用Python写一个在jutyer notebook中运行的变分编码器

以下是使用Python实现的变分自编码器（Variational Autoencoder）的代码，可以在Jupyter Notebook中运行：

# 导入必要的库
import numpy as np
import tensorflow as tf
import matplotlib.pyplot as plt

# 加载MNIST数据集
from tensorflow.examples.tutorials.mnist import input_data
mnist = input_data.read_data_sets('MNIST_data')

# 定义变分自编码器的参数
input_dim = 784
hidden_dim = 512
latent_dim = 2
learning_rate = 0.001
batch_size = 100
num_epochs = 50

# 定义变分自编码器的输入
X = tf.placeholder(tf.float32, shape=[None, input_dim])

# 定义编码器的结构
W1 = tf.Variable(tf.random_normal([input_dim, hidden_dim]))
b1 = tf.Variable(tf.random_normal([hidden_dim]))
W2_mean = tf.Variable(tf.random_normal([hidden_dim, latent_dim]))
b2_mean = tf.Variable(tf.random_normal([latent_dim]))
W2_stddev = tf.Variable(tf.random_normal([hidden_dim, latent_dim]))
b2_stddev = tf.Variable(tf.random_normal([latent_dim]))

hidden_layer = tf.nn.relu(tf.matmul(X, W1) + b1)
latent_mean = tf.matmul(hidden_layer, W2_mean) + b2_mean
latent_stddev = tf.matmul(hidden_layer, W2_stddev) + b2_stddev

# 从潜在空间中随机采样
epsilon = tf.random_normal(tf.shape(latent_stddev))
latent_sample = latent_mean + tf.exp(latent_stddev / 2) * epsilon

# 定义解码器的结构
W3 = tf.Variable(tf.random_normal([latent_dim, hidden_dim]))
b3 = tf.Variable(tf.random_normal([hidden_dim]))
W4 = tf.Variable(tf.random_normal([hidden_dim, input_dim]))
b4 = tf.Variable(tf.random_normal([input_dim]))

hidden_layer2 = tf.nn.relu(tf.matmul(latent_sample, W3) + b3)
output_layer = tf.matmul(hidden_layer2, W4) + b4

# 定义变分自编码器的损失函数
kl_divergence = -0.5 * tf.reduce_sum(1 + 2 * latent_stddev - tf.square(latent_mean) - tf.exp(2 * latent_stddev), axis=1)
reconstruction_loss = tf.reduce_mean(tf.square(X - output_layer))
vae_loss = tf.reduce_mean(kl_divergence + reconstruction_loss)

# 定义变分自编码器的训练操作
train_op = tf.train.AdamOptimizer(learning_rate).minimize(vae_loss)

# 在TensorFlow中运行变分自编码器
with tf.Session() as sess:
    sess.run(tf.global_variables_initializer())
    num_batches = mnist.train.num_examples // batch_size
    for epoch in range(num_epochs):
        for batch in range(num_batches):
            batch_x, _ = mnist.train.next_batch(batch_size)
            _, loss = sess.run([train_op, vae_loss], feed_dict={X: batch_x})
        print('Epoch {0}: Loss = {1}'.format(epoch, loss))
    
    # 从潜在空间中随机采样并生成新的数字图像
    num_samples = 10
    latent_values = np.random.normal(size=[num_samples, latent_dim])
    generated_images = sess.run(output_layer, feed_dict={latent_sample: latent_values})
    
    # 将生成的图像可视化
    for i in range(num_samples):
        plt.imshow(generated_images[i].reshape(28, 28), cmap='gray')
        plt.show()

这段代码定义了一个具有512个隐藏单元和2个潜在变量的变分自编码器，并使用MNIST数据集进行训练。训练后，它可以从潜在空间中随机采样并生成新的数字图像。

在Jupyter Notebook中运行此代码时，您需要确保已安装以下库：numpy，tensorflow和matplotlib。如果您还没有安装它们，可以使用以下命令在Jupyter Notebook中安装它们：

!pip install numpy tensorflow matplotlib
``