Task1-机器学习算法基础

·损失函数：单一样本预测错误程度————越小越好
·代价函数：全部样本集的平均误差
目标函数：代价函数、正则化函数，最终优化者

设定目标函数的原因：代价函数可以度量全部样本集的平均误差。模型过大，预测测试集会出现过拟合。

练习

#os.environ["CUDA_VISIBLE_DEVICES"] = "1"
#生成数据
import numpy as np
#生成随机数
np.random.seed(1234)
x = np.random.rand(500,3)
#构建映射关系时，模拟真实的数据待预测值，映射关系为：y=4.2+5.7*x1+10.8*x2,可自行设置值进行尝试
y = x.dot(np.array([4.2,5.7,10.8]))
#lr = sklearn.linear_model.LinearRegression(fit_intercept=True, normalize=False, copy_X=True, n_jobs=1)
from sklearn.linear_model import LinearRegression
import matplotlib.pyplot as plt
#% matplotlib inline
#sklearn模型
#调用模型
lr = LinearRegression(fit_intercept=True)
#训练模型
lr.fit(x,y)
print("估计参数为：%s" %(lr.coef_))
#计算R平方
print('R2:%s' %(lr.score(x,y)))
#任意设定变量，预测目标值
x_test = np.array([2,4,5]).reshape(1,-1)
y_hat = lr.predict(x_test)
print("预测值为：%s" %(y_hat))
#===========================
#==========================
#最小二乘法矩阵模型
class LR_LS():
    def __init__(self):
        self.w = None
    def fit(self, X, y):
        # 最小二乘法矩阵求解
        #============================= show me your code =======================
        self.w = np.linalg.inv(X.T.dot(X)).dot(X.T).dot(y)
        #============================= show me your code =======================
    def predict(self, X):
        # 用已经拟合的参数值预测新自变量
        #============================= show me your code =======================
        y_pred = X.dot(self.w)
        #============================= show me your code =======================
        return y_pred

if __name__ == "__main__":
    lr_ls = LR_LS()
    lr_ls.fit(x,y)
    print("估计的参数值：%s" %(lr_ls.w))
    x_test = np.array([2,4,5]).reshape(1,-1)
    print("预测值为: %s" %(lr_ls.predict(x_test)))

#梯度下降模型
class LR_GD():
    def __init__(self):
        self.w = None
    def fit(self,X,y,alpha=0.02,loss = 1e-10): # 设定步长为0.002,判断是否收敛的条件为1e-10
        y = y.reshape(-1,1) #重塑y值的维度以便矩阵运算
        [m,d] = np.shape(X) #自变量的维度
        self.w = np.zeros((d)) #将参数的初始值定为0
        tol = 1e5
        #============================= show me your code =======================
        while tol > loss:
            h_f = X.dot(self.w).reshape(-1,1)
            theta = self.w + alpha*np.mean(X*(y - h_f),axis=0) #计算迭代的参数值
            tol = np.sum(np.abs(theta - self.w))
            self.w = theta
        #============================= show me your code =======================
    def predict(self, X):
        # 用已经拟合的参数值预测新自变量
        y_pred = X.dot(self.w)
        return y_pred

if __name__ == "__main__":
    lr_gd = LR_GD()
    lr_gd.fit(x,y)
    print("估计的参数值为：%s" %(lr_gd.w))
    x_test = np.array([2,4,5]).reshape(1,-1)
    print("预测值为：%s" %(lr_gd.predict(x_test)))

#os.environ["CUDA_VISIBLE_DEVICES"] = "1"
#生成数据
import numpy as np
#生成随机数
np.random.seed(1234)
x = np.random.rand(500,3)
#构建映射关系时，模拟真实的数据待预测值，映射关系为：y=4.2+5.7*x1+10.8*x2,可自行设置值进行尝试
y = x.dot(np.array([4.2,5.7,10.8]))
#lr = sklearn.linear_model.LinearRegression(fit_intercept=True, normalize=False, copy_X=True, n_jobs=1)
from sklearn.linear_model import LinearRegression
import matplotlib.pyplot as plt
#% matplotlib inline
#sklearn模型
#调用模型
lr = LinearRegression(fit_intercept=True)
#训练模型
lr.fit(x,y)
print("估计参数为：%s" %(lr.coef_))
#计算R平方
print('R2:%s' %(lr.score(x,y)))
#任意设定变量，预测目标值
x_test = np.array([2,4,5]).reshape(1,-1)
y_hat = lr.predict(x_test)
print("预测值为：%s" %(y_hat))
#===========================
#==========================
#最小二乘法矩阵模型
class LR_LS():
    def __init__(self):
        self.w = None
    def fit(self, X, y):
        # 最小二乘法矩阵求解
#============================= show me your code =======================
self.w = np.linalg.inv(X.T.dot(X)).dot(X.T).dot(y)
        #============================= show me your code =======================
def predict(self, X):
        # 用已经拟合的参数值预测新自变量
#============================= show me your code =======================
y_pred = X.dot(self.w)
        #============================= show me your code =======================
return y_pred

if __name__ == "__main__":
    lr_ls = LR_LS()
    lr_ls.fit(x,y)
    print("估计的参数值：%s" %(lr_ls.w))
    x_test = np.array([2,4,5]).reshape(1,-1)
    print("预测值为: %s" %(lr_ls.predict(x_test)))

#梯度下降模型
class LR_GD():
    def __init__(self):
        self.w = None
    def fit(self,X,y,alpha=0.02,loss = 1e-10): # 设定步长为0.002,判断是否收敛的条件为1e-10
y = y.reshape(-1,1) #重塑y值的维度以便矩阵运算
[m,d] = np.shape(X) #自变量的维度
self.w = np.zeros((d)) #将参数的初始值定为0
tol = 1e5
#============================= show me your code =======================
while tol > loss:
            h_f = X.dot(self.w).reshape(-1,1)
            theta = self.w + alpha*np.mean(X*(y - h_f),axis=0) #计算迭代的参数值
tol = np.sum(np.abs(theta - self.w))
            self.w = theta
        #============================= show me your code =======================
def predict(self, X):
        # 用已经拟合的参数值预测新自变量
y_pred = X.dot(self.w)
        return y_pred

if __name__ == "__main__":
    lr_gd = LR_GD()
    lr_gd.fit(x,y)
    print("估计的参数值为：%s" %(lr_gd.w))
    x_test = np.array([2,4,5]).reshape(1,-1)
    print("预测值为：%s" %(lr_gd.predict(x_test)))