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Canonical correlation analysis (CCA) is a popular statistical technique forexploring relationships between datasets. In recent years, the estimation ofsparse canonical vectors has emerged as an important but challenging variant ofthe CCA problem, with widespread applications. Unfortunately, existingrate-optimal estimators for sparse canonical vectors have high computationalcost. We propose a quasi-Bayesian estimation procedure that not only achievesthe minimax estimation rate, but also is easy to compute by Markov Chain MonteCarlo (MCMC). The method builds on Tan et al. (2018) and uses a re-scaledRayleigh quotient function as the quasi-log-likelihood. However, unlike Tan etal. (2018), we adopt a Bayesian framework that combines thisquasi-log-likelihood with a spike-and-slab prior to regularize the inferenceand promote sparsity. We investigate the empirical behavior of the proposedmethod on both continuous and truncated data, and we demonstrate that itoutperforms several state-of-the-art methods. As an application, we use theproposed methodology to maximally correlate clinical variables and proteomicdata for better understanding the Covid-19 disease.

Minimax Quasi-Bayesian estimation in sparse canonical correlation analysis via a Rayleigh quotient function