深度学习3.2 线性回归的从零开始实现

lixy5792025-04-20 18:53

3.2.1 生成数据集

python 复制代码

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

def synthetic_data(w, b, num_examples):
    # 生成特征矩阵X，形状为(num_examples, len(w))，符合标准正态分布
    X = torch.normal(0, 1, (num_examples, len(w)))
    # 计算标签y = Xw + b
    y = torch.matmul(X, w) + b
    # 添加均值为0、标准差为0.01的噪声
    y += torch.normal(0, 0.01, y.shape)
    # 将y转换为列向量（形状：num_examples × 1）
    return X, y.reshape((-1, 1))

python 复制代码

true_w = torch.tensor([2, -3.4])  # 定义真实权重
true_b = 4.2                      # 定义真实偏置
features, labels = synthetic_data(true_w, true_b, 1000)  # 生成1000个样本

d2l.set_figsize()
d2l.plt.scatter(features[:, 1].detach().numpy(), labels.detach().numpy(), 1)

features $:, 1$ : 选取所有样本的第二个特征（索引为1的列）。

3.2.1 读取数据集

python 复制代码

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(X, '\n', y)
    break

tensor( $\[ 1.6556, 0.1851$ ,

$-1.4880, 0.0684$ ,

$1.0536, 0.9818$ ,

$-0.7794, -1.9199$ ,

$-0.3383, 0.2244$ ,

$-0.2260, 3.1530$ ,

$-2.3626, 1.1877$ ,

$-0.3301, 0.1781$ ,

$-0.6136, -1.2974$ ,

$-0.3397, -0.2088$ ])

tensor( $\[ 6.8888$ ,

$0.9887$ ,

$2.9757$ ,

$9.1748$ ,

$2.7541$ ,

$-6.9671$ ,

$-4.5522$ ,

$2.9436$ ,

$7.3728$ ,

$4.2270$ ])