importrandomimporttorch#1.生成数据集defsyntheticData(w:torch.Tensor,b:float,numExaples:int)->tuple[torch.Tensor]:'''生成y=Xw+b+噪声'''X:torch.Tensor=torch.normal(0,1,(numExaples,len(w)))y:torch.Tensor=torch.matmul(X,w)+by+=torch.normal(0,0.01,y.shape)#添加噪声数据returnX,y.reshape((-1,1))trueW:torch.Tensor=torch.tensor([2.0,-3.4])trueB:float=4.2features,labels=syntheticData(trueW,trueB,1000)#2.读取数据集defdataIter(batchSize:int,features:torch.Tensor,labels:torch.Tensor):numExamples:int=len(features)indices:list[int]=list(range(numExamples))#样本随机读取无特定的顺序random.shuffle(indices)foridxinrange(0,numExamples,batchSize):batchIndices:torch.Tensor=torch.tensor(indices[idx:min(idx+batchSize,numExamples)])yieldfeatures[batchIndices],labels[batchIndices]#3.初始化模型参数initW:torch.Tensor=torch.normal(0.0,0.01,size=(2,1),requires_grad=True)initB:torch.Tensor=torch.zeros(1,requires_grad=True)#4.定义模型deflinearRegModel(X:torch.Tensor,w:torch.Tensor,b:torch.Tensor)->torch.Tensor:'''线性回归模型'''returntorch.matmul(X,w)+b#5.定义损失函数defsquaredLoss(PreY:torch.Tensor,TrueY:torch.Tensor)->torch.Tensor:'''均方损失函数'''return(PreY-TrueY.reshape(PreY.shape))**2/2.0#6.定义优化算法defSGD(params:list[torch.Tensor],lr:float,batchSize:int):'''小批量随机梯度下降法params:模型参数集合lr:学习率，确定每一步更新的大小batchSize:批量样本大小'''withtorch.no_grad():forparaminparams:param-=lr*param.grad/batchSizeparam.grad.zero_()#7.训练lr:float=0.03#学习率numEporchs:int=3#循环次数batchSize:int=10#小批量样本数net=linearRegModelloss=squaredLossforepochinrange(numEporchs):forX,yindataIter(batchSize,features,labels):#a.计算损失l=loss(net(X,initW,initB),y)#X和y的小批量损失#b.反向传播求导#因为l形状是(batchSize,1)，而不是一个标量。l中的所有元素被加到一起，#并以此计算关于[w,b]的梯度l.sum().backward()#c.更新参数SGD([initW,initB],lr,batchSize)#使用参数的梯度更新参数#每一次循环后计算全局损失的平均值withtorch.no_grad():train_l=loss(net(features,initW,initB),labels)print(f'epoch{epoch+1},loss{float(train_l.mean()):f}')#完成模型训练后显示训练参数和真实参数间的误差print(f'w的估计误差:{trueW-initW.reshape(trueW.shape)}')print(f'b的估计误差:{trueB-initB}')来源：檐苔
