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Chapter3 Linear Neural Networks
3.2 Implementations of Linear Regression from Scratch
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
import random
import torch
from d2l import torch as d2ldef synthetic_data(w, b, num_examples): #saveGenerate y Xw b noise.#generates a random matrix X with dimensions (num_examples, len(w)) using a normal distribution with a mean of 0 and standard deviation of 1.X torch.normal(0, 1, (num_examples, len(w)),dtypetorch.float32) #calculates the target values y by multiplying the input matrix X with the weight vector w and adding the bias term b. y torch.matmul(X, w) b #And then adds some random noise to the target values y. The noise is generated from a normal distribution with mean 0 and standard deviation 0.01. y torch.normal(0, 0.01, y.shape) return X, y.reshape((-1, 1)) #The -1 in the first dimension means that PyTorch should automatically infer the size of that dimension based on the total number of elements. In other words, it is used to ensure that the reshaped tensor has the same total number of elements as the original tensor.true_wtorch.tensor([2,-3.4],dtypetorch.float32)
true_b4.2
features,labelssynthetic_data(true_w,true_b,1000)
print(features:,features[0],\nlabel:,labels[0])d2l.set_figsize()
d2l.plt.scatter(features[:,(1)].detach().numpy(),labels.detach().numpy(),1)
#plt.show()#显示散点图
#features[:, 1] selects the second column of the features tensor.
#The detach() method is used to create a new tensor that shares no memory with the original tensor, and numpy() is then called to convert it to a NumPy array.
#1 is the size of the markers in the scatter plot.def data_iter(batch_size,features,labels):num_exampleslen(features)indiceslist(range(num_examples))#随机读取文本random.shuffle(indices)#Shuffle the indices意为打乱索引 for i in range(0,num_examples,batch_size):batch_indicestorch.tensor(indices[i:min(ibatch_size,num_examples)])#min(i batch_size, num_examples) is used to handle the last batch, which might have fewer examples than batch_size.yield features[batch_indices],labels[batch_indices]#初始化参数。从均值为0标准差为0.01的正态分布中抽取随机数来初始化权重并将偏置量置为0
wtorch.normal(0,0.01,size(2,1),requires_gradTrue)
btorch.zeros(1,requires_gradTrue)#定义线性回归模型
def linreg(X,w,b): #savereturn torch.matmul(X,w)b #广播机制用一个向量加一个标量时标量会加到向量的每一个分量上#定义均方损失函数
def squared_loss(y_hat,y): #savereturn (y_hat-y.reshape(y_hat.shape))**2/2#定义优化算法小批量随机梯度下降
def sgd(params,lr,batch_size): #savewith torch.no_grad():for param in params:param-lr*param.grad/batch_sizeparam.grad.zero_()#轮数num_epochs和学习率lr都是超参数先分别设为3和0.03具体方法后续讲解
lr0.03
num_epochs3
batch_size10for epoch in range(num_epochs):for X,y in data_iter(batch_size,features,labels):lsquared_loss(linreg(X,w,b),y)l.sum().backward()#因为l是一个向量而不是标量因此需要把l的所有元素加到一起来计算关于(w,b)的梯度sgd([w,b],lr,batch_size)with torch.no_grad():train_lsquared_loss(linreg(features,w,b),labels)print(fepoch {epoch1}:squared_loss {float(train_l.mean()):f})
print(fw的估计误差:{true_w-w.reshape(true_w.shape)})
#结果中的grad_fnSubBackward0表示这个tensor是由一个正向减法操作生成的
print(fb的估计误差:{true_b-b})#RsubBackward1表示由一个反向减法操作生成
