時(shí)間序列是指在一段時(shí)間內(nèi)發(fā)生的任何可量化的度量或事件。盡管這聽起來微不足道,但幾乎任何東西都可以被認(rèn)為是時(shí)間序列。一個(gè)月里你每小時(shí)的平均心率,一年里一只股票的日收盤價(jià),一年里某個(gè)城市每周發(fā)生的交通事故數(shù)。在任何一段時(shí)間段內(nèi)記錄這些信息都被認(rèn)為是一個(gè)時(shí)間序列。對(duì)于這些例子中的每一個(gè),都有事件發(fā)生的頻率(每天、每周、每小時(shí)等)和事件發(fā)生的時(shí)間長度(一個(gè)月、一年、一天等)。
在本教程中,我們將使用PyTorch-LSTM進(jìn)行深度學(xué)習(xí)時(shí)間序列預(yù)測(cè)。
(資料圖)
我們的目標(biāo)是接收一個(gè)值序列,預(yù)測(cè)該序列中的下一個(gè)值。最簡單的方法是使用自回歸模型,我們將專注于使用LSTM來解決這個(gè)問題。
數(shù)據(jù)準(zhǔn)備
讓我們看一個(gè)時(shí)間序列樣本。下圖顯示了2013年至2018年石油價(jià)格的一些數(shù)據(jù)。
這只是一個(gè)日期軸上單個(gè)數(shù)字序列的圖。下表顯示了這個(gè)時(shí)間序列的前10個(gè)條目。每天都有價(jià)格數(shù)據(jù)。
date ? ? ? dcoilwtico
2013-01-01 NaN
2013-01-02 93.14
2013-01-03 92.97
2013-01-04 93.12
2013-01-07 93.20
2013-01-08 93.21
2013-01-09 93.08
2013-01-10 93.81
2013-01-11 93.60
2013-01-14 94.27
許多機(jī)器學(xué)習(xí)模型在標(biāo)準(zhǔn)化數(shù)據(jù)上的表現(xiàn)要好得多。標(biāo)準(zhǔn)化數(shù)據(jù)的標(biāo)準(zhǔn)方法是對(duì)數(shù)據(jù)進(jìn)行轉(zhuǎn)換,使得每一列的均值為0,標(biāo)準(zhǔn)差為1。下面的代碼scikit-learn進(jìn)行標(biāo)準(zhǔn)化
from sklearn.preprocessing import StandardScaler
# Fit scalers
scalers = {}
for x in df.columns:
scalers[x] = StandardScaler().fit(df[x].values.reshape(-1, 1))
# Transform data via scalers
norm_df = df.copy()
for i, key in enumerate(scalers.keys()):
norm = scalers[key].transform(norm_df.iloc[:, i].values.reshape(-1, 1))
norm_df.iloc[:, i] = norm
我們還希望數(shù)據(jù)具有統(tǒng)一的頻率——在這個(gè)例子中,有這5年里每天的石油價(jià)格,如果你的數(shù)據(jù)情況并非如此,Pandas有幾種不同的方法來重新采樣數(shù)據(jù)以適應(yīng)統(tǒng)一的頻率,請(qǐng)參考我們公眾號(hào)以前的文章
對(duì)于訓(xùn)練數(shù)據(jù)我們需要將完整的時(shí)間序列數(shù)據(jù)截取成固定長度的序列。假設(shè)我們有一個(gè)序列:[1, 2, 3, 4, 5, 6]。
通過選擇長度為 3 的序列,我們可以生成以下序列及其相關(guān)目標(biāo):
[Sequence] ? ?Target?
[1, 2, 3] → 4
[2, 3, 4] → 5
[3, 4, 5] → 6
或者說我們定義了為了預(yù)測(cè)下一個(gè)值需要回溯多少步。我們將這個(gè)值稱為訓(xùn)練窗口,而要預(yù)測(cè)的值的數(shù)量稱為預(yù)測(cè)窗口。在這個(gè)例子中,它們分別是3和1。下面的函數(shù)詳細(xì)說明了這是如何完成的。
# Defining a function that creates sequences and targets as shown above
def generate_sequences(df: pd.DataFrame, tw: int, pw: int, target_columns, drop_targets=False):
"""
df: Pandas DataFrame of the univariate time-series
tw: Training Window - Integer defining how many steps to look back
pw: Prediction Window - Integer defining how many steps forward to predict
returns: dictionary of sequences and targets for all sequences
"""
data = dict() # Store results into a dictionary
L = len(df)
for i in range(L-tw):
# Option to drop target from dataframe
if drop_targets:
df.drop(target_columns, axis=1, inplace=True)
# Get current sequence ?
sequence = df[i:i+tw].values
# Get values right after the current sequence
target = df[i+tw:i+tw+pw][target_columns].values
data[i] = {"sequence": sequence, "target": target}
return data
這樣我們就可以在PyTorch中使用Dataset類自定義數(shù)據(jù)集
class SequenceDataset(Dataset):
def __init__(self, df):
self.data = df
def __getitem__(self, idx):
sample = self.data[idx]
return torch.Tensor(sample["sequence"]), torch.Tensor(sample["target"])
def __len__(self):
return len(self.data)
然后,我們可以使用PyTorch DataLoader來遍歷數(shù)據(jù)。使用DataLoader的好處是它在內(nèi)部自動(dòng)進(jìn)行批處理和數(shù)據(jù)的打亂,所以我們不必自己實(shí)現(xiàn)它,代碼如下:
# Here we are defining properties for our model
BATCH_SIZE = 16 # Training batch size
split = 0.8 # Train/Test Split ratio
sequences = generate_sequences(norm_df.dcoilwtico.to_frame(), sequence_len, nout, "dcoilwtico")
dataset = SequenceDataset(sequences)
# Split the data according to our split ratio and load each subset into a
# separate DataLoader object
train_len = int(len(dataset)*split)
lens = [train_len, len(dataset)-train_len]
train_ds, test_ds = random_split(dataset, lens)
trainloader = DataLoader(train_ds, batch_size=BATCH_SIZE, shuffle=True, drop_last=True)
testloader = DataLoader(test_ds, batch_size=BATCH_SIZE, shuffle=True, drop_last=True)
在每次迭代中,DataLoader將產(chǎn)生16個(gè)(批量大小)序列及其相關(guān)目標(biāo),我們將這些目標(biāo)傳遞到模型中。
模型架構(gòu)
我們將使用一個(gè)單獨(dú)的LSTM層,然后是模型的回歸部分的一些線性層,當(dāng)然在它們之間還有dropout層。該模型將為每個(gè)訓(xùn)練輸入輸出單個(gè)值。
class LSTMForecaster(nn.Module):
def __init__(self, n_features, n_hidden, n_outputs, sequence_len, n_lstm_layers=1, n_deep_layers=10, use_cuda=False, dropout=0.2):
"""
n_features: number of input features (1 for univariate forecasting)
n_hidden: number of neurons in each hidden layer
n_outputs: number of outputs to predict for each training example
n_deep_layers: number of hidden dense layers after the lstm layer
sequence_len: number of steps to look back at for prediction
dropout: float (0
"""
super().__init__()
self.n_lstm_layers = n_lstm_layers
self.nhid = n_hidden
self.use_cuda = use_cuda # set option for device selection
# LSTM Layer
self.lstm = nn.LSTM(n_features,
n_hidden,
num_layers=n_lstm_layers,
batch_first=True) # As we have transformed our data in this way
# first dense after lstm
self.fc1 = nn.Linear(n_hidden * sequence_len, n_hidden)
# Dropout layer
self.dropout = nn.Dropout(p=dropout)
# Create fully connected layers (n_hidden x n_deep_layers)
dnn_layers = []
for i in range(n_deep_layers):
# Last layer (n_hidden x n_outputs)
if i == n_deep_layers - 1:
dnn_layers.append(nn.ReLU())
dnn_layers.append(nn.Linear(nhid, n_outputs))
# All other layers (n_hidden x n_hidden) with dropout option
else:
dnn_layers.append(nn.ReLU())
dnn_layers.append(nn.Linear(nhid, nhid))
if dropout:
dnn_layers.append(nn.Dropout(p=dropout))
# compile DNN layers
self.dnn = nn.Sequential(*dnn_layers)
def forward(self, x):
# Initialize hidden state
hidden_state = torch.zeros(self.n_lstm_layers, x.shape[0], self.nhid)
cell_state = torch.zeros(self.n_lstm_layers, x.shape[0], self.nhid)
# move hidden state to device
if self.use_cuda:
hidden_state = hidden_state.to(device)
cell_state = cell_state.to(device)
self.hidden = (hidden_state, cell_state)
# Forward Pass
x, h = self.lstm(x, self.hidden) # LSTM
x = self.dropout(x.contiguous().view(x.shape[0], -1)) # Flatten lstm out
x = self.fc1(x) # First Dense
return self.dnn(x) # Pass forward through fully connected DNN.
我們?cè)O(shè)置了2個(gè)可以自由地調(diào)優(yōu)的參數(shù)n_hidden和n_deep_players。更大的參數(shù)意味著模型更復(fù)雜和更長的訓(xùn)練時(shí)間,所以這里我們可以使用這兩個(gè)參數(shù)靈活調(diào)整。
剩下的參數(shù)如下:sequence_len指的是訓(xùn)練窗口,nout定義了要預(yù)測(cè)多少步;將sequence_len設(shè)置為180,nout設(shè)置為1,意味著模型將查看180天(半年)后的情況,以預(yù)測(cè)明天將發(fā)生什么。
nhid = 50 # Number of nodes in the hidden layer
n_dnn_layers = 5 # Number of hidden fully connected layers
nout = 1 # Prediction Window
sequence_len = 180 # Training Window
# Number of features (since this is a univariate timeseries we"ll set
# this to 1 -- multivariate analysis is coming in the future)
ninp = 1
# Device selection (CPU | GPU)
USE_CUDA = torch.cuda.is_available()
device = "cuda" if USE_CUDA else "cpu"
# Initialize the model
model = LSTMForecaster(ninp, nhid, nout, sequence_len, n_deep_layers=n_dnn_layers, use_cuda=USE_CUDA).to(device)
模型訓(xùn)練
定義好模型后,我們可以選擇損失函數(shù)和優(yōu)化器,設(shè)置學(xué)習(xí)率和周期數(shù),并開始我們的訓(xùn)練循環(huán)。由于這是一個(gè)回歸問題(即我們?cè)噲D預(yù)測(cè)一個(gè)連續(xù)值),最簡單也是最安全的損失函數(shù)是均方誤差。這提供了一種穩(wěn)健的方法來計(jì)算實(shí)際值和模型預(yù)測(cè)值之間的誤差。
優(yōu)化器和損失函數(shù)如下:
# Set learning rate and number of epochs to train over
lr = 4e-4
n_epochs = 20
# Initialize the loss function and optimizer
criterion = nn.MSELoss().to(device)
optimizer = torch.optim.AdamW(model.parameters(), lr=lr)
下面就是訓(xùn)練循環(huán)的代碼:在每次訓(xùn)練迭代中,我們將計(jì)算之前創(chuàng)建的訓(xùn)練集和驗(yàn)證集的損失:
# Lists to store training and validation losses
t_losses, v_losses = [], []
# Loop over epochs
for epoch in range(n_epochs):
train_loss, valid_loss = 0.0, 0.0
# train step
model.train()
# Loop over train dataset
for x, y in trainloader:
optimizer.zero_grad()
# move inputs to device
x = x.to(device)
y = y.squeeze().to(device)
# Forward Pass
preds = model(x).squeeze()
loss = criterion(preds, y) # compute batch loss
train_loss += loss.item()
loss.backward()
optimizer.step()
epoch_loss = train_loss / len(trainloader)
t_losses.append(epoch_loss)
# validation step
model.eval()
# Loop over validation dataset
for x, y in testloader:
with torch.no_grad():
x, y = x.to(device), y.squeeze().to(device)
preds = model(x).squeeze()
error = criterion(preds, y)
valid_loss += error.item()
valid_loss = valid_loss / len(testloader)
v_losses.append(valid_loss)
print(f" - train: , valid: ")
plot_losses(t_losses, v_losses)
這樣模型已經(jīng)訓(xùn)練好了,可以評(píng)估預(yù)測(cè)了。
推理
我們調(diào)用訓(xùn)練過的模型來預(yù)測(cè)未打亂的數(shù)據(jù),并比較預(yù)測(cè)與真實(shí)觀察有多大不同。
def make_predictions_from_dataloader(model, unshuffled_dataloader):
model.eval()
predictions, actuals = [], []
for x, y in unshuffled_dataloader:
with torch.no_grad():
p = model(x)
predictions.append(p)
actuals.append(y.squeeze())
predictions = torch.cat(predictions).numpy()
actuals = torch.cat(actuals).numpy()
return predictions.squeeze(), actuals
我們的預(yù)測(cè)看起來還不錯(cuò)!預(yù)測(cè)的效果還可以,表明我們沒有過度擬合模型,讓我們看看能否用它來預(yù)測(cè)未來。
預(yù)測(cè)
如果我們將歷史定義為預(yù)測(cè)時(shí)刻之前的序列,算法很簡單:
從歷史(訓(xùn)練窗口長度)中獲取最新的有效序列。
將最新的序列輸入模型并預(yù)測(cè)下一個(gè)值。
將預(yù)測(cè)值附加到歷史記錄上。
迭代重復(fù)步驟1。
這里需要注意的是,根據(jù)訓(xùn)練模型時(shí)選擇的參數(shù),你預(yù)測(cè)的越長(遠(yuǎn)),模型就越容易表現(xiàn)出它自己的偏差,開始預(yù)測(cè)平均值。因此,如果沒有必要,我們不希望總是預(yù)測(cè)得太超前,因?yàn)檫@會(huì)影響預(yù)測(cè)的準(zhǔn)確性。
這在下面的函數(shù)中實(shí)現(xiàn):
def one_step_forecast(model, history):
"""
model: PyTorch model object
history: a sequence of values representing the latest values of the time
series, requirement ->len(history.shape) == 2
outputs a single value which is the prediction of the next value in the
sequence.
"""
model.cpu()
model.eval()
with torch.no_grad():
pre = torch.Tensor(history).unsqueeze(0)
pred = self.model(pre)
return pred.detach().numpy().reshape(-1)
def n_step_forecast(data: pd.DataFrame, target: str, tw: int, n: int, forecast_from: int=None, plot=False):
"""
n: integer defining how many steps to forecast
forecast_from: integer defining which index to forecast from. None if
you want to forecast from the end.
plot: True if you want to output a plot of the forecast, False if not.
"""
history = data[target].copy().to_frame()
# Create initial sequence input based on where in the series to forecast
# from.
if forecast_from:
pre = list(history[forecast_from - tw : forecast_from][target].values)
else:
pre = list(history[self.target])[-tw:]
# Call one_step_forecast n times and append prediction to history
for i, step in enumerate(range(n)):
pre_ = np.array(pre[-tw:]).reshape(-1, 1)
forecast = self.one_step_forecast(pre_).squeeze()
pre.append(forecast)
# The rest of this is just to add the forecast to the correct time of
# the history series
res = history.copy()
ls = [np.nan for i in range(len(history))]
# Note: I have not handled the edge case where the start index + n is
# before the end of the dataset and crosses past it.
if forecast_from:
ls[forecast_from : forecast_from + n] = list(np.array(pre[-n:]))
res["forecast"] = ls
res.columns = ["actual", "forecast"]
else:
fc = ls + list(np.array(pre[-n:]))
ls = ls + [np.nan for i in range(len(pre[-n:]))]
ls[:len(history)] = history[self.target].values
res = pd.DataFrame([ls, fc], index=["actual", "forecast"]).T
return res
我們來看看實(shí)際的效果
我們?cè)谶@個(gè)時(shí)間序列的中間從不同的地方進(jìn)行預(yù)測(cè),這樣我們就可以將預(yù)測(cè)與實(shí)際發(fā)生的情況進(jìn)行比較。我們的預(yù)測(cè)程序,可以從任何地方對(duì)任何合理數(shù)量的步驟進(jìn)行預(yù)測(cè),紅線表示預(yù)測(cè)。(這些圖表顯示的是y軸上的標(biāo)準(zhǔn)化后的價(jià)格)
預(yù)測(cè)2013年第三季度后200天
預(yù)測(cè)2014/15 后200天
從2016年第一季度開始預(yù)測(cè)200天
從數(shù)據(jù)的最后一天開始預(yù)測(cè)200天
總結(jié)
我們這個(gè)模型表現(xiàn)的還算一般!但是我們通過這個(gè)示例完整的介紹了時(shí)間序列預(yù)測(cè)的全部過程,我們可以通過嘗試架構(gòu)和參數(shù)的調(diào)整使模型變得得更好,預(yù)測(cè)得更準(zhǔn)確。
本文只處理單變量時(shí)間序列,其中只有一個(gè)值序列。還有一些方法可以使用多個(gè)系列來進(jìn)行預(yù)測(cè)。這被稱為多元時(shí)間序列預(yù)測(cè),我將在以后的文章中介紹。
本文的代碼在這里:
https://drive.google.com/file/d/1ZzxQISX0519T347j3Sx71iHKsdYDOzcl/view?usp=sharing
作者:Zain Baquar