Approximate method improves inference for regime switching differential systems

Broadly Applicable Approximate MCMC for Switching Stochastic Differential Equations Using Uniformization and Time-Conditioned Factorized Neural Likelihood Estimation

Machine Learning

Summary

Many real-world systems switch between different behaviors over time, like weather patterns or stock markets. These changes can be modeled by switching stochastic differential equations (SSDEs), but figuring out the hidden switching patterns and parameters is very hard. The authors developed a new approximate method using advanced math and neural networks to better estimate these hidden regimes and their dynamics, even when the math behind the system is complex or unknown. They tested their method on made-up data and a real dataset, successfully detecting regime changes where previous approaches struggled.

What this means in practice

  • For financial modelers: Identify hidden regime shifts in financial time series with complex stochastic dynamics using the new approximate inference method.
  • For medical data analysts: Detect regime transitions in physiological data modeled by switching stochastic differential equations without requiring simplified assumptions.

Authors

Shion Hosoda, Michiaki Hamada

Abstract

Switching stochastic differential equations (SSDEs) describe continuous-time dynamics whose parameters switch according to a latent regime process that follows a continuous-time Markov chain (CTMC). By allowing dynamics to change between regimes, SSDEs represent heterogeneous system behavior and have been applied across diverse fields. However, Bayesian inference for SSDEs remains difficult, and existing SSDE inference methods have limited applicability, with restrictions such as noise-free observations, univariate states, linear drift, or state-independent diffusion. In this study, we propose an approximate Markov chain Monte Carlo sampler for SSDEs using uniformization and factorized neural likelihood estimation (FNLE), a simulation-based inference method. Uniformization provides an exact representation of the CTMC but requires SDE transition densities over arbitrary time intervals. We approximate these densities by training a time-conditioned FNLE model. The resulting sampler is broadly applicable to SSDEs without requiring analytically tractable transition densities. In synthetic-data experiments, our method recovered regime paths and parameters for three SSDE models for which previous methods have limited applicability. We also applied our method to a real dataset and detected a regime transition.
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