pytorch 实现线性回归（深度学习）

一查看原始函数

$y=2x+4.2$

初始化

%matplotlib inline
import random
import torch
from d2l import torch as d2l

1.1 生成原始数据

def synthetic_data(w, b, num_examples):
    x = torch.normal(0, 1, (num_examples, len(w)))
    y = torch.matmul(x, w) + b
    print('x:', x)
    print('y:', y)
    y += torch.normal(0, 0.01, y.shape)  # 噪声
    return x, y.reshape((-1 , 1))

true_w = torch.tensor([2.])
true_b = 4.2
print(f'true_w: {true_w}, true_b: {true_b}')

features, labels = synthetic_data(true_w, true_b, 10)

1.2 数据转换

def data_iter(batch_size, features, labels):
    num_examples = len(features)
    indices = list(range(num_examples))
    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(f'x: {x}, \ny: {y}')

1.3 初始化权重

随机初始化，w使用均值0，方差 0.01 的随机值， b 初始化为1。

w = torch.normal(0, 0.01, size = (1,1), requires_grad=True)
b = torch.zeros(1, requires_grad=True)
w, b

二执行训练

查看训练过程中的参数变化：

print(f'true_w: {true_w}, true_b: {true_b}')

def squared_loss(y_hat, y):
    return (y_hat - y.reshape(y_hat.shape)) ** 2 / 2

def linreg(x, w, b):
    return torch.matmul(x, w) + b

def sgd(params, lr, batch_size):
    with torch.no_grad():
        for param in params:
            # print('param:', param, 'param.grad:', param.grad)
            param -= lr * param.grad / batch_size
            param.grad.zero_()

lr = 0.03
num_epochs = 1000
for epoch in range(num_epochs):
    for x, y in data_iter(batch_size, features, labels):
        l = squared_loss(linreg(x, w, b), y)   # 计算总损失
        print('w:', w, 'b:', b)  # l:', l, '\n
        l.sum().backward()
        sgd([w, b], lr, batch_size)

三测试梯度更新

初始化数据

%matplotlib inline
import random
import torch
from d2l import torch as d2l

def synthetic_data(w, b, num_examples):
    x = torch.normal(0, 1, (num_examples, len(w)))
    y = torch.matmul(x, w) + b
    print('x:', x)
    print('y:', y)
    y += torch.normal(0, 0.01, y.shape)  # 噪声
    return x, y.reshape((-1 , 1))

true_w = torch.tensor([2.])
true_b = 4.2
print(f'true_w: {true_w}, true_b: {true_b}')

features, labels = synthetic_data(true_w, true_b, 10)

def data_iter(batch_size, features, labels):
    num_examples = len(features)
    indices = list(range(num_examples))
    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(f'x: {x}, \ny: {y}')
    
w = torch.normal(0, 0.01, size = (1,1), requires_grad=True)
b = torch.zeros(1, requires_grad=True)
w, b

3.1 测试更新

print(f'true_w: {true_w}, true_b: {true_b}')

def squared_loss(y_hat, y):
    return (y_hat - y.reshape(y_hat.shape)) ** 2 / 2

def linreg(x, w, b):
    return torch.matmul(x, w) + b

def sgd(params, lr, batch_size):
    with torch.no_grad():
        for param in params:
            print('param:', param, 'param.grad:', param.grad)
#             param -= lr * param.grad / batch_size
#             param.grad.zero_()

lr = 0.03
num_epochs = 2
for epoch in range(num_epochs):
    for x, y in data_iter(batch_size, features, labels):
        l = squared_loss(linreg(x, w, b), y)   # 计算总损失
        print(f'\nepoch: {epoch},w:', w, 'b:', b)  # l:', l, '\n
        l.sum().backward()  # 计算更新梯度
        sgd([w, b], lr, batch_size)

使用 l.sum().backward() # 计算更新梯度：

不使用更新时：

print(f'true_w: {true_w}, true_b: {true_b}')

def squared_loss(y_hat, y):
    return (y_hat - y.reshape(y_hat.shape)) ** 2 / 2

def linreg(x, w, b):
    return torch.matmul(x, w) + b

def sgd(params, lr, batch_size):
    with torch.no_grad():
        for param in params:
            print('param:', param, 'param.grad:', param.grad)
#             param -= lr * param.grad / batch_size
#             param.grad.zero_()

lr = 0.03
num_epochs = 2
for epoch in range(num_epochs):
    for x, y in data_iter(batch_size, features, labels):
        l = squared_loss(linreg(x, w, b), y)   # 计算总损失
        print(f'\nepoch: {epoch},w:', w, 'b:', b)  # l:', l, '\n
        # l.sum().backward()  # 计算更新梯度
        sgd([w, b], lr, batch_size)
        
#     break