NadarayaWatson.py

import matplotlib.pyplot as plt
import torch
from torch import nn
from d2l import torch as d2l

n_train = 50 # 训练样本数
x_train, _ = torch.sort(torch.rand(n_train) * 5) # 排序后的训练样本

def f(x):
    return 2 * torch.sin(x) + x**0.8

y_train = f(x_train) + torch.normal(0.0, 0.5, (n_train,)) # 训练样本的输出
x_test = torch.arange(0, 5, 0.1) # 测试样本
y_truth = f(x_test) # 测试样本的真实输出
n_test = len(x_test) # 测试样本数


def plot_kernel_reg(y_hat):
    d2l.plot(x_test, [y_truth, y_hat], 'x', 'y', legend=['Truth', 'Pred'],
                xlim=[0, 5], ylim=[-1, 5])
    d2l.plt.plot(x_train, y_train, 'o', alpha=0.5);

y_hat = torch.repeat_interleave(y_train.mean(), n_test)
#plot_kernel_reg(y_hat)




# X_repeat的形状:(n_test,n_train),
# 每⼀⾏都包含着相同的测试输⼊（例如：同样的查询）
X_repeat = x_test.repeat_interleave(n_train).reshape((-1, n_train))
# x_train包含着键。attention_weights的形状：(n_test,n_train),
# 每⼀⾏都包含着要在给定的每个查询的值（y_train）之间分配的注意⼒权重
attention_weights = nn.functional.softmax(-(X_repeat - x_train)**2 / 2, dim=1)
# y_hat的每个元素都是值的加权平均值，其中的权重是注意⼒权重
y_hat = torch.matmul(attention_weights, y_train)
#plot_kernel_reg(y_hat)

d2l.show_heatmaps(attention_weights.unsqueeze(0).unsqueeze(0),
xlabel='Sorted training inputs',
ylabel='Sorted testing inputs')

X = torch.ones((2, 1, 4))
Y = torch.ones((2, 4, 6))

weights = torch.ones((2, 10)) * 0.1
values = torch.arange(20.0).reshape((2, 10))

class NWKernelRegression(nn.Module):
    def __init__(self, **kwargs):
        super().__init__(**kwargs)
        self.w = nn.Parameter(torch.rand((1,), requires_grad=True))
    def forward(self, queries, keys, values):
        # queries和attention_weights的形状为(查询个数，“键－值”对个数)
        queries = queries.repeat_interleave(keys.shape[1]).reshape((-1, keys.shape[1]))
        self.attention_weights = nn.functional.softmax(-((queries - keys) * self.w)**2 / 2, dim=1)
        # values的形状为(查询个数，“键－值”对个数)
        return torch.bmm(self.attention_weights.unsqueeze(1),
                values.unsqueeze(-1)).reshape(-1)

# X_tile的形状:(n_train，n_train)，每⼀⾏都包含着相同的训练输⼊
X_tile = x_train.repeat((n_train, 1))
# Y_tile的形状:(n_train，n_train)，每⼀⾏都包含着相同的训练输出
Y_tile = y_train.repeat((n_train, 1))
# keys的形状:('n_train'，'n_train'-1)
keys = X_tile[(1 - torch.eye(n_train)).type(torch.bool)].reshape((n_train, -1))
# values的形状:('n_train'，'n_train'-1)
values = Y_tile[(1 - torch.eye(n_train)).type(torch.bool)].reshape((n_train, -1))

net = NWKernelRegression()
loss = nn.MSELoss(reduction='none')
trainer = torch.optim.SGD(net.parameters(), lr=0.5)
animator = d2l.Animator(xlabel='epoch', ylabel='loss', xlim=[1, 5])
for epoch in range(5):
    trainer.zero_grad()
    l = loss(net(x_train, keys, values), y_train)
    l.sum().backward()
    trainer.step()
    print(f'epoch {epoch + 1}, loss {float(l.sum()):.6f}')
    animator.add(epoch + 1, float(l.sum()))

# keys的形状:(n_test，n_train)，每⼀⾏包含着相同的训练输⼊（例如，相同的键）
keys = x_train.repeat((n_test, 1))
# value的形状:(n_test，n_train)
values = y_train.repeat((n_test, 1))
y_hat = net(x_test, keys, values).unsqueeze(1).detach()
plot_kernel_reg(y_hat)
d2l.show_heatmaps(net.attention_weights.unsqueeze(0).unsqueeze(0),
    xlabel='Sorted training inputs',
    ylabel='Sorted testing inputs')


plt.show()