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Title: Bayesian non-conjugate regression via variational belief updating Authors:  Cristian Castiglione - University of Padova (Italy) [presenting]
Mauro Bernardi - University of Padova (Italy)
Abstract: A new variational algorithm is presented in order to provide a flexible tool for approximating the general posterior distribution of Bayesian models that combine subjective prior beliefs with an empirical risk function. Particular attention is delivered to regression and classification models linking data and parameters through a continuous convex loss function and a linear predictor. Many remarkable examples belonging to this class are of particular interest for statistical applications, such as generalized linear models, support vector machines, quantile and expectile regression. The proposed iterative procedure lies in the family of semiparametric variational Bayes and enjoys closed-form updating formulas along with efficient integration of the evidence lower bound. Neither conjugacy nor elaborate data augmentation strategies are required. Structured prior distributions, e.g., cross-random effects, spatial or temporal processes, inducing shrinkage and sparsity priors, can be easily accommodated into such a framework without additional effort since the modularity of mean field variational Bayes is preserved. The properties of the algorithm are then assessed through a simulation study and a real data application, where the proposed method is compared with Markov chain Monte Carlo and conjugate mean field variational Bayes in terms of posterior approximation accuracy, prediction error and computational runtime.