pytorch第四章模型选择、欠拟合和过拟合

1.导包

import math
import numpy as np
import torch
from torch import nn
from d2l import torch as d2l

2.生成训练和测试数据

max_degree = 20  # 多项式的最大阶数
n_train, n_test = 100, 100  # 训练和测试数据集大小
true_w = np.zeros(max_degree)  # 分配大量的空间
true_w[0:4] = np.array([5, 1.2, -3.4, 5.6])

features = np.random.normal(size=(n_train + n_test, 1))
np.random.shuffle(features)
poly_features = np.power(features, np.arange(max_degree).reshape(1, -1))
for i in range(max_degree):
    poly_features[:, i] /= math.gamma(i + 1)  # gamma(n)=(n-1)!
# labels的维度:(n_train+n_test,)
labels = np.dot(poly_features, true_w)
labels += np.random.normal(scale=0.1, size=labels.shape)

3.NumPy ndarray转换为tensor

true_w, features, poly_features, labels = [torch.tensor(x, dtype=
    torch.float32) for x in [true_w, features, poly_features, labels]]

features[:2], poly_features[:2, :], labels[:2]

4.做训练的准备

def evaluate_loss(net, data_iter, loss):  #@save
    """评估给定数据集上模型的损失"""
    metric = d2l.Accumulator(2)  # 损失的总和,样本数量
    for X, y in data_iter:
        out = net(X)
        y = y.reshape(out.shape)
        l = loss(out, y)
        metric.add(l.sum(), l.numel())
    return metric[0] / metric[1]

from torch.utils import data
def load_array(data_arrays, batch_size, is_train=True):
    """构造一个PyTorch数据迭代器"""
    dataset = data.TensorDataset(*data_arrays)
    return data.DataLoader(dataset, batch_size, shuffle=is_train)

def train(train_features, test_features, train_labels, test_labels,
          num_epochs=400):
    loss = nn.MSELoss(reduction='none')
    input_shape = train_features.shape[-1]
    # 不设置偏置，因为我们已经在多项式中实现了它
    net = nn.Sequential(nn.Linear(input_shape, 1, bias=False))
    batch_size = min(10, train_labels.shape[0])
    train_iter = load_array((train_features, train_labels.reshape(-1,1)),
                                batch_size)
    test_iter = load_array((test_features, test_labels.reshape(-1,1)),
                               batch_size, is_train=False)
    trainer = torch.optim.SGD(net.parameters(), lr=0.01)
    for epoch in range(num_epochs):
        d2l.train_epoch_ch3(net, train_iter, loss, trainer)
        if epoch == 0 or (epoch + 1) % 20 == 0:
            print(f'epoch {epoch+1}, train_iter_evaluate_loss {evaluate_loss(net,train_iter,loss)}, test_iter_evaluate_loss {evaluate_loss(net,test_iter,loss)}')
    print('weight:', net[0].weight.data.numpy())

5.从多项式特征中选择前4个维度

train(poly_features[:n_train, :4], poly_features[n_train:, :4],
      labels[:n_train], labels[n_train:])

6.从多项式特征中选择前2个维度，即1和x

train(poly_features[:n_train, :2], poly_features[n_train:, :2],
      labels[:n_train], labels[n_train:])

7.从多项式特征中选取所有维度

train(poly_features[:n_train, :], poly_features[n_train:, :],
      labels[:n_train], labels[n_train:], num_epochs=1500)