一、问题描述

        糖尿病数据集是Sklearn 提供的数据集。它从442例糖尿病患者的资料中取10个特征：年龄、性别、体重、血压和6个血清测试量值，以及患者在一年后疾病发展的量化值（标签）。

二、实验目的

        根据上述10个特征，预测病情发展的量化值。

三、实验内容

        包括数据导入、数据预处理、算法描述、主要代码。

四、实验结果及分析

结论：正规方程和Scikit-learn的模型预测比岭回归算法的预测模型好

五、完整代码

机器学习GitHub：https://github.com/wanglei18/machine_learning

ridge_regression.py

import numpy as npclass RidgeRegression:   def __init__(self, Lambda):self.Lambda = Lambdadef fit(self, X, y):m, n = X.shaper = np.diag(self.Lambda * np.ones(n))  self.w = np.linalg.inv(X.T.dot(X) + r).dot(X.T).dot(y)return def predict(self, X):return X.dot(self.w)

# 第二次作业.2部分
import sklearn.datasets
import numpy as np
import machine_learning.linear_regression.lib.linear_regression as lib
import machine_learning.linear_regression.lib.ridge_regression as Rg
from sklearn import linear_model
from sklearn.preprocessing import PolynomialFeatures
from sklearn.model_selection import train_test_splitdef process_features(X):m, n = X.shapeX = np.c_[np.ones((m, 1)), X]return Xnp.random.seed(100)
X, y = sklearn.datasets.load_diabetes(return_X_y = True)#1.正规方程求解法
x_train, x_test, y_train, y_test = train_test_split(X, y, test_size=0.4, random_state=5)
x_train = process_features(x_train)             #特征处理
x_test = process_features(x_test)model = lib.LinearRegression()
model.fit(x_train, y_train)                     #训练数据y_pred=model.predict(x_test)
mse = lib.mean_squared_error(y_test,y_pred)     #h的均方误差
r2 = lib.r2_score(y_test,y_pred)                #R^2的决定系数
print("mse={}andr2={}".format(mse,r2))'''
#2.岭回归算法
x_train, x_test, y_train, y_test = train_test_split(X, y, test_size=0.4, random_state=5)
polt = PolynomialFeatures(degree = 2)
x_poly = polt.fit_transform(x_train)            #特征处理
model = Rg.RidgeRegression(Lambda = 0.2)
model.fit(x_poly,y_train)                       #训练数据x_test = polt.fit_transform(x_test)             #X特征标准化
y_pred = model.predict(x_test)                  #预测数据mse = lib.mean_squared_error(y_test,y_pred)     #h的均方误差
r2 = lib.r2_score(y_test,y_pred)                #R^2的决定系数
print("mse={}andr2={}".format(mse,r2))
''''''
#3.Scikit-learn
x_train, x_test, y_train, y_test = train_test_split(X, y, test_size=0.4, random_state=5)x_train = process_features(x_train)         #特征处理
x_test = process_features(x_test)           #h的均方误差
clf = linear_model.LinearRegression()
clf.fit(x_train, y_train)                   #训练数据y_pred=clf.predict(x_test)                  #预测数据
mse = lib.mean_squared_error(y_test,y_pred) #h的均方误差
r2 = lib.r2_score(y_test,y_pred)            #R^2的决定系数
print("mse={}andr2={}".format(mse,r2))
'''