[论文解读] Think Globally, Act Locally: A Deep Neural Network Approach to High-Dimensional Time Series Forecasting

Rajat Sen, Hsiang‐Fu Yu+1 more|arXiv (Cornell University)|May 9, 2019

Stock Market Forecasting Methods参考文献 23被引用 95

一句话总结

DeepGLO 将全局时序卷积基础的矩阵分解与本地每序列模型相结合，用于预测超高维时间序列，在不进行大量每序列归一化的前提下实现强劲性能提升和可扩展性。

ABSTRACT

Forecasting high-dimensional time series plays a crucial role in many applications such as demand forecasting and financial predictions. Modern datasets can have millions of correlated time-series that evolve together, i.e they are extremely high dimensional (one dimension for each individual time-series). There is a need for exploiting global patterns and coupling them with local calibration for better prediction. However, most recent deep learning approaches in the literature are one-dimensional, i.e, even though they are trained on the whole dataset, during prediction, the future forecast for a single dimension mainly depends on past values from the same dimension. In this paper, we seek to correct this deficiency and propose DeepGLO, a deep forecasting model which thinks globally and acts locally. In particular, DeepGLO is a hybrid model that combines a global matrix factorization model regularized by a temporal convolution network, along with another temporal network that can capture local properties of each time-series and associated covariates. Our model can be trained effectively on high-dimensional but diverse time series, where different time series can have vastly different scales, without a priori normalization or rescaling. Empirical results demonstrate that DeepGLO can outperform state-of-the-art approaches; for example, we see more than 25% improvement in WAPE over other methods on a public dataset that contains more than 100K-dimensional time series.

研究动机与目标

• 为彼此共同演化的百万级时间序列数据集提供准确预测的动机。
• 开发一个模型，能够捕捉全局模式，同时为每个序列提供本地校准。
• 在高维数据上实现稳定训练，而无需对各序列进行先验归一化。

提出的方法

• 引入 Temporal Convolution Networks 的 LeveledInit，以在不进行先验归一化的情况下处理多样化尺度。
• 提出 TCN-MF：将 Y(tr) 进行低秩分解为 F 和 X(tr)，并通过 Temporal Convolution Network 正则化，以在 X 中促进时间结构。
• 开发混合模型 DeepGLO：将全局模型输出用作局部 TCN 的协变量，从而实现全局与局部的联合预测。
• 全局训练，使用小批量 SGD，并在因子矩阵与时序网络之间交替优化。
• 提供滚动和多步前瞻预测框架，不需要为每个窗口重新训练。

实验结果

研究问题

• RQ1 多个时间序列的全局低秩表示是否能有效捕捉共享的时间模式？
• RQ2 将全局 TCN-正则化矩阵分解与本地逐序列网络相结合，是否在预测准确性上优于最先进方法？
• RQ3 该模型是否能扩展到非常高维的数据集（例如>100K 时间序列）并且对尺度变化具有鲁棒性且无需预处理归一化？

主要发现

算法	electricity normalized	electricity unnormalized	traffic normalized	traffic unnormalized	wiki normalized	wiki unnormalized
DeepGLO (Unnormalized)	0.133/0.453/0.162	0.082/0.341/0.121	0.166/0.210/0.179	0.148/0.168/0.142	0.569/3.335/1.036	0.237/0.441/0.395
DeepGLO (Normalized)	0.133/0.453/0.162	0.082/0.341/0.121	0.166/0.210/0.179	0.148/0.168/0.142	0.569/3.335/1.036	0.237/0.441/0.395
Local TCN (LeveledInit)	0.143/0.356/0.207	0.092/0.237/0.126	0.157/0.201/0.156	0.169/0.177/0.169	0.243/0.545/0.431	0.212/0.316/0.296
Global TCN-MF	0.144/0.485/0.174	0.106/0.525/0.188	0.336/0.415/0.451	0.226/0.284/0.247	1.19/8.46/1.56	0.433/1.59/0.686
Local-Only LSTM	0.109/0.264/0.154	0.896/0.672/0.768	0.276/0.389/0.361	0.270/0.357/0.263	0.427/2.170/0.590	0.789/0.686/0.493
DeepAR	0.086/0.259/0.141	0.994/0.818/1.85	0.140/0.201/0.114	0.211/0.331/0.267	0.429/2.980/0.424	0.993/8.120/1.475
TCN (no LeveledInit)	0.147/0.476/0.156	0.423/0.769/0.523	0.204/0.284/0.236	0.239/0.425/0.281	0.336/1.322/0.497	0.511/0.884/0.509
Prophet	0.197/0.393/0.221	0.221/0.586/0.524	0.313/0.600/0.420	0.303/0.559/0.403	-	-
TRMF (retrained)	0.104/0.280/0.151	0.105/0.431/0.183	0.159/0.226/0.181	0.210/0.322/0.275	0.309/0.847/0.451	0.320/0.938/0.503
SVD+TCN	0.219/0.437/0.238	0.368/0.779/0.346	0.468/0.841/0.580	0.329/0.687/0.340	0.697/3.51/0.886	0.639/2.000/0.893
STGCN (Cheb)	-	-	-	-	-	-
STGCN (First)	-	-	-	-	-	-

• DeepGLO 在四个真实世界数据集上优于基线，包括一个维度超过 110K 的公开 wiki 数据集。
• 在一个大型高维数据集上，相较其他方法，WAPE 提升超过 25% 的结果被报道。
• LeveledInit 使 Temporal Convolution Networks 在跨越多样化时间序列时无需先验归一化即可实现可靠训练。
• 全局 TCN-MF 模型捕捉全局模式，且支持滚动预测无需重新训练。
• DeepGLO 的混合设计允许滚动预测和多步前瞻，无需频繁重新训练，从而提升可扩展性。