Structured Matrix Completion with Applications to Genomic Data Integration

TL;DR

This paper introduces a structured matrix completion framework tailored for genomic data integration, providing theoretical guarantees and demonstrating improved predictive accuracy in ovarian cancer survival analysis.

Contribution

It proposes a novel structured matrix completion method for data with structured missingness, with theoretical analysis and real-world genomic application.

Findings

Method achieves optimal recovery rates for low-rank matrices.

Simulation results show strong finite-sample performance.

Application improves ovarian cancer survival prediction.

Abstract

Matrix completion has attracted significant recent attention in many fields including statistics, applied mathematics and electrical engineering. Current literature on matrix completion focuses primarily on independent sampling models under which the individual observed entries are sampled independently. Motivated by applications in genomic data integration, we propose a new framework of structured matrix completion (SMC) to treat structured missingness by design. Specifically, our proposed method aims at efficient matrix recovery when a subset of the rows and columns of an approximately low-rank matrix are observed. We provide theoretical justification for the proposed SMC method and derive lower bound for the estimation errors, which together establish the optimal rate of recovery over certain classes of approximately low-rank matrices. Simulation studies show that the method performs well in finite sample under a variety of configurations. The method is applied to integrate several ovarian cancer genomic studies with different extent of genomic measurements, which enables us to construct more accurate prediction rules for ovarian cancer survival.