Simple RNN时间序列预测
- 2020 年 2 月 17 日
- 筆記
本文将介绍利用朴素的RNN模型进行时间序列预测
比方说现在我们有如下图所示的一段正弦曲线，输入红色部分，通过训练输出下一段的值
首先分析一下，假设我们一次输入50个点，batch设为1，每个点就一个值，所以input的shape就是[50, 1, 1]，这里我们换一种表示形式，把batch放在前面，那么shape就是[1, 50, 1]，可以这么理解这个shape，1条曲线，一共有50个点，每个点都是1个实数
import numpy.random import randint import numpy as np import torch from torch import nn, optim from matplotlib import pyplot as plt start = randint(3) # [0, 3) time_steps = np.linspace(start, start + 10, num_time_steps) # 返回num_time_steps个点 data = np.sin(time_steps) # [50] data = data.reshape(num_time_steps, -1) # [50, 1] x = torch.tensor(data[:-1]).float().view(1, num_time_steps - 1, 1) # 0~48 y = torch.tensor(data[1:]).float().view(1, num_time_steps - 1, 1) # 1~49
start表示的含义从几何上来说就是图上红色左边框的对应的横坐标的值，因为我们要确定一个起点，从这个起点开始向后取50个点，如果每次这个起点都是相同的，就会被这个网络记住
x是50个数据点中的前49个，我们利用这49个点，每个点都向后预测一个单位的数据，得到$hat y$，然后将$hat y$与$y$进行对比
接下来是构建网络架构
class Net(nn.Module): def __init__(self): super(Net, self).__init__() self.rnn = nn.RNN( input_size=input_size, hidden_size=hidden_size, num_layers=1, batch_first=True, ) self.linear = nn.Linear(hidden_size, output_size) def forward(self, x, h0): out, h0 = self.rnn(x, h0) # [b, seq, h] => [seq, h] out = out.view(-1, hidden_size) out = self.linear(out) # [seq, h] => [seq, 1] out = out.unsqueeze(dim=0) # => [1, seq, 1] return out, h0
首先里面是一个simple RNN，其中有个参数batch_first，因为我们数据传入的格式是batch在前，所以要把这个参数设为True。RNN之后接了个Linear，将memory的size输出为`output_size=1方便进行比较，因为我们就只需要一个值
然后我们定义网络Train的代码
model = Net() criterion = nn.MSELoss() optimizer = optim.Adam(model.parameters(), lr) h0 = torch.zeros(1, 1, hidden_size) # [b, 1, hidden_size] for iter in range(6000): start = np.random.randint(3, size=1)[0] time_steps = np.linspace(start, start + 10, num_time_steps) data = np.sin(time_steps) data = data.reshape(num_time_steps, 1) x = torch.tensor(data[:-1]).float().view(1, num_time_steps - 1, 1) y = torch.tensor(data[1:]).float().view(1, num_time_steps - 1, 1) output, h0 = model(x, h0) h0 = h0.detach() loss = criterion(output, y) model.zero_grad() loss.backward() optimizer.step() if iter % 100 == 0: print("Iteration: {} loss {}".format(iter, loss.item()))
最后是Predict的部分
predictions = [] input = x[:, 0, :] for _ in range(x.shape[1]): input = input.view(1, 1, 1) (pred, h0) = model(input, h0) input = pred predictions.append(pred.detach().numpy().ravel()[0])
假设x的shape是[b, seq, 1]，经过x[:, 0, :]之后就变成了[b, 1]，但其实前面说过了，batch值是1，所以input的shape就是[1, 1]，然后再展开成[1, 1, 1]是为了能匹配网络的输入维度
倒数第二行和第三行的代码做的事情是，首先带入第一个值，得到一个输出pred，然后把pred作为下一次的输入，又得到一个pred，如此循环往复，就把上一次的输出，作为下一次的输入
最后的输出图像如下所示
完整代码如下：
from numpy.random import randint import numpy as np import torch import torch.nn as nn import torch.optim as optim from matplotlib import pyplot as plt num_time_steps = 50 input_size = 1 hidden_size = 16 output_size = 1 lr=0.01 class Net(nn.Module): def __init__(self): super(Net, self).__init__() self.rnn = nn.RNN( input_size=input_size, hidden_size=hidden_size, num_layers=1, batch_first=True, ) self.linear = nn.Linear(hidden_size, output_size) def forward(self, x, h0): out, h0 = self.rnn(x, h0) # [b, seq, h] out = out.view(-1, hidden_size) out = self.linear(out) out = out.unsqueeze(dim=0) return out, h0 model = Net() criterion = nn.MSELoss() optimizer = optim.Adam(model.parameters(), lr) h0 = torch.zeros(1, 1, hidden_size) for iter in range(6000): start = randint(3) time_steps = np.linspace(start, start + 10, num_time_steps) data = np.sin(time_steps) data = data.reshape(num_time_steps, 1) x = torch.tensor(data[:-1]).float().view(1, num_time_steps - 1, 1) y = torch.tensor(data[1:]).float().view(1, num_time_steps - 1, 1) output, h0 = model(x, h0) h0 = h0.detach() loss = criterion(output, y) model.zero_grad() loss.backward() optimizer.step() if iter % 100 == 0: print("Iteration: {} loss {}".format(iter, loss.item())) start = randint(3) time_steps = np.linspace(start, start + 10, num_time_steps) data = np.sin(time_steps) data = data.reshape(num_time_steps, 1) x = torch.tensor(data[:-1]).float().view(1, num_time_steps - 1, 1) y = torch.tensor(data[1:]).float().view(1, num_time_steps - 1, 1) predictions = [] input = x[:, 0, :] for _ in range(x.shape[1]): input = input.view(1, 1, 1) (pred, h0) = model(input, h0) input = pred predictions.append(pred.detach().numpy().ravel()[0]) x = x.data.numpy().ravel() # flatten操作 y = y.data.numpy() plt.scatter(time_steps[:-1], x.ravel(), s=90) plt.plot(time_steps[:-1], x.ravel()) plt.scatter(time_steps[1:], predictions) plt.show()
