On-the-fly Approximation of Multivariate Total Variation Minimization

TL;DR

This paper introduces an approximate on-the-fly algorithm for multivariate total variation minimization in change-point detection, balancing solution quality and computational efficiency, outperforming standard methods.

Contribution

It extends univariate on-the-fly total variation minimization to multivariate data with an approximate algorithm controlled by a tunable parameter.

Findings

High-quality solutions achieved on-the-fly

Computational costs significantly lower than standard methods

Algorithm provides practical multivariate change-point detection

Abstract

In the context of change-point detection, addressed by Total Variation minimization strategies, an efficient on-the-fly algorithm has been designed leading to exact solutions for univariate data. In this contribution, an extension of such an on-the-fly strategy to multivariate data is investigated. The proposed algorithm relies on the local validation of the Karush-Kuhn-Tucker conditions on the dual problem. Showing that the non-local nature of the multivariate setting precludes to obtain an exact on-the-fly solution, we devise an on-the-fly algorithm delivering an approximate solution, whose quality is controlled by a practitioner-tunable parameter, acting as a trade-off between quality and computational cost. Performance assessment shows that high quality solutions are obtained on-the-fly while benefiting of computational costs several orders of magnitude lower than standard iterative procedures. The proposed algorithm thus provides practitioners with an efficient multivariate change-point detection on-the-fly procedure.