arXiv：cs.LG· Shion Hosoda, Michiaki Hamada·· 4 小时前AI 评分30
利用均匀化与时间条件因子化神经似然估计实现广泛适用的切换随机微分方程近似 MCMC
Broadly Applicable Approximate MCMC for Switching Stochastic Differential Equations Using Uniformization and Time-Conditioned Factorized Neural Likelihood Estimation
AI 导读
研究提出一种针对切换随机微分方程（SSDE）的近似 MCMC 采样器，结合均匀化与因子化神经似然估计（FNLE）。该方法无需解析可解的转移密度，可用于含噪声观测、多元状态等场景。在合成数据实验中，它成功恢复了三个此前方法适用性有限的 SSDE 模型的 regime 路径与参数，并在真实数据集上检测到一次 regime 转换。
正文
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.
| Subjects: | Machine Learning (stat.ML); Machine Learning (cs.LG) |
| Cite as: | arXiv:2610.10194 [stat.ML] |
| (or arXiv:2610.10194v1 [stat.ML] for this version) | |
| https://doi.org/10.48550/arXiv.2610.10194 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Shion Hosoda [view email]
[v1]
Wed, 7 Oct 2026 14:56:12 UTC (4,847 KB)
来源：arXiv：cs.LG · arxiv.org