Neural Markov Jump Processes

• URL: http://arxiv.org/abs/2305.19744v1
• Date: Wed, 31 May 2023 11:10:29 GMT
• Title: Neural Markov Jump Processes
• Authors: Patrick Seifner and Ramses J. Sanchez
• Abstract summary: We introduce an alternative, variational inference algorithm for Markov jump processes which relies on neural ordinary differential equations. 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. We test our approach on synthetic data sampled from ground-truth Markov jump processes, experimental switching ion channel data and molecular dynamics simulations.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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