一、目标
寻找一条直线，最大程度的“拟合”样本特征和样本输出标记之间的关系。在回归问题中我们预测的是一个具体的数值，这个具体的数值是在一个连续的空间里的，如果想看两个特征的回归问题就需要在三维空间里进行观察。样本特征有多个的回归称为多元线性回归
损失函数
对a求偏导数：
最后得到的结果：
求a、b的Python代码：
封装SampleLinearRegression算法的代码实现
"""coding:utf-8"""
import numpy as np
class SimpleLinearRegression(object):
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):
"""给定单个待预测数据x，返回x的预测结果值"""
return self.a_ * x +self.b_
def __repr__(self):
return "SimpleLinearRegression1()"
检验封装算法的测试代码
"""coding:utf-8"""
import numpy as np
import matplotlib.pyplot as plt
X = np.array([1.,2.,3.,4.,5.])
y = np.array([1.,3.,2.,3.,5.])
plt.scatter(X,y)
plt.axis([0,6,0,6])
plt.show()
from play_ML.SimpleLinearRrgression import SimpleLinearRegression
slr = SimpleLinearRegression()
slr.fit(X,y)
y_hat = slr.predict(X)
plt.scatter(X,y)
plt.plot(X,y_hat,color="r")
plt.axis([0,6,0,6])
plt.show()
测试结果
