Journal article
Minimax Quasi-Bayesian Estimation in Sparse Canonical Correlation Analysis via a Rayleigh Quotient Function
Journal of the American Statistical Association, Vol.119(548), pp.2647-2657
10/01/2024
DOI: 10.1080/01621459.2023.2271199
Abstract
Canonical correlation analysis (CCA) is a popular statistical technique for exploring relationships between datasets. In recent years, the estimation of sparse canonical vectors has emerged as an important but challenging variant of the CCA problem, with widespread applications. Unfortunately, existing rate-optimal estimators for sparse canonical vectors have high computational cost. We propose a quasi-Bayesian estimation procedure that not only achieves the minimax estimation rate, but also is easy to compute by Markov chain Monte Carlo (MCMC). The method builds on (Tan et al.) and uses a rescaled Rayleigh quotient function as the quasi-log-likelihood. However, unlike (Tan et al.), we adopt a Bayesian framework that combines this quasi-log-likelihood with a spike-and-slab prior to regularize the inference and promote sparsity. We investigate the empirical behavior of the proposed method on both continuous and truncated data, and we demonstrate that it outperforms several state-of-the-art methods. As an application, we use the proposed methodology to maximally correlate clinical variables and proteomic data for better understanding the Covid-19 disease. Supplementary materials for this article are available online.
Details
- Title: Subtitle
- Minimax Quasi-Bayesian Estimation in Sparse Canonical Correlation Analysis via a Rayleigh Quotient Function
- Creators
- Qiuyun Zhu - Boston UniversityYves Atchade - Boston University
- Resource Type
- Journal article
- Publication Details
- Journal of the American Statistical Association, Vol.119(548), pp.2647-2657
- DOI
- 10.1080/01621459.2023.2271199
- ISSN
- 0162-1459
- eISSN
- 1537-274X
- Publisher
- Taylor & Francis
- Number of pages
- 11
- Grant note
- DMS 2015485 / NSF; National Science Foundation (NSF)
- Language
- English
- Date published
- 10/01/2024
- Academic Unit
- Statistics and Actuarial Science
- Record Identifier
- 9984936508702771
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