  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.
