机器学习-P2 手动实现线性回归算法_第2关:动手实现线性回归

一，简单线性回归实现

1，一元线性回归算法

公式：
y = ax + b
a = Σ[(x.i - x.mean)(y.i - y.mean)] / Σ[(x.i - x.mean)**2]
b = y.mean - a*x.mean

num = 0.0
d = 0.0
for x_i, y_i in zip(x, y):
    num += (x_i - np.mean(x)) * (y_i - np.mean(y))
    d += (x_i - np.mean(x)) **2
# 得到回归系数和截距
a = num / d
b = y_mean - a*x_mean
# 单一数据预测
y_hat = a*x +b
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绘制出数据与回归函数

2，封装自己的简单线性回归

class SimpleLinearRegression:

    def __init__(self):
        self.a_ = None
        self.b_ = None

    def fit(self, x_train, y_train):
        """
        训练参数
        :param x_train:属性数据集
        :param y_train: 标签数据集
        :return: a 回归系数，b 截距
        """
        assert x_train.ndim == 1, "一元线性回归只能有一个属性"
        assert len(x_train) == len(y_train), "属性——标签一一对应"

        x_mean = np.mean(x_train)
        y_mean = np.mean(y_train)

        num = 0.0
        d = 0.0
        for x_i, y_i in zip(x_train, y_train):
            num += (x_i - x_mean) * (y_i - y_mean)
            d += (x_i - x_mean) ** 2

        self.a_ = num / d
        self.b_ = y_mean - self.a_ * x_mean

        return self

    def predict(self, x_predict):
        """
        预测一组数据
        :param x_predict:预测数据集
        :return: 预测结果
        """
        assert x_predict.ndim == 1, "只能有一个属性"
        assert self.a_ is not None and self.b_ is not None, "need use .fit()"

        return np.array([self._predict(x) for x in x_predict])

    def _predict(self, x_single):
        """
        对单一数据进行线性回归
        :param x_single: 单一预测数据
        :return: 预测结果
        """
        return self.a_ * x_single + self.b_

    def __repr__(self):
        return "一元线性规划"
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使用

创建对象，导入训练数据

reg1 = SimpleLinearRegression1()
reg1.fit(x, y)
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进行预测

reg1.predict(np.array([x_predict]))
>>>array([5.2])
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3，使用向量运算计算回归系数

向量运算的效率更高
只改变 reg.fit()函数其他不变

def fit(self, x_train, y_train):
        """
        训练参数---使用矩阵乘法代替循环
        :param x_train:属性数据集
        :param y_train: 标签数据集
        :return: a 回归系数，b 截距
        """
        assert x_train.ndim == 1, "一元线性回归只能有一个属性"
        assert len(x_train) == len(y_train), "属性——标签一一对应"
        
        """矩阵乘法代替循环"""
        x_mean = np.mean(x_train)
        y_mean = np.mean(y_train)

        num = (x_train - x_mean).dot(y_train - y_mean)
        d = (x_train - x_mean).dot(x_train - x_mean)
        
        self.a_ = num 
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