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

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.

References in corpus (10)

• Alternating minimal energy methods for linear systems in higher dimensions. Part I: SPD systems
• Alternating minimal energy methods for linear systems in higher dimensions. Part II: Faster algorithm and application to nonsymmetric systems
• Pooling single-cell recordings: Scalable inference through heterogeneous kinetics
• Spectral tensor-train decomposition
• Inference for reaction networks using the Linear Noise Approximation
• A finite state projection algorithm for the stationary solution of the chemical master equation
• MCMC inference for Markov Jump Processes via the Linear Noise Approximation
• Perfect Sampling of the Master Equation for Gene Regulatory Networks
• Parameter estimation for biochemical reaction networks using Wasserstein distances
• A variational approach to moment-closure approximations for the kinetics of biomolecular reaction networks

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