Tensor-train approximation of the chemical master equation and its application for parameter inference

TL;DR

This paper introduces a tensor-train based approach to efficiently perform Bayesian inference for the chemical master equation, enabling high-dimensional data representation, parameter dependency incorporation, and significant computational savings.

Contribution

The work develops a tensor-train framework for the chemical master equation, allowing efficient high-dimensional data representation and parameter inference with reduced computational cost.

Findings

High compression ratio for probability mass function storage

Significant reduction in computational time

Effective incorporation of parameter dependence

Abstract

In this work, we perform Bayesian inference tasks for the chemical master equation in the tensor-train format. The tensor-train approximation has been proven to be very efficient in representing high dimensional data arising from the explicit representation of the chemical master equation solution. An additional advantage of representing the probability mass function in the tensor train format is that parametric dependency can be easily incorporated by introducing a tensor product basis expansion in the parameter space. Time is treated as an additional dimension of the tensor and a linear system is derived to solve the chemical master equation in time. We exemplify the tensor-train method by performing inference tasks such as smoothing and parameter inference using the tensor-train framework. A very high compression ratio is observed for storing the probability mass function of the solution. Since all linear algebra operations are performed in the tensor-train format, a significant reduction of the computational time is observed as well.