Tensor cross interpolation for global discrete optimization with application to Bayesian network inference

TL;DR

This paper introduces a tensor cross interpolation method to efficiently solve global discrete optimization problems, demonstrated on epidemic network inference, and applicable to various discrete optimization tasks.

Contribution

The paper presents a novel tensor cross approximation technique for global discrete optimization, enabling efficient inference of epidemic contact networks from observational data.

Findings

Accurate network inference via tensor cross interpolation

Efficient optimization without exhaustive search

Applicable to hyperparameter tuning and other discrete problems

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.