LinerProgression

手动实现线性回归

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import torch
	import pandas as pd
	import numpy as np
	import matplotlib.pyplot as plt
	import random
	from torch.utils import data

构造一个人造数据集

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	def synthetic_data(w, b, num_examples):
		"""生成 y = Xw + b +噪声"""
	 x = torch.normal(0, 1, (num_examples, len(w)))  # 均值为0，方差为1 的随机数，行数为num，列数为len（x）
	 y = torch.matmul(x, w) + b
		y += torch.normal(0, 0.1, y.shape)  # 随机噪音
	 return x, y.reshape(-1, 1)  # 将y转换成一列  

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

每次读取一个batch数据量

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	def data_iter(batch_size, features, labels):
		num_examples = len(features)  # 样本数量
	 indices = list(range(num_examples))  # 生成一个下标列表
	 random.shuffle(indices)  # 将列表中顺序打乱，否则就会有序提取不好，我们要随机取样本
	 for i in range(0, num_examples, batch_size):  # 从0开始到num_examples结束，每次拿batch_size个数据
	 batch_indices = torch.tensor(indices[i:min(i + batch_size, num_examples)])  # 将拿出的下标拿出来，如果最后不够一个batchsize则拿到最后位置
	 yield features[batch_indices], labels[batch_indices]  # 每次返回一个x，一个y直到完全返回  

	batch_size = 10  

	for x, y in data_iter(batch_size, features, labels):
		print(x, '\n', y)
		break  

	w = torch.normal(0, 0.01, size=(2, 1), requires_grad=True)  # 生成一个均值为0方差为0.1 的两行一列的张量
	b = torch.zeros(1, requires_grad=True)  # 生成了一个0

定义模型

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

损失函数 均方误差

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

优化算法 小批量下降

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	def sgd(params, lr, batch_size):
		"""小批量下降"""
	 with torch.no_grad():
			for param in params:
				param -= lr * param.grad / batch_size
				param.grad.zero_()

实现

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	lr = 0.01
	num_epochs = 5
	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， y的小批量损失
	 l.sum().backward()
			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}')  

	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}')

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