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Abstract:
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Canonical correlation analysis (CCA) is a popular statistical technique for exploring the relationship between datasets. The estimation of sparse canonical correlation vectors has emerged in recent years as an important but challenging variation of the CCA problem, with widespread applications. Currently available rate-optimal estimators for sparse canonical correlation vectors are expensive to compute. We propose a quasi-Bayesian estimation procedure that achieves the minimax estimation rate, and yet is easy to compute by Markov Chain Monte Carlo (MCMC). The method uses a re-scaled Rayleigh quotient function as a quasi-log-likelihood, together with spike-and-slab priors. We investigated the empirical behavior of the proposed method on both continuous and truncated data, and we noted that it outperforms several state-of-the-art methods. As an application, we use the methodology to maximally correlate clinical variables and proteomic data for a better understanding of covid-19 disease.
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