<-- home

Simple Linear Regression Implement

March 25, 2019

ML

线性回归简单实现

根据上一小结得出的结论，简单实现一个线性回归算法。

import numpy as np
import matplotlib.pyplot as plt

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

plt.scatter(x, y)
plt.axis([0,6,0,6])
plt.show()

png

实现最小二乘法

\[a = \frac{\sum_{i=1}^m(x^{(i)} - \bar{x})(y^{(i)} - \bar{y})}{\sum_{i=1}^m(x^{(i)} - \bar{x})^2}\] \[b = \bar{y} - a\bar{x}\] 
x_mean = np.mean(x)
y_mean = np.mean(y)

num = 0.0
d = 0.0

a = np.sum((x - x_mean) * (y - y_mean)) / np.sum((x - x_mean) ** 2)
b = y_mean - a * x_mean

a

0.8

b

0.39999999999999947

y_hat = a * x + b

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

png

x_predict = 6.0
y_predict = a * x_predict + b
y_predict

5.2

使用自己封装的线性回归

import numpy as np

class SimpleLinearRegressionV1:

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

    def fit(self, x_train, y_train):
        assert x_train.ndim == 1 and y_train.ndim == 1,\
            "needs single feature train data"
        assert len(x_train) == len(y_train),\
            "the size of x and y must be equals"
        x_mean = np.mean(x_train)
        y_mean = np.mean(y_train)
        self.a_ = np.sum((x_train - x_mean) * (y_train - y_mean)) / np.sum((x_train - x_mean) ** 2)
        self.b_ = y_mean - self.a_ * x_mean
        return self

    def predict(self, x_predict):
        assert isinstance(x_predict, (int, float)) or x_predict.ndim == 1,\
            "needs single feature data to predict"
        assert self.a_ is not None and self.b_ is not None,\
            "must be fit before oredict"
        return self.a_ * x_predict + self.b_

    def __repr__(self):
        return "SimpleLinearRegressionV1()"

slr = SimpleLinearRegressionV1()
slr.fit(x, y)

SimpleLinearRegressionV1

slr.predict(x_predict)

5.2