论文标题
马尔可夫链蒙特卡洛用于连续时间开关动态系统
Markov Chain Monte Carlo for Continuous-Time Switching Dynamical Systems
论文作者
论文摘要
开关动态系统是用于分析时间序列数据的表达模型类。就像在自然和工程科学中的许多领域一样，研究系统通常会及时不断发展，自然要考虑由基础马尔可夫跳跃过程控制的连续时间模型配方，包括切换随机微分方程。但是，这些类型的模型的推断很难，而且易于处理的计算方案很少见。在这项工作中，我们提出了一种使用马尔可夫链蒙特卡洛方法的新型推理算法。提出的Gibbs采样器允许从确切的连续时间后验过程中有效获取样品。我们的框架自然可以实现贝叶斯参数估计，我们还包括扩散协方差的估计值，这通常假定在随机微分方程模型中固定。我们在建模假设下评估我们的框架，并将其与现有的变分推理方法进行比较。
Switching dynamical systems are an expressive model class for the analysis of time-series data. As in many fields within the natural and engineering sciences, the systems under study typically evolve continuously in time, it is natural to consider continuous-time model formulations consisting of switching stochastic differential equations governed by an underlying Markov jump process. Inference in these types of models is however notoriously difficult, and tractable computational schemes are rare. In this work, we propose a novel inference algorithm utilizing a Markov Chain Monte Carlo approach. The presented Gibbs sampler allows to efficiently obtain samples from the exact continuous-time posterior processes. Our framework naturally enables Bayesian parameter estimation, and we also include an estimate for the diffusion covariance, which is oftentimes assumed fixed in stochastic differential equation models. We evaluate our framework under the modeling assumption and compare it against an existing variational inference approach.
