Structured Matrix Completion with Applications to Genomic Data Integration
This work addresses structured missing data in genomic integration, enabling more accurate cancer survival predictions, though it is incremental in extending matrix completion to specific missingness patterns.
The authors tackled the problem of matrix completion with structured missingness, proposing a new framework (SMC) that achieves optimal recovery rates and improves prediction accuracy for ovarian cancer survival by integrating genomic data.
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.