Markov jump processes are continuous-time stochastic processes widely used in statistical applications in the natural sciences, and more recently in machine learning. Inference for these models typically proceeds via Markov chain Monte Carlo, and can suffer from various computational challenges. In this work, we propose a novel collapsed variational inference algorithm to address this issue. Our work leverages ideas from discrete-time Markov chains, and exploits a connection between these two through an idea called uniformization.

The authors present a variational inference algorithm for continuous time Markov jump processes. Following previous work, they use "uniformization" to produce a discrete time skeleton at which they infer the latent states. Unlike previous work, however, the authors propose to learn this skeleton (a point estimate, via random search) and to integrate out, or collapse, the transition matrix during latent state inference. They compare their algorithm to existing MCMC schemes, which also use uniformization, but which do not collapse out the transition matrix. While this work is well motivated, I found it difficult to tease out which elements of the inference algorithm led to the observed improvement.

Markov jump processes are continuous-time stochastic processes widely used in statistical applications in the natural sciences, and more recently in machine learning. Inference for these models typically proceeds via Markov chain Monte Carlo, and can suffer from various computational challenges. In this work, we propose a novel collapsed variational inference algorithm to address this issue. Our work leverages ideas from discrete-time Markov chains, and exploits a connection between these two through an idea called uniformization. We apply our ideas to synthetic data as well as a dataset of check-in recordings, where we demonstrate superior performance over state-of-the-art MCMC methods.