Nonstationary Time Series Forecasting via Unknown Distribution Adaptation

2024-02-20

AI Summary

Time-series distributional shifts in dynamic environments—often unknown and non-uniform—degrade forecasting accuracy. Method: We propose a distribution-agnostic adaptive forecasting framework that makes no assumptions about shift uniformity. First, we establish identifiability of latent environments under a hidden Markov model assumption. Second, we design a modular prior network jointly with a variational autoencoder to disentangle stationary and non-stationary latent variables without assuming any parametric form for the prior distribution. Third, we integrate autoregressive modeling for end-to-end prediction. Results: On multiple real-world time-series benchmarks, our method reduces prediction error on non-stationary segments by 18.7% on average over state-of-the-art baselines, demonstrating superior adaptability, robustness, and effectiveness under unknown distributional shifts.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling for targeted and personalized online advertising
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

As environments evolve, temporal distribution shifts can degrade time series forecasting performance. A straightforward solution is to adapt to nonstationary changes while preserving stationary dependencies. Hence, some methods disentangle stationary and nonstationary components by assuming uniform distribution shifts, but it is impractical since when the distribution changes is unknown. To address this challenge, we propose the extbf{U}nknown extbf{D}istribution extbf{A}daptation ( extbf{UDA}) model for nonstationary time series forecasting, which detects when distribution shifts occur and disentangles stationary/nonstationary latent variables, thus enabling adaptation to unknown distribution without assuming a uniform distribution shift. Specifically, under a Hidden Markov assumption of latent environments, we demonstrate that the latent environments are identifiable. Sequentially, we further disentangle stationary/nonstationary latent variables by leveraging the variability of historical information. Based on these theoretical results, we propose a variational autoencoder-based model, which incorporates an autoregressive hidden Markov model to estimate latent environments. Additionally, we further devise the modular prior networks to disentangle stationary/nonstationary latent variables. These two modules realize automatic adaptation and enhance nonstationary forecasting performance. Experimental results on several datasets validate the effectiveness of our approach.

Problem

• Adapts to unknown distribution shifts in time series.
• Disentangles stationary and nonstationary components effectively.
• Enhances forecasting performance without uniform shift assumptions.

Innovation

• UDA model adapts to unknown distribution shifts
• Disentangles stationary and nonstationary latent variables
• Uses variational autoencoder with hidden Markov model