发表机构
Waseda University; National Institute of Advanced Industrial Science and Technology; Nippon Medical School（早稻田大学; 日本产业技术综合研究所; 日本医科大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出一种基于均匀化和时间条件化因子化神经似然估计的近似MCMC采样器，用于切换随机微分方程的贝叶斯推断，无需解析转移密度，并在合成与真实数据上验证了其广泛适用性。
AI 中文摘要
切换随机微分方程（SSDEs）描述的是连续时间动态系统，其参数根据一个遵循连续时间马尔可夫链（CTMC）的潜在状态过程进行切换。通过允许动态在不同状态之间变化，SSDEs能够表示异质的系统行为，并已应用于多个不同领域。然而，对SSDEs进行贝叶斯推断仍然困难，且现有的SSDE推断方法适用性有限，存在诸如无噪声观测、单变量状态、线性漂移或状态无关扩散等限制。在本研究中，我们提出了一种基于均匀化和因子化神经似然估计（FNLE）的SSDE近似马尔可夫链蒙特卡洛采样器，FNLE是一种基于模拟的推断方法。均匀化提供了CTMC的精确表示，但需要任意时间间隔内的SDE转移密度。我们通过训练一个时间条件化的FNLE模型来近似这些密度。所得到的采样器广泛适用于SSDEs，无需解析可处理的转移密度。在合成数据实验中，我们的方法恢复了三个先前方法适用性有限的SSDE模型的状态路径和参数。我们还将该方法应用于真实数据集，并检测到一次状态转换。
英文摘要
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.
