🤖 AI Summary
This work addresses the intractability of exact Bayesian inference for latent states in continuous-time Markov jump processes—such as chemical reaction networks and stochastic Lotka–Volterra systems. We propose an analytically tractable expectation propagation (EP) framework grounded in entropy matching: by embedding entropy matching into the EP formalism, we derive closed-form approximations to the latent-state posterior distribution and integrate them with an approximate EM algorithm for efficient parameter estimation. Our approach overcomes the high computational complexity and poor scalability inherent in conventional methods for discrete-state continuous-time models. Evaluated on multiple systems biology benchmarks, the method achieves high-accuracy latent-state inference and parameter estimation while significantly improving computational scalability and practical applicability.
📝 Abstract
This paper addresses the problem of statistical inference for latent continuous-time stochastic processes, which is often intractable, particularly for discrete state space processes described by Markov jump processes. To overcome this issue, we propose a new tractable inference scheme based on an entropic matching framework that can be embedded into the well-known expectation propagation algorithm. We demonstrate the effectiveness of our method by providing closed-form results for a simple family of approximate distributions and apply it to the general class of chemical reaction networks, which are a crucial tool for modeling in systems biology. Moreover, we derive closed form expressions for point estimation of the underlying parameters using an approximate expectation maximization procedure. We evaluate the performance of our method on various chemical reaction network instantiations, including a stochastic Lotka-Voltera example, and discuss its limitations and potential for future improvements. Our proposed approach provides a promising direction for addressing complex continuous-time Bayesian inference problems.