线性回归模型的从零实现

从零开始构建线性回归模型

整体步骤：

#1.构建数据集
#2.打乱数据集，获取更小批次的数据
#3.初始化权重参数
#4.模型定义
#5.损失函数定义
#6.优化算法定义
#7.开始训练

具体实现：

import torch
import random
from d2l import torch as d2l

#真实的模型参数
true_w = torch.tensor([2, -3.4])
true_b = 4.2

#1.首先生成随机数据集, 生成一个1000 * 2的特征矩阵， 标签为1000 * 1的向量
def synthetic_data(w, b, num_samples):
    X = torch.normal(0, 1, (num_samples, len(w)))
    y = torch.matmul(X, w) + b
    y += torch.normal(0, 0.01, y.shape)
    return X, y.reshape(-1, 1)
features, labels = synthetic_data(true_w, true_b, 1000)


#2. 将数据集分割成等大小的批量数据，为后续的批量梯度下降做准备
def data_iter(batch_size, features, labels):
    num_examples = len(features)
    #得到一个随机顺序的数据集
    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)])#获取索引号列表
        yield features[batch_indices], labels[batch_indices]

#3. 初始化模型参数
w = torch.normal(0, 0.01, (2,1), requires_grad=True)
b = torch.zeros(1, requires_grad=True)

#4. 定义模型
def liner_regression(w, b, X):
    y_hat = torch.matmul(X, w) + b.reshape(-1, 1)
    return y_hat

#5. 定义损失函数
def square_loss(y_hat, y):
    return 0.5 * ((y_hat - y) ** 2)

#6. 定义优化算法 小批量随机梯度下降
def sgd(params, lr, batch_size):
    with torch.no_grad():
        for param in params:
            param -= lr * param.grad / batch_size
            #可以简单的理解为我们对一个批量的数据进行了batch_size次的累积求梯度，现在取一个梯度的平均值
            param.grad.zero_()
#7. 开始训练
def train():
    lr = 0.03
    batch_size = 10
    num_epochs = 3
    net = liner_regression
    loss = square_loss
    for epoch in range(num_epochs):
        for X, y in data_iter(batch_size, features, labels):
            y_pred = net(w, b, X)
            l = loss(y_pred, y)
            l.sum().backward()
            sgd([w, b], lr, batch_size)
        with torch.no_grad():
            train_l = loss(net(w, b, features), labels)
            print(f'epoch {epoch + 1}, loss {float(train_l.mean()):f}')