Tensor cross interpolation for global discrete optimization with application to Bayesian network inference
- Authors: Dolgov S.1, Savostyanov D.2
-
Affiliations:
- University of Bath
- University of Essex
- Issue: Vol 65, No 7 (2025)
- Pages: 1077-1090
- Section: General numerical methods
- URL: https://jdigitaldiagnostics.com/0044-4669/article/view/688549
- DOI: https://doi.org/10.31857/S0044466925070023
- EDN: https://elibrary.ru/JXGDIL
- ID: 688549
Cite item
Abstract
Global discrete optimization is notoriously difficult due to the lack of gradient information and the curse of dimensionality, making exhaustive search infeasible. Tensor cross approximation is an efficient technique to approximate multivariate tensors (and discretized functions) by tensor product decompositions based on a small number of tensor elements, evaluated on adaptively selected fibers of the tensor, that intersect on submatrices of (nearly) maximum volume. The submatrices of maximum volume are empirically known to contain large elements, hence the entries selected for cross interpolation can also be good candidates for the globally maximal element within the tensor. In this paper we consider evolution of epidemics on networks, and infer the contact network from observations of network nodal states over time. By numerical experiments we demonstrate that the contact network can be inferred accurately by finding the global maximum of the likelihood using tensor cross interpolation. The proposed tensor product approach is flexible and can be applied to global discrete optimization for other problems, e.g. discrete hyperparameter tuning.
About the authors
S. Dolgov
University of Bath
Email: S.Dolgov@bath.ac.uk
Bath, United Kingdom
D. Savostyanov
University of Essex
Email: D.Savostyanov@essex.ac.uk
Colchester, United Kingdom
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