基于GAN的时序缺失数据填补前言（1）——RNN介绍及pytorch代码实现

本专栏将主要介绍基于GAN的时序缺失数据填补。提起时序数据，就离不开一个神经网络——循环神经网络（Recurrent Neural Network, RNN）。RNN是一类用于处理序列数据的神经网络。RNN对具有序列特性的数据非常有效，它能挖掘数据中的时序信息。因为在介绍时序缺失数据填补，就离不开RNN的身影。本文将介绍循环神经网络RNN，并再次基础上完成基于pytorch的简单RNN代码实现，帮助更加深入了解RNN。

一、RNN介绍

关于循环神经网络RNN的介绍可以参考这篇文章：循环神经网络RNN入门介绍，这里不进行过多赘述。

二、PyTorch相关语法介绍 2.1 RNNcell

RNNcell结构如下： h0为先验，若不存在先验，则h0是维度与h1，h2相同的全零向量。 语法如下：

torch.nn.RNNCell(input_size, hidden_size, bias=True, nonlinearity='tanh', device=None, dtype=None)

具有tanh或ReLU非线性的RNN单元。

• input_size：输入维度；
• hidden_size：隐藏维度；
• bias：如果为False，则该层不使用偏置权重b_ih和b_hh，默认为True；
• nonlinearity：使用的非线性层，可以是’tanh’或’relu’，默认为’tanh’;

即 h 1 = R N N C e l l ( x 1 , h 0 ) h_1=RNNCell(x_1,h_0) h1​=RNNCell(x1​,h0​) 输入维度：(batch_size,input_size) 隐含层维度：(batch_size,hidden_size) 输出维度：(batch_size,hidden_size)

因此数据集尺寸：(seqLen,batch_size,input_size)

代码示例：

import torch
import torch.nn as nn

batch_size=1
seq_len=3
input_size=4
hidden_size=2

cell=nn.RNNCell(input_size=input_size,hidden_size=hidden_size)

#(seq_len,batch,input)
dataset=torch.randn(seq_len,batch_size,input_size)
hidden=torch.zeros(batch_size,hidden_size)  # h0

for idx,input in enumerate(dataset):    # 3
    print('='*20,idx,'='*20)
    print('Input size:',input.shape)
    hidden=cell(input,hidden)
    print('output size:',hidden.shape)
    print(hidden)

运行结果：

2.2 RNN

RNN用于定义多层循环神经网络。 上图中num_layers=3. 语法如下：

torch.nn.RNN(input_size, hidden_size, num_layers, bias=True, nonlinearity='tanh', batch_first, dropout, bidirectional)

batch_first：如果为True，则输入和输出张量将作为(batch,seq,feature)而不是(seq,batch,feature)，默认为False；

out,hidden=rnn(x,h0) x=[x1,x2,…,xn] out=[h1,h2,…,hn] hidden=hn（最后一个h）

输入维度：(seq_len, batch_size,input_size) 隐含层维度：(num_layers, batch_size,hidden_size) 输出维度：(seq_len, batch_size,hidden_size) 隐含层维度：(num_layers, batch_size,hidden_size)

代码示例：

import torch
import torch.nn as nn

batch_size=1
seq_len=3
input_size=4
hidden_size=2
num_layers=1

rnn=nn.RNN(input_size=input_size,hidden_size=hidden_size,num_layers=num_layers)

#(seq_len,batch,input)
input=torch.randn(seq_len,batch_size,input_size)
hidden=torch.zeros(num_layers,batch_size,hidden_size)  # h0

out,hidden=rnn(input,hidden)

print('Output size:',out.shape)
print(out)
print('Hidden size:',hidden.shape)
print(hidden)

运行结果：

三、代码实战（1） 3.1 功能描述

本代码实现将文本序列“hello”转为序列“ohlol”。

3.2 利用RNNcell实现

首先需要将文本转为独热编码：

idx2char=['e','h','l','o']
x_data=[1,0,2,2,3]
y_data=[3,1,2,3,2]

one_hot_lookup=[[1,0,0,0],
               [0,1,0,0],
               [0,0,1,0],
               [0,0,0,1]]
x_one_hot=[one_hot_lookup[x] for x in x_data]

相关维度： input_size=4 hidden_size=4 输入维度：(batch_size,input_size) 隐含层维度：(batch_size,hidden_size) 输出维度：(batch_size,hidden_size)

因此序列尺寸：(seqLen,batch_size,input_size)

完整代码如下：

import torch
import torch.nn as nn

input_size=4
hidden_size=4
batch_size=1

idx2char=['e','h','l','o']
x_data=[1,0,2,2,3]
y_data=[3,1,2,3,2]

one_hot_lookup=[[1,0,0,0],
               [0,1,0,0],
               [0,0,1,0],
               [0,0,0,1]]
x_one_hot=[one_hot_lookup[x] for x in x_data]

inputs=torch.Tensor(x_one_hot).view(-1,batch_size,input_size) #(5,1,4)
labels=torch.LongTensor(y_data).view(-1,1) #(5,1)


class RNN(nn.Module):
    def __init__(self, input_size, hidden_size, batch_size):
        super(RNN, self).__init__()
        self.input_size = input_size
        self.hidden_size = hidden_size
        self.batch_size = batch_size
        self.rnncell = nn.RNNCell(input_size=input_size, hidden_size=hidden_size)

    def forward(self, input, hidden):
        hidden = self.rnncell(input, hidden)
        return hidden

    def init_hidden(self):
        return torch.zeros(self.batch_size, self.hidden_size)  # h0


rnn = RNN(input_size, hidden_size, batch_size)

criterion = nn.CrossEntropyLoss()
optimizer = torch.optim.Adam(rnn.parameters(),lr=0.1)

for epoch in range(20):
    loss = 0
    optimizer.zero_grad()  # 梯度清零

    hidden = rnn.init_hidden()  # 初始化h0
    print('Predicted string: ', end='')
    for input, label in zip(inputs, labels):
        hidden = rnn(input, hidden)
        loss += criterion(hidden, label)
        _, idx = hidden.max(dim=1)  # 下标最大值
        print(idx2char[idx.item()], end='')
    loss.backward()
    optimizer.step()
    print(',Epoch [%d/15] loss=%.4f' % (epoch + 1, loss.item()))

运行结果：

3.3 利用RNN实现

代码示例：

import torch
import torch.nn as nn

input_size=4
hidden_size=4
batch_size=1
num_layers=1
seq_len=5

idx2char=['e','h','l','o']
x_data=[1,0,2,2,3]
y_data=[3,1,2,3,2]

one_hot_lookup=[[1,0,0,0],
               [0,1,0,0],
               [0,0,1,0],
               [0,0,0,1]]
x_one_hot=[one_hot_lookup[x] for x in x_data]

inputs=torch.Tensor(x_one_hot).view(seq_len,batch_size,input_size) #(5,1,4)
labels=torch.LongTensor(y_data) #(5,)


class RNN(nn.Module):
    def __init__(self, input_size, hidden_size, batch_size,num_layers):
        super(RNN, self).__init__()
        self.num_layers=num_layers
        self.input_size = input_size
        self.hidden_size = hidden_size
        self.batch_size = batch_size
        self.rnn = nn.RNN(input_size=input_size, hidden_size=hidden_size,num_layers=num_layers)

    def forward(self, input,):
        hidden=torch.zeros(self.num_layers,self.batch_size, self.hidden_size) # h0
        out,_ = self.rnn(input, hidden)
        return out.view(-1,self.hidden_size)


rnn = RNN(input_size, hidden_size, batch_size,num_layers)

criterion = nn.CrossEntropyLoss()
optimizer = torch.optim.Adam(rnn.parameters(),lr=0.1)

for epoch in range(20):
    optimizer.zero_grad()  # 梯度清零
    outputs = rnn(inputs)
    loss = criterion(outputs, labels)
    loss.backward()
    optimizer.step()
    _, idx = outputs.max(dim=1)  # 下标最大值
    idx=idx.data.numpy()
    print('Predicted: ',''.join([idx2char[x] for x in idx]), end='')
    print(',Epoch [%d/15] loss=%.4f' % (epoch + 1, loss.item()))

运行结果：

四、代码实战（2） 4.1 功能描述

本案例将实现利用输入正弦sin输出余弦cos曲线。

4.2 利用RNN实现

首先进行参数定义：

input_size=1
hidden_size=16
batch_size=1
num_layers=1
seq_len=50

定义RNN网络框架：

class RNN(nn.Module):
    def __init__(self):
        super(RNN, self).__init__()
        self.rnn = nn.RNN(input_size=input_size, hidden_size=hidden_size,num_layers=num_layers)
        self.linear=nn.Linear(hidden_size,1)


    def forward(self,x,hidden):
        out,_= self.rnn(x, hidden)
        out=out.view(-1, hidden_size)
        out=self.linear(out)
        out=out.unsqueeze(dim=1)    # 扩充维度 由(50,1)扩充为(50,1,1)
        return out

模型实例化：

rnn = RNN()
print(rnn)
# RNN(
#   (rnn): RNN(1, 16)
#   (linear): Linear(in_features=16, out_features=1, bias=True)
# )
loss_fun = nn.MSELoss()
optimizer = torch.optim.Adam(rnn.parameters(),lr=0.01)

模型训练：

hidden_prev = torch.zeros(num_layers,batch_size,hidden_size)     #h0

plt.figure(figsize=(20, 4))
plt.ion()   # 不断绘制
for it in range(1000+1):
    steps = np.linspace(it * np.pi, (it + 1) * np.pi, seq_len, dtype=np.float32)
    x_np = np.sin(steps)
    y_np = np.cos(steps)
    x = torch.from_numpy(x_np[:, np.newaxis, np.newaxis])   # 扩展维度(50,1,1)
    y = torch.from_numpy(y_np[:, np.newaxis, np.newaxis])   # 扩展维度(50,1,1)
    y_pred = rnn(x, hidden_prev)
    loss = loss_fun(y_pred, y)
    optimizer.zero_grad()
    loss.backward()
    optimizer.step()

    # 模型可视化
    plt.plot(steps, y_np, 'b-')
    plt.plot(steps, y_pred.data.numpy().flatten(), 'r-')
    plt.draw()  # 重新绘制
    plt.pause(0.05)

    if it % 100 ==0:
        print("Iter:{} loss:{}".format(it,loss))
plt.ioff()  # 停止绘制
plt.show()

最后进行测试：

#测试
steps = np.linspace(10 * np.pi, (10 + 1) * np.pi, seq_len, dtype=np.float32)
x_np = np.sin(steps)
y_np = np.cos(steps)
# 模型可视化
plt.scatter(steps, y_np, c='b')
x = torch.from_numpy(x_np[:, np.newaxis, np.newaxis])  # 扩展维度(50,1,1)
y_pred= rnn(x,hidden_prev)
plt.scatter(steps, y_pred.data.numpy().flatten(), c='r')
plt.show()

4.3 完整代码

完整代码如下：

import torch
import torch.nn as nn
import numpy as np
import matplotlib.pyplot as plt

input_size=1
hidden_size=16
batch_size=1
num_layers=1
seq_len=50


class RNN(nn.Module):
    def __init__(self):
        super(RNN, self).__init__()
        self.rnn = nn.RNN(input_size=input_size, hidden_size=hidden_size,num_layers=num_layers)
        self.linear=nn.Linear(hidden_size,1)


    def forward(self,x,hidden):
        out,_= self.rnn(x, hidden)
        out=out.view(-1, hidden_size)
        out=self.linear(out)
        out=out.unsqueeze(dim=1)    # 扩充维度 由(50,1)扩充为(50,1,1)
        return out


rnn = RNN()
print(rnn)
# RNN(
#   (rnn): RNN(1, 16)
#   (linear): Linear(in_features=16, out_features=1, bias=True)
# )

loss_fun = nn.MSELoss()
optimizer = torch.optim.Adam(rnn.parameters(),lr=0.01)

hidden_prev = torch.zeros(num_layers,batch_size,hidden_size)     #h0

plt.figure(figsize=(12, 3))
plt.ion()   # 不断绘制
for it in range(1000+1):
    steps = np.linspace(it * np.pi, (it + 1) * np.pi, seq_len, dtype=np.float32)
    x_np = np.sin(steps)
    y_np = np.cos(steps)
    x = torch.from_numpy(x_np[:, np.newaxis, np.newaxis])   # 扩展维度(50,1,1)
    y = torch.from_numpy(y_np[:, np.newaxis, np.newaxis])   # 扩展维度(50,1,1)
    y_pred = rnn(x, hidden_prev)
    loss = loss_fun(y_pred, y)
    optimizer.zero_grad()
    loss.backward()
    optimizer.step()

    # 模型可视化
    plt.plot(steps, y_np, 'b-')
    plt.plot(steps, y_pred.data.numpy().flatten(), 'r-')
    plt.draw()  # 重新绘制
    plt.pause(0.05)

    if it % 100 ==0:
        print("Iter:{} loss:{}".format(it,loss))
plt.ioff()  # 停止绘制
plt.show()

#测试
steps = np.linspace(10 * np.pi, (10 + 1) * np.pi, seq_len, dtype=np.float32)
x_np = np.sin(steps)
y_np = np.cos(steps)
# 模型可视化
plt.scatter(steps, y_np, c='b')
x = torch.from_numpy(x_np[:, np.newaxis, np.newaxis])  # 扩展维度(50,1,1)
y_pred= rnn(x,hidden_prev)
plt.scatter(steps, y_pred.data.numpy().flatten(), c='r')
plt.show()

4.4 运行结果

运行结果如下： loss损失如下： 测试结果如下：

【解释】：这里前4-5个点存在较大的偏差，原因可能是前面点没有先验h，因此存在偏差较大，为获得测试较小偏差，可以对测试代码进行适度修改：

#测试
steps = np.linspace(10 * np.pi, (10 + 1) * np.pi, seq_len, dtype=np.float32)
x_np = np.sin(steps)
y_np = np.cos(steps)
# 模型可视化
plt.scatter(steps[5:,], y_np[5:,], c='b')
x = torch.from_numpy(x_np[:, np.newaxis, np.newaxis])  # 扩展维度(50,1,1)
y_pred= rnn(x,hidden_prev)
plt.scatter(steps[5:,], y_pred.data.numpy().flatten()[5:,], c='r')
plt.show()

运行效果如下：

参考：

1. https://blog.csdn.net/qq_41775769/article/details/121707309
2. http://www.ichenhua.cn/read/302
3. https://www.sohu.com/a/402391876_100286367