向量化实现SimpleLinearRegression

In [23]:

import datetime
print("Run by CYJ,",datetime.datetime.now())

from playML.SimpleLinearRegression import SimpleLinearRegression2
reg2 = SimpleLinearRegression2()
reg2.fit(x, y)

Run by CYJ, 2022-01-17 21:09:49.796743

Out[23]:

SimpleLinearRegression2()

In [21]:

reg2.a_,reg2.b_

Out[21]:

(0.8, 0.39999999999999947)

In [20]:

y_hat2 = reg2.predict(x)
plt.scatter(x, y)
plt.plot(x, y_hat2, color='r')
plt.axis([0, 6, 0, 6])
plt.show()

向量化实现的性能测试（向量运算效率/for循环代数运算效率=76倍）

In [24]:

import datetime
print("Run by CYJ,",datetime.datetime.now())

m = 1000000
big_x = np.random.random(size=m)
big_y = big_x * 2 + 3 + np.random.normal(size=m)

%timeit reg1.fit(big_x, big_y)
%timeit reg2.fit(big_x, big_y)

Run by CYJ, 2022-01-17 21:11:39.840437
1.33 s ± 11.3 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)
17.3 ms ± 358 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)

In [25]:

reg1.a_

Out[25]:

2.002845878151015

In [26]:

reg1.b_

Out[26]:

2.9993915955553723

In [27]:

reg2.a_

Out[27]:

2.0028458781509695

In [28]:

reg2.b_

Out[28]:

2.9993915955553945

封装的SimpleLinearRegression1和2类

import numpy as np


class SimpleLinearRegression1:

    def __init__(self):
        """初始化Simple Linear Regression 模型"""
        self.a_ = None
        self.b_ = None

    def fit(self, x_train, y_train):
        """根据训练数据集x_train,y_train训练Simple Linear Regression模型"""
        assert x_train.ndim == 1, \
            "Simple Linear Regressor can only solve single feature training data."
        assert len(x_train) == len(y_train), \
            "the size of x_train must be equal to the size of y_train"

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

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

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

        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 x_predict.ndim == 1, \
            "Simple Linear Regressor can only solve single feature training data."
        assert self.a_ is not None and self.b_ is not None, \
            "must fit before predict!"

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

    def _predict(self, x_single):
        """给定单个待预测数据x，返回x的预测结果值"""
        return self.a_ * x_single + self.b_

    def __repr__(self):
        return "SimpleLinearRegression1()"


class SimpleLinearRegression2:

    def __init__(self):
        """初始化Simple Linear Regression模型"""
        self.a_ = None
        self.b_ = None

    def fit(self, x_train, y_train):
        """根据训练数据集x_train,y_train训练Simple Linear Regression模型"""
        assert x_train.ndim == 1, \
            "Simple Linear Regressor can only solve single feature training data."
        assert len(x_train) == len(y_train), \
            "the size of x_train must be equal to the size of y_train"

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

        self.a_ = (x_train - x_mean).dot(y_train - y_mean) / (x_train - x_mean).dot(x_train - x_mean)
        self.b_ = y_mean - self.a_ * x_mean

        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 x_predict.ndim == 1, \
            "Simple Linear Regressor can only solve single feature training data."
        assert self.a_ is not None and self.b_ is not None, \
            "must fit before predict!"

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

    def _predict(self, x_single):
        """给定单个待预测数据x_single，返回x_single的预测结果值"""
        return self.a_ * x_single + self.b_

    def __repr__(self):
        return "SimpleLinearRegression2()"