santander-value-prediction-challenge.ipynb

{
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A walk through a Gradient Boosting Method : LightGBM\n",
    "\n",
    "\n",
    "Microsoft's Light GBM is a gradient boosting framework that uses tree based learning algorithm. As opposed to other trees based algorithms, LightGBM grows leafwise rather than level-wise. With approach of max_delta loss it will choose the leaf to grow. When growing the same leaf, Leaf-wise algorithm can reduce more loss than a level-wise algorithm. \n",
    "\n",
    "LightGBM is efficient on large volume of data and has compatilbility configurations to run on a GPU as well. It provides for 3 parallel learning algorithms:\n",
    "\n",
    "* Data parallel\t\n",
    "\n",
    "\n",
    "* Feature parallel\n",
    "\n",
    "\n",
    "* Voting parallel\n",
    "\n",
    "\n",
    "\n",
    "These provide for effective execution given different combinations of volume of Data and volume of features provided.\n",
    "[Santander Value Challenge](https://www.kaggle.com/c/santander-value-prediction-challenge/data) provided with an anonymized dataset containing numeric feature variables, the numeric target column, and a string ID column.\n",
    "\n",
    "The task was to predict the value of target column in the test set.\n",
    "\n",
    "This notebook walks through the pipeline of:\n",
    "\n",
    "* Exploratory Data Analysis (E.D.A.) including Data Preprocessing/Cleansing\n",
    "\n",
    "\n",
    "* Normality test of **target** variable\n",
    "\n",
    "\n",
    "* Dimensionality Reduction using PCA\n",
    "\n",
    "\n",
    "* Modelling using LightGBM\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import pandas as pd\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 3.94 s, sys: 256 ms, total: 4.19 s\n",
      "Wall time: 4.22 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "train_df = pd.read_csv('./Data/train.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 54.9 s, sys: 8.42 s, total: 1min 3s\n",
      "Wall time: 1min 6s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "test_df = pd.read_csv('./Data/test.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 227,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(Index([u'ID', u'target', u'48df886f9', u'0deb4b6a8', u'34b15f335',\n",
       "        u'a8cb14b00', u'2f0771a37', u'30347e683', u'd08d1fbe3', u'6ee66e115',\n",
       "        ...\n",
       "        u'3ecc09859', u'9281abeea', u'8675bec0b', u'3a13ed79a', u'f677d4d13',\n",
       "        u'71b203550', u'137efaa80', u'fb36b89d9', u'7e293fbaf', u'9fc776466'],\n",
       "       dtype='object', length=4993), 4459)"
      ]
     },
     "execution_count": 227,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_df.columns, len(train_df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are 4993 columns and 4459 records for training with no name explanatory column names. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exploratory Data Analysis (E.D.A.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_df.isnull().values.any()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**No Null Values recorded, so no need of imputation**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
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       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>00ce2134f</td>\n",
       "      <td>3600000.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>00e7ba121</td>\n",
       "      <td>2786000.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7280000.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>00ecc53f2</td>\n",
       "      <td>40000.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>20 rows × 4993 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "           ID      target  48df886f9  0deb4b6a8  34b15f335  a8cb14b00  \\\n",
       "0   000d6aaf2  38000000.0        0.0          0        0.0          0   \n",
       "1   000fbd867    600000.0        0.0          0        0.0          0   \n",
       "2   0027d6b71  10000000.0        0.0          0        0.0          0   \n",
       "3   0028cbf45   2000000.0        0.0          0        0.0          0   \n",
       "4   002a68644  14400000.0        0.0          0        0.0          0   \n",
       "5   002dbeb22   2800000.0        0.0          0        0.0          0   \n",
       "6   003925ac6    164000.0        0.0          0        0.0          0   \n",
       "7   003eb0261    600000.0        0.0          0        0.0          0   \n",
       "8   004b92275    979000.0        0.0          0        0.0          0   \n",
       "9   0067b4fef    460000.0        0.0          0        0.0          0   \n",
       "10  00689ee2c   1100000.0        0.0          0        0.0          0   \n",
       "11  0069007ac  16000000.0        0.0          0        0.0          0   \n",
       "12  006b60dd7    354000.0        0.0          0        0.0          0   \n",
       "13  008057126   7000000.0        0.0          0        0.0          0   \n",
       "14  008825875    100000.0        0.0          0        0.0          0   \n",
       "15  0096e207e    800000.0        0.0          0        0.0          0   \n",
       "16  00c2deb75    200000.0        0.0          0        0.0          0   \n",
       "17  00ce2134f   3600000.0        0.0          0        0.0          0   \n",
       "18  00e7ba121   2786000.0        0.0          0        0.0          0   \n",
       "19  00ecc53f2     40000.0        0.0          0        0.0          0   \n",
       "\n",
       "    2f0771a37  30347e683  d08d1fbe3  6ee66e115    ...      3ecc09859  \\\n",
       "0           0          0          0          0    ...            0.0   \n",
       "1           0          0          0          0    ...            0.0   \n",
       "2           0          0          0          0    ...            0.0   \n",
       "3           0          0          0          0    ...            0.0   \n",
       "4           0          0          0          0    ...            0.0   \n",
       "5           0          0          0          0    ...        12000.0   \n",
       "6           0          0          0          0    ...            0.0   \n",
       "7           0          0          0          0    ...            0.0   \n",
       "8           0          0          0          0    ...            0.0   \n",
       "9           0          0          0          0    ...            0.0   \n",
       "10          0          0          0          0    ...            0.0   \n",
       "11          0          0          0          0    ...            0.0   \n",
       "12          0          0          0          0    ...            0.0   \n",
       "13          0          0          0          0    ...            0.0   \n",
       "14          0          0          0          0    ...            0.0   \n",
       "15          0          0          0          0    ...            0.0   \n",
       "16          0          0          0          0    ...            0.0   \n",
       "17          0          0          0          0    ...            0.0   \n",
       "18          0          0          0          0    ...            0.0   \n",
       "19          0          0          0          0    ...            0.0   \n",
       "\n",
       "    9281abeea   8675bec0b  3a13ed79a  f677d4d13  71b203550  137efaa80  \\\n",
       "0         0.0         0.0          0          0          0          0   \n",
       "1         0.0         0.0          0          0          0          0   \n",
       "2         0.0         0.0          0          0          0          0   \n",
       "3         0.0         0.0          0          0          0          0   \n",
       "4         0.0         0.0          0          0          0          0   \n",
       "5   5600000.0  20000000.0          0          0          0          0   \n",
       "6         0.0         0.0          0          0          0      40000   \n",
       "7         0.0         0.0          0          0          0          0   \n",
       "8         0.0   4000000.0          0          0          0          0   \n",
       "9         0.0         0.0          0          0          0          0   \n",
       "10        0.0    400000.0          0          0          0          0   \n",
       "11        0.0         0.0          0          0          0          0   \n",
       "12        0.0         0.0          0          0          0          0   \n",
       "13        0.0   2100000.0          0          0          0          0   \n",
       "14        0.0         0.0          0          0          0          0   \n",
       "15        0.0         0.0          0          0          0          0   \n",
       "16        0.0         0.0          0          0          0          0   \n",
       "17        0.0         0.0          0          0          0          0   \n",
       "18        0.0   7280000.0          0          0          0          0   \n",
       "19        0.0         0.0          0          0          0          0   \n",
       "\n",
       "    fb36b89d9  7e293fbaf  9fc776466  \n",
       "0           0          0          0  \n",
       "1           0          0          0  \n",
       "2           0          0          0  \n",
       "3           0          0          0  \n",
       "4           0          0          0  \n",
       "5           0          0      11000  \n",
       "6           0          0          0  \n",
       "7           0          0          0  \n",
       "8           0          0          0  \n",
       "9           0          0     400000  \n",
       "10          0          0          0  \n",
       "11          0          0          0  \n",
       "12          0          0          0  \n",
       "13          0          0          0  \n",
       "14          0          0          0  \n",
       "15          0          0          0  \n",
       "16          0          0          0  \n",
       "17          0          0          0  \n",
       "18          0          0          0  \n",
       "19          0          0          0  \n",
       "\n",
       "[20 rows x 4993 columns]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_df.head(20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 228,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "No. of columns with single unique value:256\n"
     ]
    }
   ],
   "source": [
    "unique_value_columns =[col for col in train_df.columns if train_df[col].nunique(dropna=False)==1 ]\n",
    "print 'No. of columns with single unique value:%s'%(len(unique_value_columns))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**As the single unique values columns doesn't contribute to the output 'target', so it's better to drop them for computation efficiency.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "drop_train_df = train_df.drop(unique_value_columns,axis=1)\n",
    "drop_test_df = test_df.drop(unique_value_columns,axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Normality Test\n",
    "**We'll inspect the distribution of 'target' variable first with some plots and then confirm with an Anderson-Darling Test.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/achyutajha/anaconda/lib/python2.7/site-packages/matplotlib/axes/_axes.py:6571: UserWarning: The 'normed' kwarg is deprecated, and has been replaced by the 'density' kwarg.\n",
      "  warnings.warn(\"The 'normed' kwarg is deprecated, and has been \"\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1287e57d0>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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sWLAAer0ejz/+OHbu3IkZM2b0e76MjGSoVMp+3xPtDHotDlVbAABFeWkw6LWBY0ajAQBw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\nRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 576x396 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "\n",
    "sns.distplot(drop_train_df.target)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from statsmodels.graphics.gofplots import qqplot\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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J27Zty/z582v9fhFpmCxff0Xj3tdyxJ2DMe/ZTfHI+yj86HPK+g0IGNjl6mcV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\n",
      "text/plain": [
       "<Figure size 576x396 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qqplot(drop_train_df.target, line='s')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**It is evident from the the plots that the distribution is clearly not Gaussian.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Examination of variation across distribution of different attributes using Coefficient of Variation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 277,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 11.67014645,  13.95790925,  20.31744654, ...,  17.5434176 ,\n",
       "        12.05958341,   6.76849665])"
      ]
     },
     "execution_count": 277,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cv =  lambda x: np.std(x) / np.mean(x)\n",
    "var = np.apply_along_axis(cv, axis=1, arr=drop_train_df.iloc[:,drop_train_df.columns!='ID'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 279,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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g4OALrv/Mrf3q1Qvy3LbWl9C3b/HFvn2xZ4m+fU1F+74oblXbqlUrrVu3TpK0detW3Xjj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\nAMCCCHgAACyIgAcAwIL+H0DNzhAkHkErAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 576x396 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(var)\n",
    "plt.title(\"Histogram of Coefficient of Variation\")\n",
    "plt.xlabel(\"Coefficient of Variation\")\n",
    "plt.ylabel(\"Count\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**As it can be seen, majority of the attributes do not have much variance and to bring all in one scale, the data would be standardised later.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 236,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Null Hypothesis(H0) : Data follows a Normal Distribution\n",
      "\n",
      "\n",
      "Statistic: 433.534\n",
      "433.533730964 0.575\n",
      "15.000: 0.575, data does not look normal (reject H0)\n",
      "433.533730964 0.655\n",
      "10.000: 0.655, data does not look normal (reject H0)\n",
      "433.533730964 0.786\n",
      "5.000: 0.786, data does not look normal (reject H0)\n",
      "433.533730964 0.917\n",
      "2.500: 0.917, data does not look normal (reject H0)\n",
      "433.533730964 1.091\n",
      "1.000: 1.091, data does not look normal (reject H0)\n"
     ]
    }
   ],
   "source": [
    "from scipy.stats import anderson\n",
    "\n",
    "print \"Null Hypothesis(H0) : Data follows a Normal Distribution\\n\\n\"\n",
    "result = anderson(drop_train_df.target)\n",
    "print('Statistic: %.3f' % result.statistic)\n",
    "p = 0\n",
    "for i in range(len(result.critical_values)):\n",
    "    sl, cv = result.significance_level[i], result.critical_values[i]\n",
    "    print result.statistic , result.critical_values[i]\n",
    "    if result.statistic < result.critical_values[i]:\n",
    "        print'%.3f: %.3f, data looks normal (fail to reject H0)' % (sl, cv)\n",
    "    else:\n",
    "        print'%.3f: %.3f, data does not look normal (reject H0)' % (sl, cv)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\"If the returned statistic is larger than these critical values then for the corresponding significance level, the null hypothesis that the data come from the chosen distribution can be rejected. \"\n",
    "Reference : https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.anderson.html\n",
    "\n",
    "**This infers that 'target' does not have a Normal Distribution**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Data Preparation\n",
    "**Prepare input by removing the prediction column 'target' as well as object data 'ID'.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4735"
      ]
     },
     "execution_count": 165,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "training_columns = list(drop_train_df.columns)\n",
    "training_columns = set(training_columns).difference(['target','ID'])\n",
    "len(training_columns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {},
   "outputs": [],
   "source": [
    "input_train_x = drop_train_df.loc[:,training_columns]\n",
    "input_test_x = drop_test_df.loc[:,drop_test_df.columns!='ID']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 231,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((49342, 4735), (4459, 4735))"
      ]
     },
     "execution_count": 231,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "input_test_x.shape, input_train_x.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 237,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4459,)"
      ]
     },
     "execution_count": 237,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = input_train_x\n",
    "y = drop_train_df.target.values\n",
    "y.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Standardisation of Data\n",
    "Data is standardised to a mean of 0 and standard deviation of 1, as data is from various scales and need to be brought in a uniform scale for better chance of convergence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "scaler_x = StandardScaler().fit(X)\n",
    "scaler_y = StandardScaler().fit(y.reshape(-1, 1))\n",
    "input_train_x = scaler_x.transform(X)\n",
    "input_test_x = scaler_x.transform(input_test_x)\n",
    "scaled_y = scaler_y.transform(y.reshape(-1, 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dimensionality reduction using PCA\n",
    "Report features which account for 95% accountability in given data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "pca = PCA(.95)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PCA(copy=True, iterated_power='auto', n_components=0.95, random_state=None,\n",
       "  svd_solver='auto', tol=0.0, whiten=False)"
      ]
     },
     "execution_count": 183,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca.fit(input_train_x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1527"
      ]
     },
     "execution_count": 184,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca.n_components_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**From 4735 features, the feature set has narrowed down to 1527 features accounting for 95% accountability in given data**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pca_train_x = pca.transform(input_train_x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4459, 1527)"
      ]
     },
     "execution_count": 186,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca_train_x.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Data Split ratio for Train/Test: 80/20**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 243,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "input_dev_x, val_x, input_dev_y, val_y = train_test_split(pca_train_x, scaled_y[:,0], test_size = 0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 244,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((3567, 1527), (3567,), (892, 1527), (892,))"
      ]
     },
     "execution_count": 244,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "input_dev_x.shape,input_dev_y.shape,val_x.shape,val_y.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Modelling using LightGBM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "import lightgbm as lgb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import multiprocessing\n",
    "cores = multiprocessing.cpu_count()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 245,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Prepare dataset for lgbm\n",
    "input_train = lgb.Dataset(input_dev_x, label=input_dev_y)\n",
    "input_val = lgb.Dataset(val_x,label=val_y,reference=input_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4459, 49342)"
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(drop_train_df),len(test_df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 247,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "params = {}\n",
    "params = {\n",
    "        \"task\": \"train\",\n",
    "        \"objective\" : \"regression\",\n",
    "        \"boosting_type\" : \"gbdt\",\n",
    "        \"metric\" : \"mse\",\n",
    "        \"num_leaves\" : 35,\n",
    "        \"learning_rate\" : 0.005,\n",
    "        \"bagging_fraction\" : 0.8,\n",
    "        \"feature_fraction\" : 0.7,\n",
    "        \"bagging_frequency\" : 6,\n",
    "        \"bagging_seed\" : 42,\n",
    "        \"verbose\" : 0,\n",
    "        \"tree_learner\" : \"feature\",\n",
    "        \"num_threads\" : cores\n",
    "}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 248,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training until validation scores don't improve for 200 rounds.\n",
      "[200]\ttraining's l2: 0.553407\tvalid_1's l2: 0.834133\n",
      "[400]\ttraining's l2: 0.355775\tvalid_1's l2: 0.800909\n",
      "[600]\ttraining's l2: 0.239855\tvalid_1's l2: 0.788883\n",
      "[800]\ttraining's l2: 0.165148\tvalid_1's l2: 0.782824\n",
      "[1000]\ttraining's l2: 0.115339\tvalid_1's l2: 0.779207\n",
      "[1200]\ttraining's l2: 0.0817027\tvalid_1's l2: 0.776659\n",
      "[1400]\ttraining's l2: 0.0587062\tvalid_1's l2: 0.774604\n",
      "[1600]\ttraining's l2: 0.0427359\tvalid_1's l2: 0.773629\n",
      "[1800]\ttraining's l2: 0.0313229\tvalid_1's l2: 0.772957\n",
      "[2000]\ttraining's l2: 0.0231797\tvalid_1's l2: 0.772525\n",
      "[2200]\ttraining's l2: 0.0173125\tvalid_1's l2: 0.771636\n",
      "[2400]\ttraining's l2: 0.0130598\tvalid_1's l2: 0.771103\n",
      "[2600]\ttraining's l2: 0.00989243\tvalid_1's l2: 0.770469\n",
      "[2800]\ttraining's l2: 0.00753432\tvalid_1's l2: 0.770146\n",
      "[3000]\ttraining's l2: 0.00576078\tvalid_1's l2: 0.770023\n",
      "[3200]\ttraining's l2: 0.00442305\tvalid_1's l2: 0.769837\n",
      "[3400]\ttraining's l2: 0.0034088\tvalid_1's l2: 0.769624\n",
      "Early stopping, best iteration is:\n",
      "[3394]\ttraining's l2: 0.00343363\tvalid_1's l2: 0.769616\n"
     ]
    }
   ],
   "source": [
    "evals_result = {} \n",
    "\n",
    "lgbm_model = lgb.train(params, input_train,\n",
    "                       valid_sets=[input_train,input_val],\n",
    "                       evals_result=evals_result,\n",
    "                       num_boost_round=4000, \n",
    "                       early_stopping_rounds=200,\n",
    "                       verbose_eval=200)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 249,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3394"
      ]
     },
     "execution_count": 249,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lgbm_model.best_iteration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 250,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Plotting feature importances...\n"
     ]
    },
    {
     "data": {
      "image/png": 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R0iS9Gi9D69egBxBDTsP9888/2bdvH0uXLmX58uXP16gQRiIpKY3r1+O5e/cu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\n",
      "text/plain": [
       "<Figure size 576x396 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print('Plotting feature importances...')\n",
    "ax = lgb.plot_importance(lgbm_model, max_num_features=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import mean_squared_error, r2_score\n",
    "def metrics_eval(val_y, target_predictions):\n",
    "    print(\"Mean squared error: %.2f\"% mean_squared_error(val_y, target_predictions))\n",
    "    # Explained variance score: 1 is perfect prediction\n",
    "    print('Variance score: %.2f' % r2_score(val_y, target_predictions))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 251,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "target_predictions = lgbm_model.predict(val_x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 252,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean squared error: 0.77\n",
      "Variance score: 0.22\n"
     ]
    }
   ],
   "source": [
    "metrics_eval(val_y, target_predictions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 253,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Features Importance...\n",
      "          feature      gain  split\n",
      "1        Column_1  9.263667    683\n",
      "2        Column_2  3.303726    304\n",
      "5        Column_5  2.742066    325\n",
      "6        Column_6  1.091807    343\n",
      "0        Column_0  0.863049    387\n",
      "157    Column_157  0.808657    265\n",
      "3        Column_3  0.775901    304\n",
      "102    Column_102  0.612791    266\n",
      "136    Column_136  0.585382    131\n",
      "7        Column_7  0.552793    215\n",
      "217    Column_217  0.538028    209\n",
      "50      Column_50  0.512558    269\n",
      "14      Column_14  0.481220    212\n",
      "4        Column_4  0.431363    312\n",
      "27      Column_27  0.397108    179\n",
      "242    Column_242  0.382198    211\n",
      "348    Column_348  0.381591     89\n",
      "53      Column_53  0.360474    127\n",
      "304    Column_304  0.338751    195\n",
      "18      Column_18  0.322254    223\n",
      "21      Column_21  0.312181    118\n",
      "54      Column_54  0.311005    202\n",
      "8        Column_8  0.308771    180\n",
      "185    Column_185  0.298208    193\n",
      "35      Column_35  0.292129    186\n",
      "112    Column_112  0.274544    102\n",
      "1526  Column_1526  0.266598    167\n",
      "10      Column_10  0.262696    326\n",
      "1460  Column_1460  0.257627    244\n",
      "1333  Column_1333  0.249359    276\n",
      "74      Column_74  0.248558    188\n",
      "491    Column_491  0.246091    158\n",
      "26      Column_26  0.240965    236\n",
      "41      Column_41  0.238595    229\n",
      "1484  Column_1484  0.235899    175\n",
      "144    Column_144  0.228700    122\n",
      "612    Column_612  0.226749    134\n",
      "17      Column_17  0.224142    138\n",
      "219    Column_219  0.221270    203\n",
      "300    Column_300  0.215162    223\n",
      "49      Column_49  0.205402    190\n",
      "788    Column_788  0.203851    130\n",
      "551    Column_551  0.203588    164\n",
      "265    Column_265  0.196664    168\n",
      "1485  Column_1485  0.193445    148\n",
      "571    Column_571  0.192531    153\n",
      "52      Column_52  0.187939    127\n",
      "467    Column_467  0.184371    117\n",
      "1328  Column_1328  0.181933     79\n",
      "55      Column_55  0.181901     78\n"
     ]
    }
   ],
   "source": [
    "print(\"Features Importance...\")\n",
    "gain = lgbm_model.feature_importance('gain')\n",
    "featureimp = pd.DataFrame({'feature':lgbm_model.feature_name(), \n",
    "                   'split':lgbm_model.feature_importance('split'), \n",
    "                   'gain':100 * gain / gain.sum()}).sort_values('gain', ascending=False)\n",
    "print(featureimp[:50])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 256,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Plotting metrics recorded during training...\n"
     ]
    },
    {
     "data": {
      "image/png": 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Emk3IhjfAgOQ+eE0vm49sC3QpIiIizSakw7t/ch9Ah85FRCS0hHR4t49pS1Jk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\nH/XgIsEuebYkAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 576x396 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print('Plotting metrics recorded during training...')\n",
    "ax = lgb.plot_metric(evals_result, metric='l2')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<lightgbm.basic.Booster at 0x1298d0050>"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lgbm_model.save_model('LGBMRegressorModel.txt')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**The model starts overfitting with lands on the plateau failing to converge with the given hyperparameter configurations. So the hyperparameters are tuned using GridSearchCV.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## GridSearchCV for hyperparameter tuning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 258,
   "metadata": {},
   "outputs": [],
   "source": [
    "param={}\n",
    "param[\"learning_rate\"] = [0.01,0.005]\n",
    "param[\"num_leaves\"] = [20,25,35]\n",
    "param[\"bagging_fraction\"] = [0.7,0.9]\n",
    "param[\"bagging_frequency\"] = [10,15]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 259,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "params = {}\n",
    "params = {\n",
    "        \"task\": [\"train\"],\n",
    "        \"objective\" : [\"regression\"],\n",
    "        \"boosting_type\" : [\"gbdt\"],\n",
    "        \"metric\" : [\"mse\"],\n",
    "        \"num_leaves\" : param[\"num_leaves\"],\n",
    "        \"learning_rate\" : param[\"learning_rate\"],\n",
    "        \"bagging_fraction\" : param[\"bagging_fraction\"],\n",
    "        \"feature_fraction\" : [0.7],\n",
    "        \"bagging_frequency\" : param[\"bagging_frequency\"],\n",
    "        \"bagging_seed\" : [42],\n",
    "        \"verbose\" : [0],\n",
    "        \"tree_learner\" : [\"feature\"],\n",
    "        \"num_threads\" : [cores],\n",
    "        \"num_boost_round\" : [4000],\n",
    "        \"eval_metric\" : [\"l2\"]\n",
    "    }"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 260,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import GridSearchCV, PredefinedSplit\n",
    "\n",
    "# 0 index for validation and -1 for dev\n",
    "data_fold = list()\n",
    "data_fold = [-1]*len(input_dev_x)\n",
    "data_fold.extend([0]*len(val_x))\n",
    "ps = PredefinedSplit(data_fold)\n",
    "\n",
    "gbm = GridSearchCV(lgb.LGBMRegressor(), param_grid=params, cv=ps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 261,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 261,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ps.get_n_splits()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 262,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('Best parameters found by grid search are:', {'bagging_seed': 42, 'num_threads': 4, 'verbose': 0, 'eval_metric': 'l2', 'num_leaves': 25, 'learning_rate': 0.005, 'bagging_frequency': 10, 'task': 'train', 'objective': 'regression', 'num_boost_round': 4000, 'feature_fraction': 0.7, 'bagging_fraction': 0.7, 'metric': 'mse', 'tree_learner': 'feature', 'boosting_type': 'gbdt'})\n"
     ]
    }
   ],
   "source": [
    "gbm.fit(pca_train_x, scaled_y[:,0])\n",
    "\n",
    "print('Best parameters found by grid search are:', gbm.best_params_)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 263,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.018157023719776927"
      ]
     },
     "execution_count": 263,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pred_y = gbm.predict(val_x)\n",
    "mean_squared_error(val_y,pred_y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Scaling back Y values to original scale"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 266,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "rescaled_pred_y = scaler_y.inverse_transform(pred_y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Conclusion\n",
    "\n",
    "The mean_squared_error was brought down to from 0.77 to 0.018 with the hyperparameter tuning. Essentially, the parameters:\n",
    "\n",
    "**num_leaves**, **max_depth** of the tree help to control the overfitting. \n",
    "\n",
    "**bagging_fraction** fraction of features considered to make the split at a node\n",
    "\n",
    "**bagging_frequency** bagging from trees at every specified frequency\n",
    "\n",
    "This was a walk-through LightGBM for a regression problem with a large number of features. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# References\n",
    "* https://lightgbm.readthedocs.io/en/latest/index.html\n",
    "* https://github.com/Microsoft/LightGBM\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
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