--- title: "torch实现线性回归模型" description: "视频：08 线性回归 + 基础优化算法【动手学深度学习v2】" canonical_url: "https://yangqiuyi.com/blog/suan-fa/ai/torch-shi-xian-xian-xing-hui-gui-mo-xing" --- > Index of every page on this site: [llms.txt](https://yangqiuyi.com/llms.txt) 视频：[08 线性回归 + 基础优化算法【动手学深度学习v2】](https://www.bilibili.com/video/BV1PX4y1g7KC?p=3) ## 生成数据 ```python import torch def synthetic_data(w, b, n_examples): # 生成数据集 """生成 y = Xw + b + 噪声""" # X是符合均值为0，方差为1的正态分布， size为(n_examples, len(w))的矩阵 X = torch.normal(0, 1, size=(n_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, -4.2]) true_b = 3.6 features,labels = synthetic_data(true_w, true_b, 1000) print("features: ", features.size()) print("labels: ", labels.size()) ``` ```txt features: torch.Size([1000, 2]) labels: torch.Size([1000, 1]) ``` ## 生成批量数据(batch) ```python import random def data_iter(batch_size, features, labels): # 生成batch(批量)数据的方法 num_examples = len(features) indices = list(range(num_examples)) # 生成样本的下标 random.shuffle(indices) # 打乱下标 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] ``` ## 定义模型 ```python # 定义模型 def linreg(X, w, b): return torch.matmul(X, w) + b ``` ## 随机梯度下降（SGD） ```python def sgd(params, lr, batch_size): """小批量随机梯度下降方法""" with torch.no_grad(): for param in params: param -= lr * param.grad / batch_size # 对参数进行优化 ''' 因为是batch模式，一次输入了多个样本，所以param.grad是多个样本的累积梯度，因此要除以batch_size，才能得到正确的梯度参数的更新方法：参数 := 参数 - 学习率*梯度 ''' param.grad.zero_() # 梯度清零 ``` ## 均方损失函数

L = \frac{1}{2} * (\hat{y} - y) ^ 2

L = 2 1 ∗ ( y ^ − y ) 2 ```python def square_loss(y_hat, y): """均方损失函数""" return (y_hat - y) **2 / 2 ``` ## 训练模型 ```python EPOCHES = 10 # 数据集循环轮数 lr = 0.01 # learning rate 学习率 net = linreg # 线性回归模型 loss = square_loss batch_size = 10 # 初始化参数 w = torch.normal(0, 0.01, size=(2, 1), requires_grad=True) b = torch.zeros(1, requires_grad=True) for i in range(EPOCHES): for X, y in data_iter(batch_size, features, labels): l = loss(net(X, w, b), y) ''' 计算出来的loss的shape是(batch_size, 1)，不是一个标量因此我们需要对loss求sum，再求梯度 ''' l.sum().backward() sgd([w, b], lr, len(X)) with torch.no_grad(): train_l = loss(net(features, w, b), labels) print("epoch %d, loss %f" % (i+1, float(train_l.mean()))) ``` 运行结果： ```txt epoch 1, loss 2.347667 epoch 2, loss 0.326492 epoch 3, loss 0.045885 epoch 4, loss 0.006559 epoch 5, loss 0.000980 epoch 6, loss 0.000182 epoch 7, loss 0.000068 epoch 8, loss 0.000052 epoch 9, loss 0.000049 epoch 10, loss 0.000049 ``` ## 简洁实现数据生成的方法是一样的，没有改动 ```python import torch def synthetic_data(w, b, n_examples): # 生成数据集 """生成 y = Xw + b + 噪声""" # X是符合均值为0，方差为1的正态分布， size为(n_examples, len(w))的矩阵 X = torch.normal(0, 1, size=(n_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, -4.2]) true_b = 3.6 features,labels = synthetic_data(true_w, true_b, 1000) print("features: ", features.size()) print("labels: ", labels.size()) ``` batch的生成方式有所不同，这里使用torch的`DataLoader`进行处理 ```python from torch.utils.data import TensorDataset, DataLoader def load_array(data_arrays, batch_size, is_train=True): dataset = TensorDataset(*data_arrays) return DataLoader(dataset, batch_size, shuffle=is_train) batch_size = 10 data_iter = load_array([features, labels], batch_size) ``` torch里的`nn.Linear`就是我们需要用的线性回归模型，也叫`全连接层` ```python from torch import nn net = nn.Sequential(nn.Linear(2, 1)) # 创建模型，用到了torch的Sequential类，可以理解成模型的容器，里面其实可以放多个模型，构成复杂神经网络 # 初始化模型 net[0].weight.data.normal_(0, 0.01) # 设置w net[0].bias.data.fill_(0) # 设置b ``` 训练模型 ```python EPOCHES = 10 for i in range(EPOCHES): for X, y in data_iter: l = loss(net(X), y) trainer.zero_grad() l.backward() trainer.step() l = loss(net(features), labels) print("epoch %d, loss %f" % (i+1, l)) ``` ## Sitemap See the full [sitemap](https://yangqiuyi.com/sitemap.md) for all pages.