5-8 实现多元线性回归

Linear Regression

import numpy as np
from sklearn.metrics import r2_score

class LinearRegression:

    def __init__(self):
        """初始化Linear Regression模型"""
        self.coef_ = None
        self.interception_ = None
        self._theta = None

    def fit_normal(self, X_train, y_train):
        """根据训练数据集X_train, y_train训练Linear Regression模型"""
        assert X_train.shape[0] == y_train.shape[0], "the size of X_train must be equal to the size of y_train"

        X_b = np.hstack([np.ones((len(X_train), 1)), X_train])
        self._theta = np.linalg.inv(X_b.T.dot(X_b)).dot(X_b.T).dot(y_train)

        self.interception_ = self._theta[0]
        self.coef_ = self._theta[1:]

        return self

    def predict(self, X_predict):
        """给定待预测数据集X_predict，返回表示X_predict的结果向量"""
        assert self.interception_ is not None and self.coef_ is not None, "must fit before predict"
        assert X_predict.shape[1] == len(self.coef_), "the feature number of X_predict must equal to X_train"

        X_b = np.hstack([np.ones((len(X_predict), 1)), X_predict])
        return X_b.dot(self._theta)

    def score(self, X_test, y_test):
        """根据测试数据集X_test, y_test确定当前模型的准确度"""

        y_predict = self.predict(X_test)
        return r2_score(y_test, y_predict)

    def __repr__(self):
        return "LinearRegression()"

boston data

import matplotlib.pyplot as plt
from sklearn import datasets

boston = datasets.load_boston()
x = boston.data
y = boston.target
x = x[y < 50.0]
y = y[y < 50.0]

训练模型与预测结果

from sklearn.model_selection import train_test_split
X_train, X_test, y_train, y_test = train_test_split(x, y, test_size=0.2, random_state=666)

reg = LinearRegression()
reg.fit_normal(X_train, y_train)
reg.score(X_test, y_test)

输出结果： 0.8129794056212832

使用多个特征训练的模型得分要高于使用单个特征训练的模型