Estimating the number of change-points in a two-dimensional segmentation model without penalization

TL;DR

This paper investigates the theoretical consistency of least-squares estimators for identifying diagonal blocks in two-dimensional segmentation models, showing that no penalty is needed to accurately estimate the number of blocks, with validation on synthetic data.

Contribution

It establishes the consistency of least-squares estimators for block detection in 2D segmentation without requiring penalization, which contrasts with 1D cases.

Findings

Estimators are consistent for block boundaries and count.

No penalty is necessary for true block number recovery.

Results validated on synthetic datasets.

Abstract

In computational biology, numerous recent studies have been dedicated to the analysis of the chromatin structure within the cell by two-dimensional segmentation methods. Motivated by this application, we consider the problem of retrieving the diagonal blocks in a matrix of observations. The theoretical properties of the least-squares estimators of both the boundaries and the number of blocks proposed by L\'evy-Leduc et al. [2014] are investigated. More precisely, the contribution of the paper is to establish the consistency of these estimators. A surprising consequence of our results is that, contrary to the onedimensional case, a penalty is not needed for retrieving the true number of diagonal blocks. Finally, the results are illustrated on synthetic data.