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Title: Estimating continuous-time Markov chain transition rate functions with neural networks Authors:  Majerle Reeves - University of California, Merced (United States) [presenting]
Harish Bhat - University of California, Merced (United States)
Abstract: Continuous-time Markov chains are used to model stochastic systems where transitions can occur at irregular times, e.g., chemical reaction networks, population dynamics, and gene regulatory networks. We develop a method to learn a continuous-time Markov chain's transition rate functions from a fully observed time series. In contrast with existing methods, our method allows for transition rates to depend nonlinearly on both state variables and external covariates. The Gillespie algorithm is used for generating trajectories of stochastic systems where propensity functions (reaction rates) are known. Our method can be viewed as the inverse: given trajectories of a stochastic reaction network, we generate estimates of the propensity functions. While previous methods used linear or log-linear methods to link transition rates to covariates, we use neural networks, increasing the capacity and potential accuracy of learned models. In the chemical context, this enables the method to learn propensity functions from non-mass-action kinetics. We test our method with synthetic data generated from a variety of systems with known transition rates. We show that our method learns these transition rates accurately, both in terms of mean absolute error between ground truth and learned transition rates, and in terms of the statistics of true and predicted trajectories.