一、问题描述

实现线性回归的梯度下降法算法，解决糖尿病预测问题，输出mse和R2的值。

二、实验目的

梯度下降算法在最小化目标函数F的搜索轨迹。

三、实验内容

3.1数据导入

自动生成的数据。
#导入数据
from sklearn.datasets import load_diabetes

3.2数据预处理

def process_features(X):
    scaler = StandardScaler()
    X = scaler.fit_transform(X)
    m, n = X.shape
    X = np.c_[np.ones((m, 1)), X]  
    return X

3.3算法描述

import numpy as np

class LinearRegression: 
    def fit(self, X, y, eta, epsilon):
        m, n = X.shape
        w = np.zeros((n,1)) 
        while True:
            e = X.dot(w) - y
            g = 2 * X.T.dot(e) / m  
            w = w - eta * g
            if np.linalg.norm(g, 2) < epsilon:
                break  
        self.w = w
    
    def predict(self, X):
        return X.dot(self.w)

3.4主要代码

import numpy as np
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
from linear_regression_gd import LinearRegression
from sklearn.metrics import mean_squared_error
from sklearn.metrics import r2_score

#导入数据
from sklearn.datasets import load_diabetes


def process_features(X):
    scaler = StandardScaler()
    X = scaler.fit_transform(X)
    m, n = X.shape
    X = np.c_[np.ones((m, 1)), X]  
    return X
    
diabetes = load_diabetes()
X = diabetes.data
y = diabetes.target.reshape(-1,1)
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=0)
X_train = process_features(X_train)
X_test = process_features(X_test)
model = LinearRegression()
model.fit(X_train, y_train, eta=0.01, epsilon=0.01)
y_pred = model.predict(X_test)
mse = mean_squared_error(y_test, y_pred)
score = r2_score(y_test, y_pred)
print("mse = {}, r2 = {}".format(mse, score))