Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are naturally described in continuous time, we present a model based on an Markov jump process modulating a subordinated diffusion process. We provide the exact evolution equations for the prior and posterior marginal densities, the direct solutions of which are however computationally intractable. Therefore, we develop a new continuous-time variational inference algorithm, combining a Gaussian process approximation on the diffusion level with posterior inference for Markov jump processes. By minimizing the path-wise Kullback-Leibler divergence we obtain (i) Bayesian latent state estimates for arbitrary points on the real axis and (ii) point estimates of unknown system parameters, utilizing variational expectation maximization. We extensively evaluate our algorithm under the model assumption and for real-world examples.
翻译:由于生物学或离散活动系统等许多领域自然地在连续时间描述,我们提出了一个基于Markov跳跃过程的模型,以调控一个次要扩散过程。我们为先前和后边边缘密度提供了精确的进化方程,这些边际密度的直接解决办法在计算上是难以做到的。因此,我们开发了一种新的连续时间变换算法,将扩散水平的高斯进程近似值与Markov跳跃过程的远地点推法结合在一起。我们通过尽量减少从路到Kullback-Leibell的差异,我们获得了(一) 巴伊西亚对实际轴任意点的潜在状态估计,和(二) 对未知系统参数的点估计,利用变式预期最大化。我们根据模型假设和真实世界实例对我们的算法进行了广泛的评价。