Structured Matrix Completion with Applications to Genomic Data Integration
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.
Code (0)
등록된 구현이 없습니다.
Tasks
Data IntegrationElectrical EngineeringMatrix CompletionSimilar Papers 제목 키워드 기반
Simple, Fast, and Flexible Framework for Matrix Completion with Infinite Width Neural Networks
Matrix completion problems arise in many applications including recommendation systems, computer vision, and genomics. Increasingly larger neural networks have been successful in many of these applications, but at consid…
Image InpaintingMatrix CompletionRecommendation SystemsCompletion of the DrugMatrix Toxicogenomics Database using 3-Dimensional Tensors
We explore applying a tensor completion approach to complete the DrugMatrix toxicogenomics dataset. Our hypothesis is that by preserving the 3-dimensional structure of the data, which comprises tissue, treatment, and tra…
DeepVir -- Graphical Deep Matrix Factorization for "In Silico" Antiviral Repositioning: Application to COVID-19
This work formulates antiviral repositioning as a matrix completion problem where the antiviral drugs are along the rows and the viruses along the columns. The input matrix is partially filled, with ones in positions whe…
Matrix CompletionGoing off the Grid: Iterative Model Selection for Biclustered Matrix Completion
We consider the problem of performing matrix completion with side information on row-by-row and column-by-column similarities. We build upon recent proposals for matrix estimation with smoothness constraints with respect…
Matrix CompletionModel SelectionStructured Low-Rank Algorithms: Theory, MR Applications, and Links to Machine Learning
In this survey, we provide a detailed review of recent advances in the recovery of continuous domain multidimensional signals from their few non-uniform (multichannel) measurements using structured low-rank matrix comple…
BIG-bench Machine Learningcompressed sensingLow-Rank Matrix CompletionMatrix Completion