Liner回归的从零实现
%matplotlib inline
import random
import torch
from d2l import torch as d2l
生成一个人造数据集
def synthetic_data(w, b, num_examples): #@save
"""生成y=Xw+b+噪声"""
X = torch.normal(0, 1, (num_examples, len(w)))
y = torch.matmul(X, w) + b
y += torch.normal(0, 0.01, y.shape)
return X, y.reshape((-1, 1))
true_w = torch.tensor([2, -3.4])
true_b = 4.2
features, labels = synthetic_data(true_w, true_b, 1000)
print('features:', features[0],'\nlabel:', labels[0])
features: tensor([-0.1284, -0.6457])
label: tensor([6.1244])
d2l.set_figsize()
d2l.plt.scatter(features[:, 1].detach().numpy(), labels.detach().numpy(), 1);
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读取数据集
def data_iter(batch_size, features, labels):
num_examples = len(features)
indices = list(range(num_examples))
# 这些样本是随机读取的，没有特定的顺序
random.shuffle(indices)
for i in range(0, num_examples, batch_size):
batch_indices = torch.tensor(
indices[i: min(i + batch_size, num_examples)])
yield features[batch_indices], labels[batch_indices]
batch_size = 10
for X, y in data_iter(batch_size, features, labels):
print(X, '\n', y)
break
tensor([[ 1.2599, -0.9327],
[ 1.1232, 0.2566],
[-0.3754, 0.7046],
[-0.6855, -1.2303],
[ 1.5169, -0.0099],
[ 0.0754, 1.1267],
[ 0.1643, -0.0296],
[-0.7567, 0.5444],
[ 0.2624, 0.4333],
[-1.9114, 0.3921]])
tensor([[ 9.8939],
[ 5.5723],
[ 1.0727],
[ 6.9968],
[ 7.2692],
[ 0.5038],
[ 4.6170],
[ 0.8265],
[ 3.2630],
[-0.9715]])
初始化模型参数
w = torch.normal(0, 0.01, size=(2,1), requires_grad=True)
b = torch.zeros(1, requires_grad=True)
定义模型
def linreg(X, w, b):
"""线性回归模型"""
return torch.matmul(X, w) + b
定义损失函数
def squared_loss(y_hat, y):
"""均方损失"""
return (y_hat - y.reshape(y_hat.shape)) ** 2 / 2
定义优化算法
def sgd(params, lr, batch_size):
"""小批量随机梯度下降"""
with torch.no_grad():
for param in params:
param -= lr * param.grad / batch_size
param.grad.zero_()
训练
lr = 0.03
num_epochs = 3
net = linreg
loss = squared_loss
for epoch in range(num_epochs):
for X, y in data_iter(batch_size, features, labels):
l = loss(net(X, w, b), y) # X和y的小批量损失
# 因为l形状是(batch_size,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()
sgd([w, b], lr, batch_size) # 使用参数的梯度更新参数
with torch.no_grad():
train_l = loss(net(features, w, b), labels)
print(f'epoch {epoch + 1}, loss {float(train_l.mean()):f}')
epoch 1, loss 0.034527
epoch 2, loss 0.000121
epoch 3, loss 0.000046
比较真实的w,b和模型学习到的差距
print(f'w的估计误差: {true_w - w.reshape(true_w.shape)}')
print(f'b的估计误差: {true_b - b}')
w的估计误差: tensor([ 0.0003, -0.0007], grad_fn=<SubBackward0>)
b的估计误差: tensor([0.0011], grad_fn=<RsubBackward1>)
Liner回归简易实现
import numpy as np
import torch
from torch.utils import data
from d2l import torch as d2l
from torch import nn
true_w = torch.tensor([2,-3.4])
true_b = 4.2
features,labels = d2l.synthetic_data(true_w,true_b,1000)
def load_array(data_arrays, batch_size, is_train = True):
dataset = data.TensorDataset(*data_arrays)
return data.DataLoader(dataset, batch_size, shuffle = is_train)
batch_size = 10
data_iter = load_array((features,labels), batch_size)
next(iter(data_iter))
输出
[tensor([[ 0.3478, -0.1429],
[-0.1305, 0.9412],
[-0.9198, -0.4407],
[-0.7321, -0.1986],
[-1.3152, -0.3509],
[-1.0748, 0.5044],
[ 0.8715, -0.2265],
[-1.0149, 0.7534],
[-0.2333, -0.2114],
[-1.7907, 1.2627]]),
tensor([[ 5.3866],
[ 0.7402],
[ 3.8383],
[ 3.4077],
[ 2.7556],
[ 0.3289],
[ 6.7145],
[-0.3806],
[ 4.4456],
[-3.6826]])]
net = nn.Sequential(nn.Linear(2,1))
net[0].weight.data.normal_(0,0.01)
net[0].bias.data.fill_(0)
loss = nn.MSELoss()
trainer = torch.optim.SGD(net.parameters(),lr = 0.03)
num_epochs = 3
for epoch in range(num_epochs):
for X,y in data_iter:
l = loss(net(X),y)
trainer.zero_grad()
l.backward()
trainer.step()
l = loss(net(features),labels)
print(f'epoch{epoch + 1},loss{l:f}')
epoch1,loss0.000327
epoch2,loss0.000103
epoch3,loss0.000103
