2022/06/17 by The Tien Mai, Pierre Alquier, Mai, The Tien +1
Engineering · Mathematics · #Computation (stat.CO) #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Sparse and Compressive Sensing Techniques #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2206.08619
openalex publication_date 2022/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The aim of reduced rank regression is to connect multiple response variables to multiple predictors. This model is very popular, especially in biostatistics where multiple measurements on individuals can be re-used to predict multiple outputs. Unfortunately, there are often missing data in such datasets, making it difficult to use standard estimation tools. In this paper, we study the problem of reduced rank regression where the response matrix is incomplete. We propose a quasi-Bayesian approach to this problem, in the sense that the likelihood is replaced by a quasi-likelihood. We provide a tight oracle inequality, proving that our method is adaptive to the rank of the coefficient matrix. We describe a Langevin Monte Carlo algorithm for the computation of the posterior mean. Numerical comparison on synthetic and real data show that our method are competitive to the state-of-the-art where the rank is chosen by cross validation, and sometimes lead to an improvement.