  This paper investigates the problem of simultaneously predicting multiple
binary responses by utilizing a shared set of covariates. Our approach
incorporates machine learning techniques for binary classification, without
making assumptions about the underlying observations. Instead, our focus lies
on a group of predictors, aiming to identify the one that minimizes prediction
error. Unlike previous studies that primarily address estimation error, we
directly analyze the prediction error of our method using PAC-Bayesian bounds
techniques. In this paper, we introduce a pseudo-Bayesian approach capable of
handling incomplete response data. Our strategy is efficiently implemented
using the Langevin Monte Carlo method. Through simulation studies and a
practical application using real data, we demonstrate the effectiveness of our
proposed method, producing comparable or sometimes superior results compared to
the current state-of-the-art method.
