When and How: Learning Identifiable Latent States for Nonstationary Time Series Forecasting
CoRR(2024)
摘要
Temporal distribution shifts are ubiquitous in time series data. One of the
most popular methods assumes that the temporal distribution shift occurs
uniformly to disentangle the stationary and nonstationary dependencies. But
this assumption is difficult to meet, as we do not know when the distribution
shifts occur. To solve this problem, we propose to learn IDentifiable latEnt
stAtes (IDEA) to detect when the distribution shifts occur. Beyond that, we
further disentangle the stationary and nonstationary latent states via
sufficient observation assumption to learn how the latent states change.
Specifically, we formalize the causal process with environment-irrelated
station- ary and environment-related nonstationary variables. Under mild
conditions, we show that latent environments and stationary/nonstationary
variables are identifiable. Based on these theories, we devise the IDEA model,
which incorporates an autoregressive hidden Markov model to estimate latent
environments and modular prior networks to identify latent states. The IDEA
model outperforms several latest nonstationary forecasting methods on various
benchmark datasets, highlighting its advantages in real-world scenarios.
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