GBRT-Regression-Demo(超參數(shù)的比較）

import matplotlib.pyplot as plt
import numpy as np
from sklearn import ensemble,datasets,model_selection

def load_data_regression():
    diabetes = datasets.load_diabetes()
    return model_selection.train_test_split(diabetes.data,diabetes.target,test_size=0.3,random_state = 0)  

def test_GradientBoostingRegression(*data):
    X_train,X_test,Y_train,Y_test = data
    regr = ensemble.GradientBoostingRegressor()
    regr.fit(X_train,Y_train)
    print("Training score:%f"%regr.score(X_train,Y_train))
    print("Testing score:%f"%regr.score(X_test,Y_test))

X_train,X_test,Y_train,Y_test = load_data_regression()
test_GradientBoostingRegression(X_train,X_test,Y_train,Y_test)

Training score:0.876188
Testing score:0.275905

考察個(gè)體回歸樹的數(shù)量對(duì)GBRT的影響

def test_GradientBoostingRegression_estimators_num(*data):
    X_train,X_test,Y_train,Y_test = data
    nums = np.arange(1,100,step=2)
    fig = plt.figure()
    ax = fig.add_subplot(1,1,1)
    train_scores = []
    test_scores = []
    for i,num in enumerate(nums):
        clf = ensemble.GradientBoostingRegressor(n_estimators=num)
        clf.fit(X_train,Y_train)
        train_scores.append(clf.score(X_train,Y_train))
        test_scores.append(clf.score(X_test,Y_test))
    ax.plot(nums,train_scores,label="training score")
    ax.plot(nums,test_scores,label="testing score")
    ax.set_xlabel("estimators num")
    ax.set_ylabel("score")
    ax.legend(loc="lower right")
    ax.set_title("GradientBoostRegression")
plt.show()

X_train,X_test,Y_train,Y_test = load_data_regression()
test_GradientBoostingRegression_estimators_num(X_train,X_test,Y_train,Y_test)
output_6_0.png
運(yùn)行結(jié)果分析：
  1. 隨著個(gè)體回歸樹數(shù)量的增長(zhǎng)，GBRT的性能對(duì)與訓(xùn)練集一直在提高。
  2. 但是對(duì)于測(cè)試集測(cè)試得分先快速上升后基本緩慢下降。

考察個(gè)體回歸樹的最大深度對(duì)于集成回歸器預(yù)測(cè)性能的影響

def test_GradientBoostingRegression_max_depth(*data):
    X_train,X_test,Y_train,Y_test = data
    maxdepths = np.arange(1,20+1)
    fig = plt.figure()
    ax = fig.add_subplot(1,1,1)
    train_scores = []
    test_scores = []
    for i,maxdepth in enumerate(maxdepths):
        clf = ensemble.GradientBoostingRegressor(max_depth=maxdepth,max_leaf_nodes=None)
        clf.fit(X_train,Y_train)
        train_scores.append(clf.score(X_train,Y_train))
        test_scores.append(clf.score(X_test,Y_test))
    ax.plot(maxdepths,train_scores,label="Training score")
    ax.plot(maxdepths,test_scores,label="Testing score")
    ax.set_xlabel("maxdepth num")
    ax.set_ylabel("score")
    ax.legend(loc="lower right")
    ax.set_ylim(-1,1.05)
    ax.set_title("GradientBoostingRegression")
    plt.show()

X_train,X_test,Y_train,Y_test = load_data_regression()
test_GradientBoostingRegression_max_depth(X_train,X_test,Y_train,Y_test)
output_10_0.png
運(yùn)行結(jié)果分析：
  • 隨著個(gè)體回歸樹的最大深度增長(zhǎng)，對(duì)訓(xùn)練集的擬合越來(lái)越好，但是對(duì)測(cè)試集的擬合越來(lái)越差，產(chǎn)生了過(guò)擬合現(xiàn)象。

考察學(xué)習(xí)率對(duì)于GBRT的預(yù)測(cè)性能的影響

def test_GradientBoostingRegression_learning_rate(*data):
    X_train,X_test,Y_train,Y_test = data
    learing_rates = np.linspace(0.01,1.0)
    fig = plt.figure()
    ax = fig.add_subplot(1,1,1)
    train_scores = []
    test_scores = []
    for i,learing_rate in enumerate(learing_rates):
        clf = ensemble.GradientBoostingRegressor(learning_rate=learing_rate)
        clf.fit(X_train,Y_train)
        train_scores.append(clf.score(X_train,Y_train))
        test_scores.append(clf.score(X_test,Y_test))
    ax.plot(learing_rates,train_scores,label="Training score")
    ax.plot(learing_rates,test_scores,label="Testing score")
    ax.set_xlabel("learing_rate")
    ax.set_ylabel("score")
    ax.legend(loc="best")
    ax.set_ylim(-1,1.05)
    ax.set_title("GradientBoostingRegression_learning_rate")
plt.show()

X_train,X_test,Y_train,Y_test = load_data_regression()
test_GradientBoostingRegression_learning_rate(X_train,X_test,Y_train,Y_test)
output_14_0.png
運(yùn)行結(jié)果分析：
  • GBRT對(duì)預(yù)測(cè)集的預(yù)測(cè)得分隨著學(xué)習(xí)率的增長(zhǎng)而一直降低

考察subsample的影響

def test_GradientBoostingRegression_subsample(*data):
    X_train,X_test,Y_train,Y_test = data
    subsamples = np.linspace(0.01,1.0)
    fig = plt.figure()
    ax = fig.add_subplot(1,1,1)
    train_scores = []
    test_scores = []
    for i,subsample in enumerate(subsamples):
        clf = ensemble.GradientBoostingRegressor(subsample=subsample,n_estimators=100)
        clf.fit(X_train,Y_train)
        train_scores.append(clf.score(X_train,Y_train))
        test_scores.append(clf.score(X_test,Y_test))
    ax.plot(subsamples,train_scores,label="Training score")
    ax.plot(subsamples,test_scores,label="Testing score")
    ax.set_xlabel("subsample")
    ax.set_ylabel("score")
    ax.legend(loc="best")
    ax.set_ylim(-1,1.05)
    ax.set_title("GradientBoostingRegression_subsample")
plt.show()

X_train,X_test,Y_train,Y_test = load_data_regression()
test_GradientBoostingRegression_subsample(X_train,X_test,Y_train,Y_test)
output_18_0.png
運(yùn)行結(jié)果分析：
  • 本問(wèn)題中，subsample對(duì)GBRT預(yù)測(cè)的影響不大，主要對(duì)GBRT的訓(xùn)練擬合能力起作用。

考察max_features參數(shù)的影響

def test_GradientBoostingRegression_max_features(*data):
    X_train,X_test,Y_train,Y_test = data
    max_features = np.linspace(0.01,1.0)
    fig = plt.figure()
    ax = fig.add_subplot(1,1,1)
    train_scores = []
    test_scores = []
    for i,features in enumerate(max_features):
        clf = ensemble.GradientBoostingRegressor(max_features=features,n_estimators=100)
        clf.fit(X_train,Y_train)
        train_scores.append(clf.score(X_train,Y_train))
        test_scores.append(clf.score(X_test,Y_test))
    ax.plot(max_features,train_scores,label="Training score")
    ax.plot(max_features,test_scores,label="Testing score")
    ax.set_xlabel("max_features")
    ax.set_ylabel("score")
    ax.legend(loc="best")
    ax.set_ylim(0,1.05)
    ax.set_title("GradientBoostingRegression_max_features")
plt.show()

X_train,X_test,Y_train,Y_test = load_data_regression()
test_GradientBoostingRegression_max_features(X_train,X_test,Y_train,Y_test)
output_22_0.png
運(yùn)行結(jié)果分析：
  • GBRT對(duì)于特征集合的選取不是很敏感

考察損失函數(shù)的影響

def test_GradientBoostingRegression_loss(*data):
    X_train,X_test,Y_train,Y_test = data
    fig = plt.figure(figsize=(15,15))
    nums = np.arange(1,200,step=2)
    ###ls:平方損失函數(shù)
    ###lad:絕對(duì)值損失函數(shù)
    ###huber:上述兩者的加權(quán)結(jié)合
    losses = ["ls","lad","huber"]
    ax = fig.add_subplot(2,1,1)
    alphas = np.linspace(0.01,1.0,endpoint=False,num=5)
    for alpha in alphas:
        test_scores = []
        train_scores = []
        for num in nums:
            regr = ensemble.GradientBoostingRegressor(n_estimators=num,loss="huber",alpha=alpha)
            regr.fit(X_train,Y_train)
            train_scores.append(regr.score(X_train,Y_train))
            test_scores.append(regr.score(X_test,Y_test))
        ax.plot(nums,train_scores,label="Training score:alpha=%f"%alpha)
        ax.plot(nums,test_scores,label="Testing score:alpha=%f"%alpha)
    ax.set_xlabel("estimator num")
    ax.set_ylabel("score")
    ax.legend(loc="best",framealpha=0.4)
    ax.set_ylim(0,1.05)
    ax.set_title("loss=huber")
    plt.suptitle("GradientBoostRegressor")
    ######繪制ls和lad#######    
    ax = fig.add_subplot(2,1,2)
    for loss in ["ls","lad"]:
        test_scores = []
        train_scores = []
        for num in nums:
            regr = ensemble.GradientBoostingRegressor(n_estimators=num,loss=loss)
            regr.fit(X_train,Y_train)
            train_scores.append(regr.score(X_train,Y_train))
            test_scores.append(regr.score(X_test,Y_test))
        ax.plot(nums,train_scores,label="Training score:loss=%s"%loss)
        ax.plot(nums,test_scores,label="Testing score:loss=%s"%loss)
        ax.set_xlabel("estimator num")
        ax.set_ylabel("score")
        ax.legend(loc="best",framealpha=0.4)
        ax.set_ylim(0,1.05)
        ax.set_title("loss=ls,lad")
        plt.suptitle("GradientBoostRegressor")
    plt.show()
output.png
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