README.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Time series transformation selection with Estimation of Distribution Algorithms"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "When working with large datasets in time series Machine Learning projects, it is common to use different time series transformations in order to improve the forecasting model. In this approach an EDA is used to find the optimum transformations of the time series.\n",
    "\n",
    "This approach is implemented and is part of EDAspy package.\n",
    "\n",
    "## Example of usage"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# loading essential libraries first\n",
    "import pandas as pd\n",
    "import statsmodels.api as sm\n",
    "from statsmodels.tsa.api import VAR\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.metrics import mean_absolute_error\n",
    "\n",
    "# EDAspy libraries\n",
    "from EDAspy.timeseries import EDA_ts_fts as EDA\n",
    "from EDAspy.timeseries import TS_transformations\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>realgdp</th>\n",
       "      <th>realcons</th>\n",
       "      <th>realinv</th>\n",
       "      <th>realgovt</th>\n",
       "      <th>realdpi</th>\n",
       "      <th>cpi</th>\n",
       "      <th>m1</th>\n",
       "      <th>tbilrate</th>\n",
       "      <th>unemp</th>\n",
       "      <th>pop</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2710.349</td>\n",
       "      <td>1707.4</td>\n",
       "      <td>286.898</td>\n",
       "      <td>470.045</td>\n",
       "      <td>1886.9</td>\n",
       "      <td>28.98</td>\n",
       "      <td>139.7</td>\n",
       "      <td>2.82</td>\n",
       "      <td>5.8</td>\n",
       "      <td>177.146</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2778.801</td>\n",
       "      <td>1733.7</td>\n",
       "      <td>310.859</td>\n",
       "      <td>481.301</td>\n",
       "      <td>1919.7</td>\n",
       "      <td>29.15</td>\n",
       "      <td>141.7</td>\n",
       "      <td>3.08</td>\n",
       "      <td>5.1</td>\n",
       "      <td>177.830</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2775.488</td>\n",
       "      <td>1751.8</td>\n",
       "      <td>289.226</td>\n",
       "      <td>491.260</td>\n",
       "      <td>1916.4</td>\n",
       "      <td>29.35</td>\n",
       "      <td>140.5</td>\n",
       "      <td>3.82</td>\n",
       "      <td>5.3</td>\n",
       "      <td>178.657</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2785.204</td>\n",
       "      <td>1753.7</td>\n",
       "      <td>299.356</td>\n",
       "      <td>484.052</td>\n",
       "      <td>1931.3</td>\n",
       "      <td>29.37</td>\n",
       "      <td>140.0</td>\n",
       "      <td>4.33</td>\n",
       "      <td>5.6</td>\n",
       "      <td>179.386</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2847.699</td>\n",
       "      <td>1770.5</td>\n",
       "      <td>331.722</td>\n",
       "      <td>462.199</td>\n",
       "      <td>1955.5</td>\n",
       "      <td>29.54</td>\n",
       "      <td>139.6</td>\n",
       "      <td>3.50</td>\n",
       "      <td>5.2</td>\n",
       "      <td>180.007</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    realgdp  realcons  realinv  realgovt  realdpi    cpi     m1  tbilrate  \\\n",
       "0  2710.349    1707.4  286.898   470.045   1886.9  28.98  139.7      2.82   \n",
       "1  2778.801    1733.7  310.859   481.301   1919.7  29.15  141.7      3.08   \n",
       "2  2775.488    1751.8  289.226   491.260   1916.4  29.35  140.5      3.82   \n",
       "3  2785.204    1753.7  299.356   484.052   1931.3  29.37  140.0      4.33   \n",
       "4  2847.699    1770.5  331.722   462.199   1955.5  29.54  139.6      3.50   \n",
       "\n",
       "   unemp      pop  \n",
       "0    5.8  177.146  \n",
       "1    5.1  177.830  \n",
       "2    5.3  178.657  \n",
       "3    5.6  179.386  \n",
       "4    5.2  180.007  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# import some data\n",
    "mdata = sm.datasets.macrodata.load_pandas().data\n",
    "df = mdata.iloc[:, 2:12]\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['realinv',\n",
       " 'tbilrate',\n",
       " 'realgdp',\n",
       " 'unemp',\n",
       " 'm1',\n",
       " 'cpi',\n",
       " 'realdpi',\n",
       " 'realcons',\n",
       " 'realgovt']"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "variables = list(df.columns)\n",
    "variable_y = 'pop'  # pop is the variable we want to forecast\n",
    "variables = list(set(variables) - {variable_y})  # array of variables to select among transformations\n",
    "variables"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Build the dataset with all the transformations desired. If some more transformations are desired, then it must be added to the dataset following the next steps:\n",
    " 1. Add the transformation postfix\n",
    " 2. Add to the dataset the respective variable with name (name + postfix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "TSTransf = TSTransformations(df)\n",
    "transformations = ['detrend', 'smooth', 'log']  # postfix to variables, to denote the transformation\n",
    "\n",
    "# build the transformations\n",
    "for var in variables:\n",
    "    transformation = TSTransf.de_trending(var)\n",
    "    df[var + 'detrend'] = transformation\n",
    "\n",
    "for var in variables:\n",
    "    transformation = TSTransf.smoothing(var, window=10)\n",
    "    df[var + 'smooth'] = transformation\n",
    "\n",
    "for var in variables:\n",
    "    transformation = TSTransf.log(var)\n",
    "    df[var + 'log'] = transformation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define the cost function to calculate the Mean Absolute Error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cost_function(variables_list, nobs=20, maxlags=15, forecastings=10):\n",
    "    \"\"\"\n",
    "    variables_list: list of variables without the variable_y\n",
    "    nobs: how many observations for validation\n",
    "    maxlags: previous lags used to predict\n",
    "    forecasting: number of observations to predict\n",
    "    \n",
    "    return: MAE of the prediction with the real validation data\n",
    "    \"\"\"\n",
    "    \n",
    "    data = df[variables_list + [variable_y]]\n",
    "\n",
    "    df_train, df_test = data[0:-nobs], data[-nobs:]\n",
    "\n",
    "    model = VAR(df_train)\n",
    "    results = model.fit(maxlags=maxlags, ic='aic')\n",
    "\n",
    "    lag_order = results.k_ar\n",
    "    array = results.forecast(df_train.values[-lag_order:], forecastings)\n",
    "\n",
    "    variables_ = list(data.columns)\n",
    "    position = variables_.index(variable_y)\n",
    "\n",
    "    validation = [array[i][position] for i in range(len(array))]\n",
    "    mae = mean_absolute_error(validation, df_test['pop'][-forecastings:])\n",
    "    \n",
    "    return mae"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We take the normal variables without any time series transformation and try to forecast the y variable using the same cost function defined. \n",
    "This value is stored to be compared with the optimum solution found"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MAE without using EDA: 5.091478009948458\n"
     ]
    }
   ],
   "source": [
    "mae_pre_eda = cost_function(variables)\n",
    "print('MAE without using EDA:', mae_pre_eda)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Initialization of the initial vector of statitstics. Each variable has a 50% probability to be or not chosen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "vector = pd.DataFrame(columns=list(variables))\n",
    "vector.loc[0] = 0.5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Run the algorithm. The code will print some further information during execution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[iteration: 0 ] 5.155357972950526\n",
      "[iteration: 1 ] 5.246309408804405\n",
      "[iteration: 2 ] 4.103723942647372\n",
      "[iteration: 3 ] 4.710694858969362\n",
      "[iteration: 4 ] 4.473166010597248\n",
      "[iteration: 5 ] 4.913511145463962\n",
      "[iteration: 6 ] 4.244706428986632\n",
      "[iteration: 7 ] 3.847353187863837\n",
      "[iteration: 8 ] 4.450659158760351\n",
      "[iteration: 9 ] 4.723562306804138\n",
      "[iteration: 10 ] 4.723562306804138\n",
      "[iteration: 11 ] 4.723562306804138\n"
     ]
    }
   ],
   "source": [
    "eda = EDA(max_it=50, dead_it=5, size_gen=15, alpha=0.7, vector=vector,\n",
    "          array_transformations=transformations, cost_function=cost_function)\n",
    "best_ind, best_MAE = eda.run(output=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Some plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solution: ['realinvsmooth', 'tbilratelog', 'realgdpdetrend', 'm1detrend', 'cpibasic', 'realconssmooth', 'realgovtbasic'] \n",
      "MAE post EDA: 3.85 \n",
      "MAE pre EDA: 5.09\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# some plots\n",
    "hist = eda.historic_best\n",
    "\n",
    "relative_plot = []\n",
    "mx = 999999999\n",
    "for i in range(len(hist)):\n",
    "    if hist[i] < mx:\n",
    "        mx = hist[i]\n",
    "        relative_plot.append(mx)\n",
    "    else:\n",
    "        relative_plot.append(mx)\n",
    "\n",
    "print('Solution:', best_ind, '\\nMAE post EDA: %.2f' % best_MAE, '\\nMAE pre EDA: %.2f' % mae_pre_eda)\n",
    "\n",
    "plt.figure(figsize = (14,6))\n",
    "\n",
    "ax = plt.subplot(121)\n",
    "ax.plot(list(range(len(hist))), hist)\n",
    "ax.title.set_text('Local cost found')\n",
    "ax.set_xlabel('iteration')\n",
    "ax.set_ylabel('MAE')\n",
    "\n",
    "ax = plt.subplot(122)\n",
    "ax.plot(list(range(len(relative_plot))), relative_plot)\n",
    "ax.title.set_text('Best global cost found')\n",
    "ax.set_xlabel('iteration')\n",
    "ax.set_ylabel('MAE')\n",
    "\n",
    "plt.show()"
   ]
  }
 ],
 "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": "3.7.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}