机器学习-决策树回归(Decision Tree Regression)

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本文深入探讨了决策树回归算法的优势，特别是在处理非线性数据时无需特征转换的特点。通过逐步分裂节点直至达到纯叶节点或停止标准，构建决策树模型。以波士顿房价数据集为例，展示了如何使用Python的sklearn库实现决策树回归，并绘制预测结果。

Section I: Brief Introduction on Decision Tree Regression

An advantage of the decision tree algorithm is that it does not require any transformation of the features if we are dealing with nonlinear data. Grow a decision tree by iteratively splitting its nodes until the leaves are pure or a topping criterion is satisfied.

FROM
Sebastian Raschka, Vahid Mirjalili. Python机器学习第二版. 南京：东南大学出版社，2018.

代码

from sklearn import datasets
from sklearn.metrics import mean_squared_error,r2_score
import matplotlib.pyplot as plt
import numpy as np
import warnings
warnings.filterwarnings("ignore")

plt.rcParams['figure.dpi']=200
plt.rcParams['savefig.dpi']=200
font = {'weight': 'light'}
plt.rc("font", **font)

#Section 1: Load data
price=datasets.load_boston()
X=price.data[:,-1]
y=price.target

#Section 2: Construct a DecisionTree model
from sklearn.tree import DecisionTreeRegressor

tree=DecisionTreeRegressor(max_depth=3)
tree.fit(X.reshape(-1,1),y)
sort_idx=X.flatten().argsort()

def lin_regplot(X,y,model):
    plt.scatter(X,y,c='steelblue',edgecolor='white',s=70,label='Original')
    plt.plot(X,model.predict(X),color='black',lw=2,label='Decision Tree')
    return None

lin_regplot(X[sort_idx].reshape(-1,1),y[sort_idx],tree)
plt.xlabel("Lower Status of the Population [LSTAT]")
plt.ylabel("Price in $1000s [MEDV]")
plt.savefig('./fig1.png')
plt.show()