Kernel Density Balancing

TL;DR

This paper introduces a statistically justified, kernel-based matrix balancing method for Hi-C data normalization, demonstrating improved consistency, convergence, and robustness over traditional approaches.

Contribution

It proposes a novel kernel-based estimator for matrix balancing in Hi-C data, with theoretical guarantees and practical advantages.

Findings

Kernel-based method is consistent under mild assumptions.

It converges faster than existing methods.

It is more robust to data sparsity.

Abstract

High-throughput chromatin conformation capture (Hi-C) data provide insights into the 3D structure of chromosomes, with normalization being a crucial pre-processing step. A common technique for normalization is matrix balancing, which rescales rows and columns of a Hi-C matrix to equalize their sums. Despite its popularity and convenience, matrix balancing lacks statistical justification. In this paper, we introduce a statistical model to analyze matrix balancing methods and propose a kernel-based estimator that leverages spatial structure. Under mild assumptions, we demonstrate that the kernel-based method is consistent, converges faster, and is more robust to data sparsity compared to existing approaches.