Efficient block boundaries estimation in block-wise constant matrices: An Application to HiC data

Estimation efficace des frontières des blocs d'une matrice constante par blocs : application aux données HiC

Vincent Brault (1) , Julien Chiquet (2) , Céline Lévy-Leduc (2)

1 SVH - Statistique pour le Vivant et l’Homme
2 MIA-Paris - Mathématiques et Informatique Appliquées

In this paper, we propose a novel modeling and a new methodology for estimating the location of block boundaries in a random matrix consisting of a block-wise constant matrix corrupted with white noise. Our method consists in rewriting this problem as a variable selection issue. A penalized least-squares criterion with an l1-type penalty is used for dealing with this problem. Firstly, some theoretical results ensuring the consistency of our block boundaries estimators are provided. Secondly, we explain how to implement our approach in a very efficient way. This implementation is available in the R package blockseg which can be found in the Comprehensive R Archive Network. Thirdly, we provide some numerical experiments to illustrate the statistical and numerical performance of our package, as well as a thorough comparison with existing methods. Fourthly, an empirical procedure is proposed for estimating the number of blocks. Finally, our approach is applied to HiC data which are used in molecular biology for better understanding the influence of the chromosomal conformation on the cells functioning.

Mots clés: change-points; HiC experiments; high-dimensional sparse linear model

Mots clés: Ruptures; Modèle linéaire sparse en grandes dimensions; Hi-C

Domaines: Méthodologie [stat.ME]; Applications [stat.AP]; Théorie [stat.TH]

Vincent Brault, Julien Chiquet, Céline Lévy-Leduc. Efficient block boundaries estimation in block-wise constant matrices: An Application to HiC data. Electronic Journal of Statistics , 2017, Electronic Journal of Statistics, 11 (1), pp.1570-1599. ⟨10.1214/17-EJS1270⟩. ⟨hal-01455732⟩