mse (mean square error) loss function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fit_model(x, y, units=1, epochs=10, verbose=0):\n",
    "    model = get_model(units=units)\n",
    "    for i in range(epochs):\n",
    "        model.fit(\n",
    "            x.values.reshape(x.shape[0], 1, 1), \n",
    "            y, \n",
    "            batch_size=1, \n",
    "            epochs=1, \n",
    "            shuffle=False,\n",
    "            verbose=verbose,\n",
    "            validation_split=0.2\n",
    "        )\n",
    "        model.reset_states()\n",
    "    return model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The model is trained with x.shape[0] samples, to generate 1 prediction ahead, with sample size of 1 (requests per hour count). I set suffle to False to keep the ordered nature of data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = fit_model(x_train, y_train, units=5, epochs=5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Are we under/overfitting?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "def predict_visualize(x, y, scaler):\n",
    "    preds = model.predict(x.values.reshape(x.shape[0], 1, 1), batch_size=1)\n",
    "    y_inv = scaler.inverse_transform(y.values.reshape(-1, 1))\n",
    "    preds_inv = scaler.inverse_transform(preds)\n",
    "\n",
    "    pyplot.title('Actual vs. predicted requests per hour')\n",
    "    pyplot.plot(y_inv, color='blue')\n",
    "    pyplot.plot(preds_inv, color='red')\n",
    "    \n",
    "    rnn_mse = mean_squared_error(y_inv, preds_inv)\n",
    "    return rnn_mse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7348315.5062668156"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Alz6qDLdbyc40ORqWQzBf+9A0mFBRX7QyZ8wBnDg4Bk42cdhBLQDdmPnsu7uz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\nxGqLJrtQ0gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f81100f2dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "predict_visualize(x_train, y_train, scaler)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Unsuprisingly (due to the low number of epochs) the model doesn't model data very well, that is it has high bias, so it underfits data. Some ways to solve this is to increase the number of epochs in training and/or to increase the model complexity, e.g. number of units."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Predict and visualize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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4YkR+hUmGjByZOya18gPulSdfch2GD7cK7pBDKm4LM35T8TvMnWu95VSUw157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\nv2GD/Z461ZbZ6DkUFMBvf5s+5VBSYj2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45xz7VAdJ9xxUdYiqtlfVIsyh/L6qngZ8AJwQ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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f810e391f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rnn_mse = predict_visualize(x_test, y_test, scaler)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Model comparision"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rnn_mse < baseline_mse"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The RNN model seems better than baseline since its error is smaller. For better/more robust estimate of the RNN model performance one needs to take the average/median mse from multiple train/predict phases. Yet the model suffers from high bias, so it requires improvement."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Next steps "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The RNN solution might be improved in different ways. Some thigs worth trying are the following:\n",
    "\n",
    "* Grid search to find better parameter values for (at least) number of epochs and LSTM units (see high bias above)\n",
    "* Helping the model by adding domain knowledge/\"hand-made\" features such as dayofweek or day/night\n",
    "* Using alternative architecture, e.g stacking stateless LSTMs, etc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.3"
  }
 },
 "nbformat": 4,
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}