【线性回归算法】{2} ——向量化实现线性回归

此处于之前创建的SimpleLinearRegression模块中，创建一个新的类，用于实现向量化线性回归。

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一、编写向量化线性回归的类：

import numpy as np

class SimpleLinearRegression2(object):
    """使用向量化实现线性回归"""

    def __init__(self):
        """计算出来的变量，后缀加上_"""
        self.a_ = None # 表示线的斜率
        self.b_ = None # 表示线的截距

    def fit(self, X_train, Y_train):
        """训练模型"""
        X_mean = np.mean(X_train)
        Y_mean = np.mean(Y_train)

		num = (X_train - X_mean).dot(Y_train - Y_mean)
        deno = (X_train - X_mean).dot(X_train - X_mean)

        self.a_ = num / deno
        self.b_ = Y_mean - self.a_ * X_mean

    def _predict(self, x):
        """预测单个x的结果"""
        return self.a_ * x + self.b_

    def predict(self, X_test):
        """预测X，X是一维的数据"""
        y_predict = [self._predict(x) for x in X_test]
        return np.array(y_predict)

    def __repr__(self):
        return 'SimpleLinearRegression2(a=%s, b=%s)' %(self.a_, self.b_)

二、向量化实现线性回归：

from playML.SimpleLinearRegression import SimpleLinearRegression2

x = np.array([1, 2, 3, 4, 5])
y = np.array([1, 3, 2, 3, 5])

reg2 = SimpleLinearRegression2()
reg2.fit(x, y)

y_hat2 = reg2.predict(x) # 预测值

plt.scatter(x, y)
plt.plot(x, y_hat2, color='r')
plt.axis([0, 6, 0, 6])
plt.show()

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三、向量化性能测试：

import numpy as np
from playML.SimpleLinearRegression import SimpleLinearRegression2


m = 1000000
big_x = np.random.random(size=m)
big_y = big_x * 2.0 + 3.0 + np.random.normal(size=m)

%timeit reg1.fit(big_x, big_y)
>>> 1.17 s ± 27.8 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)
%timeit reg2.fit(big_x, big_y)
>>> 16.1 ms ± 390 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)

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参考资料：bobo老师机器学习教程