線性迴歸 李沐

簡介

採用傳統的梯度下降進行線性迴歸，線性函數 一般爲 $$y = <w,x> + b$$ 的形式

code

import random
import torch
from d2l import torch as d2l



# 人造數據集
def synthetic_data(w, b, num_example):
    """生成 y=Xw+b+噪聲"""
    X = torch.normal(0, 1, (num_example, len(w))) # 生成均值爲0,方差爲1的隨即數， num_example 個樣本， 列數爲 w 的長度
    y = torch.matmul(X, w) + b
    y += torch.normal(0, 0.01, y.shape) # 加入正態分佈的噪音
    return X, y.reshape((-1, 1)) # y 從行向量轉爲列向量

true_w = torch.tensor([2, -3.4])
true_b = 4.2
features, labels = synthetic_data(true_w, true_b, 1000)


# 讀數據集
def data_iter(batch_size, features, labels):
    num_examples = len(features)
    indices = list(range(num_examples))
    random.shuffle(indices) # 將序列的元素隨即打亂
    for i in range(0, num_examples, batch_size): # i 從0 開始 然後
        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:", X, '\n y:', y)
    break;

# 初始化模型參數
w = torch.normal(0, 0.01, size=(2, 1), requires_grad = True) # requres_grad = True 表明需要計算梯度
b = torch.zeros(1, requires_grad = True) # 偏差 b 直接賦值爲0, 標量

# 定義模型
def linreg(X, w, b):
    """現行迴歸模型"""
    return torch.matmul(X, w) + b

# 定義損失函數
def squared_loss(y_hat, y):
    """均方損失"""
    return (y_hat - y.reshape(y_hat.shape)) ** 2 / 2

# 定義優化算法
# param: [w, b], lr 即學習率
def sgd(params, lr, batch_size):
    """小批量隨即梯度下降(mini-batch stochastic gradient descent)"""
    with torch.no_grad():
        for param in params:
            param -= lr * param.grad / batch_size
            param.grad.zero_()

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) # 因爲 l 形狀是 (batch_size, 1), 而不是一個標量
        l.sum().backward() # https://blog.csdn.net/qq_42750982/article/details/125023492 偏導數求和計算
        #  https://img-blog.csdnimg.cn/008c9c1f7b4b47ddac40a25b46439131.jpeg#pic_center  如何將l 關於 w 和b的偏導數  傳遞到 sgd 函數 猜測，應該存儲在了 param.grad
        sgd([w, b], lr, batch_size)
    with torch.no_grad():
        train_l = loss(net(features, w, b), labels)
        print(f'epoch {epoch + 1}, loss {float(train_l.mean()) : f}') # https://zhuanlan.zhihu.com/p/541191036  格式化輸出


print(f'w的估計誤差: {true_w - w.reshape(true_w.shape)}')
print(f'b的估計誤差: {true_b - b}')
print("w ", w, " b ", b)d

簡易實現

import numpy as np
import torch
from torch.utils import data
from d2l import torch as d2l

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):
    """構造一個Pyorch數據迭代器"""
    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))

from torch import nn
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}')

w = net[0].weight.data
print('w的估計誤誤差: ', true_w - w.reshape(true_w.shape))
b = net[0].bias.data
print('b的估計誤差: ', true_b - b)