## Abstract

We consider a problem of inferring contact network from nodal states observed during an epidemiological process. In a black-box Bayesian optimisation framework this problem reduces to a discrete likelihood optimisation over the set of possible networks. The cardinality of this set grows combinatorially with the number of network nodes, which makes this optimisation computationally challenging. For each network, its likelihood is the probability for the observed data to appear during the evolution of the epidemiological process on this network. This probability can be very small, particularly if the network is significantly different from the ground truth network, from which the observed data actually appear. A commonly used stochastic simulation algorithm struggles to recover rare events and hence to estimate small probabilities and likelihoods. In this paper we replace the stochastic simulation with solving the chemical master equation for the probabilities of all network states. Since this equation also suffers from the curse of dimensionality, we apply tensor train approximations to overcome it and enable fast and accurate computations. Numerical simulations demonstrate efficient black-box Bayesian inference of the network.

Original language | English |
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Article number | 285 |

Journal | BMC Bioinformatics |

Volume | 25 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2 Sept 2024 |

### Data Availability Statement

Numerical experiments in this work are based on synthetic randomly generated datasets. All data and code required to reproduce experiments are available on github.com/savostyanov/ttsir.## Keywords

- 15A69
- 34A30
- 37N25
- 60J28
- 62F15
- 65F55
- 90B15
- 95C42
- Bayesian inference
- Epidemiological modelling
- Markov chain Monte Carlo
- Networks
- Stochastic simulation algorithm
- Tensor train

## ASJC Scopus subject areas

- Structural Biology
- Biochemistry
- Molecular Biology
- Computer Science Applications
- Applied Mathematics