zhusimaji/gbdt_lr.ipynb

## gbdt_lr.ipynb
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "# Feature transformations with ensembles of trees\n",
    "\n",
    "\n",
    "Transform your features into a higher dimensional, sparse space. Then\n",
    "train a linear model on these features.\n",
    "\n",
    "First fit an ensemble of trees (totally random trees, a random\n",
    "forest, or gradient boosted trees) on the training set. Then each leaf\n",
    "of each tree in the ensemble is assigned a fixed arbitrary feature\n",
    "index in a new feature space. These leaf indices are then encoded in a\n",
    "one-hot fashion.\n",
    "\n",
    "Each sample goes through the decisions of each tree of the ensemble\n",
    "and ends up in one leaf per tree. The sample is encoded by setting\n",
    "feature values for these leaves to 1 and the other feature values to 0.\n",
    "\n",
    "The resulting transformer has then learned a supervised, sparse,\n",
    "high-dimensional categorical embedding of the data.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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kk1x77bUsWrSICy+8MNkhmQrSqk8h2tHspFcuNCbpdu3axV//+ld+/vOf0717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\nEEJGNAohhBAyolEIIYSQEY1CCCGEjP8By3JShdkg6YwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fdca790>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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0/NM5Le80Ts87nWmZ04bxqQyDSlsd1O2xBCBytCB0hXvndcaPFos+4/GwDp8A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\nqAKWiciLqvq+r9oPgGdV9SEROR14GSgF9gCXqOo2EZkIvAK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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f2ca3d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Author: Tim Head <betatim@gmail.com>\n",
    "#\n",
    "# License: BSD 3 clause\n",
    "\n",
    "import numpy as np\n",
    "np.random.seed(10)\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from sklearn.datasets import make_classification\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.ensemble import (RandomTreesEmbedding, RandomForestClassifier,\n",
    "                              GradientBoostingClassifier)\n",
    "from sklearn.preprocessing import OneHotEncoder\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.metrics import roc_curve\n",
    "from sklearn.pipeline import make_pipeline\n",
    "\n",
    "\n",
    "n_estimator = 10\n",
    "X, y = make_classification(n_samples=80000)\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.5)\n",
    "# It is important to train the ensemble of trees on a different subset\n",
    "# of the training data than the linear regression model to avoid\n",
    "# overfitting, in particular if the total number of leaves is\n",
    "# similar to the number of training samples\n",
    "X_train, X_train_lr, y_train, y_train_lr = train_test_split(X_train,\n",
    "                                                            y_train,\n",
    "                                                            test_size=0.5)\n",
    "\n",
    "# Unsupervised transformation based on totally random trees\n",
    "rt = RandomTreesEmbedding(max_depth=3, n_estimators=n_estimator,\n",
    "\trandom_state=0)\n",
    "\n",
    "rt_lm = LogisticRegression()\n",
    "pipeline = make_pipeline(rt, rt_lm)\n",
    "pipeline.fit(X_train, y_train)\n",
    "y_pred_rt = pipeline.predict_proba(X_test)[:, 1]\n",
    "fpr_rt_lm, tpr_rt_lm, _ = roc_curve(y_test, y_pred_rt)\n",
    "\n",
    "# Supervised transformation based on random forests\n",
    "rf = RandomForestClassifier(max_depth=3, n_estimators=n_estimator)\n",
    "rf_enc = OneHotEncoder()\n",
    "rf_lm = LogisticRegression()\n",
    "rf.fit(X_train, y_train)\n",
    "rf_enc.fit(rf.apply(X_train))\n",
    "rf_lm.fit(rf_enc.transform(rf.apply(X_train_lr)), y_train_lr)\n",
    "\n",
    "y_pred_rf_lm = rf_lm.predict_proba(rf_enc.transform(rf.apply(X_test)))[:, 1]\n",
    "fpr_rf_lm, tpr_rf_lm, _ = roc_curve(y_test, y_pred_rf_lm)\n",
    "\n",
    "grd = GradientBoostingClassifier(n_estimators=n_estimator)\n",
    "grd_enc = OneHotEncoder()\n",
    "grd_lm = LogisticRegression()\n",
    "grd.fit(X_train, y_train)\n",
    "grd_enc.fit(grd.apply(X_train)[:, :, 0])\n",
    "grd_lm.fit(grd_enc.transform(grd.apply(X_train_lr)[:, :, 0]), y_train_lr)\n",
    "\n",
    "y_pred_grd_lm = grd_lm.predict_proba(\n",
    "    grd_enc.transform(grd.apply(X_test)[:, :, 0]))[:, 1]\n",
    "fpr_grd_lm, tpr_grd_lm, _ = roc_curve(y_test, y_pred_grd_lm)\n",
    "\n",
    "\n",
    "# The gradient boosted model by itself\n",
    "y_pred_grd = grd.predict_proba(X_test)[:, 1]\n",
    "fpr_grd, tpr_grd, _ = roc_curve(y_test, y_pred_grd)\n",
    "\n",
    "\n",
    "# The random forest model by itself\n",
    "y_pred_rf = rf.predict_proba(X_test)[:, 1]\n",
    "fpr_rf, tpr_rf, _ = roc_curve(y_test, y_pred_rf)\n",
    "\n",
    "plt.figure(1)\n",
    "plt.plot([0, 1], [0, 1], 'k--')\n",
    "plt.plot(fpr_rt_lm, tpr_rt_lm, label='RT + LR')\n",
    "plt.plot(fpr_rf, tpr_rf, label='RF')\n",
    "plt.plot(fpr_rf_lm, tpr_rf_lm, label='RF + LR')\n",
    "plt.plot(fpr_grd, tpr_grd, label='GBT')\n",
    "plt.plot(fpr_grd_lm, tpr_grd_lm, label='GBT + LR')\n",
    "plt.xlabel('False positive rate')\n",
    "plt.ylabel('True positive rate')\n",
    "plt.title('ROC curve')\n",
    "plt.legend(loc='best')\n",
    "plt.show()\n",
    "\n",
    "plt.figure(2)\n",
    "plt.xlim(0, 0.2)\n",
    "plt.ylim(0.8, 1)\n",
    "plt.plot([0, 1], [0, 1], 'k--')\n",
    "plt.plot(fpr_rt_lm, tpr_rt_lm, label='RT + LR')\n",
    "plt.plot(fpr_rf, tpr_rf, label='RF')\n",
    "plt.plot(fpr_rf_lm, tpr_rf_lm, label='RF + LR')\n",
    "plt.plot(fpr_grd, tpr_grd, label='GBT')\n",
    "plt.plot(fpr_grd_lm, tpr_grd_lm, label='GBT + LR')\n",
    "plt.xlabel('False positive rate')\n",
    "plt.ylabel('True positive rate')\n",
    "plt.title('ROC curve (zoomed in at top left)')\n",
    "plt.legend(loc='best')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(20000, 80)\n",
      "  (0, 76)\t1.0\n",
      "  (0, 68)\t1.0\n",
      "  (0, 61)\t1.0\n",
      "  (0, 52)\t1.0\n",
      "  (0, 42)\t1.0\n",
      "  (0, 34)\t1.0\n",
      "  (0, 26)\t1.0\n",
      "  (0, 18)\t1.0\n",
      "  (0, 10)\t1.0\n",
      "  (0, 2)\t1.0\n"
     ]
    }
   ],
   "source": [
    "#onehot编码对gbdt输出的数据编码\n",
    "onehot=grd_enc.transform(grd.apply(X_train_lr)[:, :, 0])\n",
    "print np.shape(onehot)\n",
    "print onehot[0,:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#将矩阵转化为libsvm格式\n",
    "from sklearn.datasets import dump_svmlight_file\n",
    "dump_svmlight_file(onehot,y_train_lr,'/Users/leiyang/test.txt')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[  6.],\n",
       "        [  6.],\n",
       "        [  6.],\n",
       "        ..., \n",
       "        [ 11.],\n",
       "        [ 10.],\n",
       "        [ 10.]],\n",
       "\n",
       "       [[  6.],\n",
       "        [  6.],\n",
       "        [  6.],\n",
       "        ..., \n",
       "        [ 11.],\n",
       "        [ 10.],\n",
       "        [ 10.]],\n",
       "\n",
       "       [[ 14.],\n",
       "        [ 14.],\n",
       "        [ 14.],\n",
       "        ..., \n",
       "        [  3.],\n",
       "        [  6.],\n",
       "        [  3.]],\n",
       "\n",
       "       ..., \n",
       "       [[ 10.],\n",
       "        [ 10.],\n",
       "        [ 10.],\n",
       "        ..., \n",
       "        [  3.],\n",
       "        [  3.],\n",
       "        [  3.]],\n",
       "\n",
       "       [[ 14.],\n",
       "        [ 14.],\n",
       "        [ 13.],\n",
       "        ..., \n",
       "        [  7.],\n",
       "        [  7.],\n",
       "        [  7.]],\n",
       "\n",
       "       [[  6.],\n",
       "        [  6.],\n",
       "        [  6.],\n",
       "        ..., \n",
       "        [ 11.],\n",
       "        [ 10.],\n",
       "        [ 10.]]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grd.apply(X_train_lr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 验证GBDT输出数据"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "apply_data=grd.apply(X_train_lr)[:, :, 0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  6.,   6.,   6.,   6.,   6.,   6.,  10.,  11.,  10.,  10.])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "apply_data[0,:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(20000, 10)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.shape(grd.apply(X_train_lr)[:, :, 0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(np.unique(apply_data[:,9]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  3.,   4.,   6.,   7.,  10.,  11.,  13.,  14.])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.unique(apply_data[:,9])"
   ]
  }
 ],
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