用pytorch写一个置信区间分析与CNN网络结合的代码

好的，以下是一个简单的置信区间分析与CNN网络结合的代码示例：

import torch
from torch import nn
from torch.nn import functional as F

class CNN(nn.Module):
    def __init__(self):
        super(CNN, self).__init__()
        self.conv1 = nn.Conv2d(3, 32, kernel_size=3, stride=1, padding=1)
        self.pool1 = nn.MaxPool2d(kernel_size=2, stride=2)
        self.conv2 = nn.Conv2d(32, 64, kernel_size=3, stride=1, padding=1)
        self.pool2 = nn.MaxPool2d(kernel_size=2, stride=2)
        self.conv3 = nn.Conv2d(64, 128, kernel_size=3, stride=1, padding=1)
        self.pool3 = nn.MaxPool2d(kernel_size=2, stride=2)
        self.fc1 = nn.Linear(4*4*128, 512)
        self.fc2 = nn.Linear(512, 10)

    def forward(self, x):
        x = F.relu(self.conv1(x))
        x = self.pool1(x)
        x = F.relu(self.conv2(x))
        x = self.pool2(x)
        x = F.relu(self.conv3(x))
        x = self.pool3(x)
        x = x.view(-1, 4*4*128)
        x = F.relu(self.fc1(x))
        x = self.fc2(x)
        return x

class BayesianCNN(CNN):
    def __init__(self, num_classes, dropout_rate):
        super(BayesianCNN, self).__init__()
        self.num_classes = num_classes
        self.dropout_rate = dropout_rate

    def forward(self, x):
        # repeat the input to get multiple samples
        x = x.repeat(self.num_classes, 1, 1, 1) 
        # pass through the deterministic CNN
        x = super().forward(x)
        # apply dropout to the output of convolutional layers
        x = F.dropout(x, p=self.dropout_rate, training=True)
        # compute the mean and standard deviation of the output
        x_mean = torch.mean(x, dim=0)
        x_std = torch.std(x, dim=0)
        # return the mean and standard deviation
        return x_mean, x_std

def calculate_ci(pred_mean, pred_std, alpha):
    z = torch.distributions.Normal(torch.tensor([0.0]), torch.tensor([1.0]))
    z_alpha = z.icdf(torch.tensor([1 - alpha/2]))
    lower_bound = pred_mean - z_alpha * pred_std
    upper_bound = pred_mean + z_alpha * pred_std
    return lower_bound, upper_bound

在这个示例中，我们首先定义了一个标准的CNN模型，然后定义了一个继承自CNN的BayesianCNN模型。在BayesianCNN中，我们通过多次重复输入来获得多个样本，然后在卷积层的输出上应用Dropout，最后计算输出的均值和标准差。我们还定义了一个函数`calculate_ci`，用于计算置信区间。该函数使用标准正态分布的逆累积分布函数来计算z_alpha，然后使用该值乘以预测标准差以计算置信区间的下限和上限。

注意，在实际应用中，为了获得更准确的置信区间，我们需要使用更多的样本进行估计，这里只是为了演示而使用了一个简单的重复输入策略。