机器学习 1.回归

线性回归：

1.目标函数增加L2正则

θ存在解析式：

使用梯度下降进行解θ：=>

代码：

import numpy as npdef regression(data, alpha, lamda):    n=len(data[0])-1    theta=np.zeros(n)    for i in range(30):        for d in data:            y_hat=np.dot(d[:-1],theta)            y_loss=y_hat-d[-1:]            theta=theta-alpha*y_loss*d[:-1]+lamda*theta        print(i,theta)data=[[1,1],[2,2],[3,3],[4,4],[5,5],[6,6],[7,7]]regression(data,0.01,0.1)

Logistic回归：二分类

1.Logistic/sigmoid函数：=>

代码：

import scipy as spimport numpy as npfrom sklearn.model_selection import train_test_splitfrom sklearn import metricsfrom sklearn.linear_model import LogisticRegressionx = np.loadtxt("wine.data", delimiter=",", usecols=(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13))  # 获取属性集y = np.loadtxt("wine.data", delimiter=",", usecols=(0))  # 获取标签集print(x)  # 查看样本# 加载数据集，切分数据集80%训练，20%测试x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.2)  # 切分数据集# 调用逻辑斯特回归model = LogisticRegression()model.fit(x_train, y_train)print(model)  # 输出模型# make predictionsexpected = y_test  # 测试样本的期望输出predicted = model.predict(x_test)  # 测试样本预测# 输出结果print(metrics.classification_report(expected, predicted))  # 输出结果，精确度、召回率、f-1分数print(metrics.confusion_matrix(expected, predicted))  # 混淆矩阵

softmax回归：多分类

概率：

似然函数(似然函数是一种关于统计模型参数的函数。给定输出x时，关于参数θ的似然函数L(θ|x)（在数值上）等于给定参数θ后变量X的概率：L(θ|x)=P(X=x|θ))：

对数似然：

梯度：=>

代码：