A Bayesian Methodology for Estimation for Sparse Canonical Correlation

• Activity Number: 424 - Priors and Model Specifications for Variable and Feature Selection
• Type: Contributed
• Date/Time: Wednesday, August 10, 2022 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Siddhesh Kulkarni* and Subhadip Pal and Jeremy Gaskins
• Companies: University of Louisville and University of Louisville and University of Louisville
• Keywords: HorseShoe Prior; Graphical Models; Canonical Correlation Analysis; Bayesian Methedology; Genomics; Breast Cancer

Abstract

In principle, it can be challenging to integrate data measured on the same individuals occurring from different experiments and model it together to get a larger understanding of the problem. Canonical Correlation Analysis (CCA) provides a useful tool for establishing relationships between such data sets. When dealing with high dimensional data sets, Structured Sparse CCA (ScSCCA) is a rapidly developing methodological area. There is less development in Bayesian methodology in this area. We propose a novel Bayesian ScSCCA method with the use of a Bayesian infinite factor model. In this model using a multiplicative half Cauchy prior process, we bring in sparsity at projection matrix level. Further, we bring in sparsity in the covariance matrix by using graphical horseshoe prior on the inverse covariance matrix. We propose this model for data sets on the same individuals from two experiments. We compare our results with some competing methods. Further we apply the developed method to omics data to understand relationship between mRNA and DNA for breast cancer.