Neural Markov Jump Processes
This work addresses a challenging inference problem in continuous-time stochastic processes for researchers in natural and social sciences, but it appears incremental as it builds on existing variational and neural methods.
The authors tackled the problem of inference in Markov jump processes by introducing a variational inference algorithm using neural ordinary differential equations, achieving results that were tested on synthetic, experimental, and simulation data.
Markov jump processes are continuous-time stochastic processes with a wide range of applications in both natural and social sciences. Despite their widespread use, inference in these models is highly non-trivial and typically proceeds via either Monte Carlo or expectation-maximization methods. In this work we introduce an alternative, variational inference algorithm for Markov jump processes which relies on neural ordinary differential equations, and is trainable via back-propagation. Our methodology learns neural, continuous-time representations of the observed data, that are used to approximate the initial distribution and time-dependent transition probability rates of the posterior Markov jump process. The time-independent rates of the prior process are in contrast trained akin to generative adversarial networks. We test our approach on synthetic data sampled from ground-truth Markov jump processes, experimental switching ion channel data and molecular dynamics simulations. Source code to reproduce our experiments is available online.