提出高效推断连续时间隐马尔可夫链耦合系统的新方法
Efficient Inference for Coupled Hidden Markov Models in Continuous Time and Discrete Space
- 用粒子系统参数化马尔可夫链生成器，实现高效建模
- 引入前瞻函数估算未来观测信息，提升推断精度
- 适用于复杂网络和真实数据的动态建模，如疫情与火灾扩散
相互作用的连续时间马尔可夫链系统是一类强大的模型，但在高维情况下推断通常不可行。典型情况是仅在离散时间点获得含噪观测，通过Doob's h-变换引入后验过程，导致难以处理。本文提出潜伏交互粒子系统，参数化每个马尔可夫链的生成器。推断方法包括估计预测未来信息的前瞻函数（扭曲势），并引入高效参数化方式。将该近似融入扭曲的序贯蒙特卡洛采样框架。在图上潜伏SIRS模型的后验推断任务以及基于真实数据训练的野火传播神经模型中验证了方法的有效性。
原文摘要 · Abstract (English)
Systems of interacting continuous-time Markov chains are a powerful model class, but inference is typically intractable in high dimensional settings. Auxiliary information, such as noisy observations, is typically only available at discrete times, and incorporating it via a Doob's $h$-transform gives rise to an intractable posterior process that requires approximation. We introduce Latent Interacting Particle Systems, a model class parameterizing the generator of each Markov chain in the system. Our inference method involves estimating look-ahead functions (twist potentials) that anticipate future information, for which we introduce an efficient parameterization. We incorporate this approximation in a twisted Sequential Monte Carlo sampling scheme. We demonstrate the effectiveness of our approach on a challenging posterior inference task for a latent SIRS model on a graph, and on a neural model for wildfire spread dynamics trained on real data.
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