Fast Detection of Block Boundaries in Block Wise Constant Matrices: An Application to HiC data

Abstract

We propose a novel approach for estimating the location of block boundaries (change-points) in a random matrix consisting of a block wise constant matrix observed in white noise. Our method consists in rephrasing this task as a variable selection issue. We use a penalized least-squares criterion with an $\ell_1$-type penalty for dealing with this issue. We first provide some theoretical results ensuring the consistency of our change-point estimators. Then, we explain how to implement our method in a very efficient way. Finally, we provide some empirical evidence to support our claims and apply our approach to HiC data which are used in molecular biology for better understanding the influence of the chromosomal conformation on the cells functioning.