多元线性回归算法（有多个特征的线性回归算法）

多元线性回归，假设我们有m个样本，n个特征，对于每一个样本的结果，每个特征都需要占一定的权重即：

当样本集为：

输出结果为：

基于多个特征得到的预测值为：

假设有矩阵

多元线性回归的正规方程：

多元线性回归正规方程解的代码实现：

"""coding:utf-8"""
import numpy as np
from play_ML.metrics import r2_score
class LinearRegression(object):
    """初始化Linear Regression模型"""
    def __init__(self):
        self.coef = None
        self.intercept = None
        self._theta = None
    def fit(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.intercept = 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的结果集向量"""
        assert self.intercept_ 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 be 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):
        """根据测试集x_test和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"