iTransformer

%load_ext autoreload
%autoreload 2

from fastcore.test import test_eq
from nbdev.showdoc import show_doc

iTransformer模型简单地采用了Transformer架构，但在反向维度上应用了注意力机制和前馈网络。这意味着每个单独系列的时间点被嵌入为标记。这样，注意力机制学习多变量相关性，而前馈网络学习非线性关系。

参考文献 - Yong Liu, Tengge Hu, Haoran Zhang, Haixu Wu, Shiyu Wang, Lintao Ma, Mingsheng Long. “iTransformer: Inverted Transformers Are Effective for Time Series Forecasting”

图 1. iTransformer 的架构.

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

import numpy as np

from math import sqrt

from neuralforecast.losses.pytorch import MAE
from neuralforecast.common._base_multivariate import BaseMultivariate

from neuralforecast.common._modules import TransEncoder, TransEncoderLayer, AttentionLayer

1. 辅助函数

1.1 注意力

class 三角因果掩码():
    """
    三角因果掩码
    """      
    def __init__(self, B, L, device="cpu"):
        mask_shape = [B, 1, L, L]
        with torch.no_grad():
            self._mask = torch.triu(torch.ones(mask_shape, dtype=torch.bool), diagonal=1).to(device)

    @property
    def mask(self):
        return self._mask

class 全神贯注(nn.Module):
    """
    全神贯注
    """  
    def __init__(self, mask_flag=True, factor=5, scale=None, attention_dropout=0.1, output_attention=False):
        super(全神贯注, self).__init__()
        self.scale = scale
        self.mask_flag = mask_flag
        self.output_attention = output_attention
        self.dropout = nn.Dropout(attention_dropout)

    def forward(self, queries, keys, values, attn_mask, tau=None, delta=None):
        B, L, H, E = queries.shape
        _, S, _, D = values.shape
        scale = self.scale or 1. / sqrt(E)

        scores = torch.einsum("blhe,bshe->bhls", queries, keys)

        if self.mask_flag:
            if attn_mask is None:
                attn_mask = 三角因果掩码(B, L, device=queries.device)

            scores.masked_fill_(attn_mask.mask, -np.inf)

        A = self.dropout(torch.softmax(scale * scores, dim=-1))
        V = torch.einsum("bhls,bshd->blhd", A, values)

        if self.output_attention:
            return (V.contiguous(), A)
        else:
            return (V.contiguous(), None)      

1.2 反向嵌入

class 数据嵌入_倒置(nn.Module):
    """
    数据嵌入_倒置
    """       
    def __init__(self, c_in, hidden_size, dropout=0.1):
        super(数据嵌入_倒置, self).__init__()
        self.value_embedding = nn.Linear(c_in, hidden_size)
        self.dropout = nn.Dropout(p=dropout)

    def forward(self, x, x_mark):
        x = x.permute(0, 2, 1)
        # x: [批次变量时间]
        if x_mark is None:
            x = self.value_embedding(x)
        else:
            # 具备将协变量（如时间戳）作为标记的潜力
            x = self.value_embedding(torch.cat([x, x_mark.permute(0, 2, 1)], 1)) 
        # x: [批次变量 隐藏层大小]
        return self.dropout(x)

2. 模型

class iTransformer(BaseMultivariate):

    """ iTransformer

    **Parameters:**<br>
    `h`: int, Forecast horizon. <br>
    `input_size`: int, autorregresive inputs size, y=[1,2,3,4] input_size=2 -> y_[t-2:t]=[1,2].<br>
    `n_series`: int, number of time-series.<br>
    `futr_exog_list`: str list, future exogenous columns.<br>
    `hist_exog_list`: str list, historic exogenous columns.<br>
    `stat_exog_list`: str list, static exogenous columns.<br>
    `hidden_size`: int, dimension of the model.<br>
    `n_heads`: int, number of heads.<br>
    `e_layers`: int, number of encoder layers.<br>
    `d_layers`: int, number of decoder layers.<br>
    `d_ff`: int, dimension of fully-connected layer.<br>
    `factor`: int, attention factor.<br>
    `dropout`: float, dropout rate.<br>
    `use_norm`: bool, whether to normalize or not.<br>
    `loss`: PyTorch module, instantiated train loss class from [losses collection](https://nixtla.github.io/neuralforecast/losses.pytorch.html).<br>
    `valid_loss`: PyTorch module=`loss`, instantiated valid loss class from [losses collection](https://nixtla.github.io/neuralforecast/losses.pytorch.html).<br>
    `max_steps`: int=1000, maximum number of training steps.<br>
    `learning_rate`: float=1e-3, Learning rate between (0, 1).<br>
    `num_lr_decays`: int=-1, Number of learning rate decays, evenly distributed across max_steps.<br>
    `early_stop_patience_steps`: int=-1, Number of validation iterations before early stopping.<br>
    `val_check_steps`: int=100, Number of training steps between every validation loss check.<br>
    `batch_size`: int=32, number of different series in each batch.<br>
    `step_size`: int=1, step size between each window of temporal data.<br>
    `scaler_type`: str='identity', type of scaler for temporal inputs normalization see [temporal scalers](https://nixtla.github.io/neuralforecast/common.scalers.html).<br>
    `random_seed`: int=1, random_seed for pytorch initializer and numpy generators.<br>
    `num_workers_loader`: int=os.cpu_count(), workers to be used by `TimeSeriesDataLoader`.<br>
    `drop_last_loader`: bool=False, if True `TimeSeriesDataLoader` drops last non-full batch.<br>
    `alias`: str, optional,  Custom name of the model.<br>
    `optimizer`: Subclass of 'torch.optim.Optimizer', optional, user specified optimizer instead of the default choice (Adam).<br>
    `optimizer_kwargs`: dict, optional, list of parameters used by the user specified `optimizer`.<br>
    `lr_scheduler`: Subclass of 'torch.optim.lr_scheduler.LRScheduler', optional, user specified lr_scheduler instead of the default choice (StepLR).<br>
    `lr_scheduler_kwargs`: dict, optional, list of parameters used by the user specified `lr_scheduler`.<br>
    `**trainer_kwargs`: int,  keyword trainer arguments inherited from [PyTorch Lighning's trainer](https://pytorch-lightning.readthedocs.io/en/stable/api/pytorch_lightning.trainer.trainer.Trainer.html?highlight=trainer).<br>
    
    **References**<br>
    - [Yong Liu, Tengge Hu, Haoran Zhang, Haixu Wu, Shiyu Wang, Lintao Ma, Mingsheng Long. "iTransformer: Inverted Transformers Are Effective for Time Series Forecasting"](https://arxiv.org/abs/2310.06625)
    """

    # Class attributes
    SAMPLING_TYPE = 'multivariate'
    EXOGENOUS_FUTR = False
    EXOGENOUS_HIST = False
    EXOGENOUS_STAT = False

    def __init__(self,
                 h,
                 input_size,
                 n_series,
                 futr_exog_list = None,
                 hist_exog_list = None,
                 stat_exog_list = None,
                 hidden_size: int = 512,
                 n_heads: int = 8,
                 e_layers: int = 2,
                 d_layers: int = 1,
                 d_ff: int = 2048,
                 factor: int = 1,
                 dropout: float = 0.1,
                 use_norm: bool = True,
                 loss = MAE(),
                 valid_loss = None,
                 max_steps: int = 1000,
                 learning_rate: float = 1e-3,
                 num_lr_decays: int = -1,
                 early_stop_patience_steps: int =-1,
                 val_check_steps: int = 100,
                 batch_size: int = 32,
                 step_size: int = 1,
                 scaler_type: str = 'identity',
                 random_seed: int = 1,
                 num_workers_loader: int = 0,
                 drop_last_loader: bool = False,
                 optimizer = None,
                 optimizer_kwargs = None,
                 lr_scheduler = None,
                 lr_scheduler_kwargs = None,            
                 **trainer_kwargs):
        
        super(iTransformer, self).__init__(h=h,
                                           input_size=input_size,
                                           n_series=n_series,
                                           stat_exog_list = None,
                                           futr_exog_list = None,
                                           hist_exog_list = None,
                                           loss=loss,
                                           valid_loss=valid_loss,
                                           max_steps=max_steps,
                                           learning_rate=learning_rate,
                                           num_lr_decays=num_lr_decays,
                                           early_stop_patience_steps=early_stop_patience_steps,
                                           val_check_steps=val_check_steps,
                                           batch_size=batch_size,
                                           step_size=step_size,
                                           scaler_type=scaler_type,
                                           random_seed=random_seed,
                                           num_workers_loader=num_workers_loader,
                                           drop_last_loader=drop_last_loader,
                                           optimizer=optimizer,
                                           optimizer_kwargs=optimizer_kwargs,
                                           lr_scheduler=lr_scheduler,
                                           lr_scheduler_kwargs=lr_scheduler_kwargs,
                                           **trainer_kwargs)
               
        self.enc_in = n_series
        self.dec_in = n_series
        self.c_out = n_series
        self.hidden_size = hidden_size
        self.n_heads = n_heads
        self.e_layers = e_layers
        self.d_layers = d_layers
        self.d_ff = d_ff
        self.factor = factor
        self.dropout = dropout
        self.use_norm = use_norm

        # Architecture
        self.enc_embedding = DataEmbedding_inverted(input_size, self.hidden_size, self.dropout)

        self.encoder = TransEncoder(
            [
                TransEncoderLayer(
                    AttentionLayer(
                        FullAttention(False, self.factor, attention_dropout=self.dropout), self.hidden_size, self.n_heads),
                    self.hidden_size,
                    self.d_ff,
                    dropout=self.dropout,
                    activation=F.gelu
                ) for l in range(self.e_layers)
            ],
            norm_layer=torch.nn.LayerNorm(self.hidden_size)
        )

        self.projector = nn.Linear(self.hidden_size, h, bias=True)
    
    def forecast(self, x_enc):
        if self.use_norm:
            # Normalization from Non-stationary Transformer
            means = x_enc.mean(1, keepdim=True).detach()
            x_enc = x_enc - means
            stdev = torch.sqrt(torch.var(x_enc, dim=1, keepdim=True, unbiased=False) + 1e-5)
            x_enc /= stdev

        _, _, N = x_enc.shape # B L N
        # B: batch_size;       E: hidden_size; 
        # L: input_size;       S: horizon(h);
        # N: number of variate (tokens), can also includes covariates

        # Embedding
        # B L N -> B N E                (B L N -> B L E in the vanilla Transformer)
        enc_out = self.enc_embedding(x_enc, None) # covariates (e.g timestamp) can be also embedded as tokens
        
        # B N E -> B N E                (B L E -> B L E in the vanilla Transformer)
        # the dimensions of embedded time series has been inverted, and then processed by native attn, layernorm and ffn modules
        enc_out, attns = self.encoder(enc_out, attn_mask=None)

        # B N E -> B N S -> B S N 
        dec_out = self.projector(enc_out).permute(0, 2, 1)[:, :, :N] # filter the covariates

        if self.use_norm:
            # De-Normalization from Non-stationary Transformer
            dec_out = dec_out * (stdev[:, 0, :].unsqueeze(1).repeat(1, self.h, 1))
            dec_out = dec_out + (means[:, 0, :].unsqueeze(1).repeat(1, self.h, 1))

        return dec_out
    
    def forward(self, windows_batch):
        insample_y = windows_batch['insample_y']

        y_pred = self.forecast(insample_y)
        y_pred = y_pred[:, -self.h:, :]
        y_pred = self.loss.domain_map(y_pred)

        # 在 n_series == 1 的情况下，domain_map 可能已经压缩了最后一个维度。
        if y_pred.ndim == 2:
            return y_pred.unsqueeze(-1)
        else:
            return y_pred

show_doc(iTransformer)

show_doc(iTransformer.fit, name='iTransformer.fit')

show_doc(iTransformer.predict, name='iTransformer.predict')

3. 使用示例

import pandas as pd
import matplotlib.pyplot as plt

from neuralforecast import NeuralForecast
from neuralforecast.models import iTransformer
from neuralforecast.utils import AirPassengersPanel, AirPassengersStatic
from neuralforecast.losses.pytorch import MSE

Y_train_df = AirPassengersPanel[AirPassengersPanel.ds<AirPassengersPanel['ds'].values[-12]].reset_index(drop=True) # 132次列车
Y_test_df = AirPassengersPanel[AirPassengersPanel.ds>=AirPassengersPanel['ds'].values[-12]].reset_index(drop=True) # 12项测试

model = iTransformer(h=12,
                     input_size=24,
                     n_series=2,
                     hidden_size=128,
                     n_heads=2,
                     e_layers=2,
                     d_layers=1,
                     d_ff=4,
                     factor=1,
                     dropout=0.1,
                     use_norm=True,
                     loss=MSE(),
                     valid_loss=MAE(),
                     early_stop_patience_steps=3,
                     batch_size=32)

fcst = NeuralForecast(models=[model], freq='M')
fcst.fit(df=Y_train_df, static_df=AirPassengersStatic, val_size=12)
forecasts = fcst.predict(futr_df=Y_test_df)

# 剧情预测
fig, ax = plt.subplots(1, 1, figsize = (20, 7))
Y_hat_df = forecasts.reset_index(drop=False).drop(columns=['unique_id','ds'])
plot_df = pd.concat([Y_test_df, Y_hat_df], axis=1)
plot_df = pd.concat([Y_train_df, plot_df])

plot_df = plot_df[plot_df.unique_id=='Airline1'].drop('unique_id', axis=1)
plt.plot(plot_df['ds'], plot_df['y'], c='black', label='True')
plt.plot(plot_df['ds'], plot_df['iTransformer'], c='blue', label='Forecast')
ax.set_title('AirPassengers Forecast', fontsize=22)
ax.set_ylabel('Monthly Passengers', fontsize=20)
ax.set_xlabel('Year', fontsize=20)
ax.legend(prop={'size': 15})
ax.grid()

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