Sparsity and Fairness in logistic regression via Penalized Mean Field Variational Inference
We propose a novel approach to Bayesian logistic regression that produces sparse and fair solutions. To do so we modify the Mean Field Variational Inference approach by adding a penalization term dependent on the unfairness of the posterior predictions and by an appropriate prior selection. This leads to a set of CAVI equations whose solutions ensure sparsity and fairness on the predictions in a private manner. Numerical results show how this new method results in a trade-off between sparsity, fairness and accuracy, which eases the decision making process for a potential user.
Keywords: Bayesian logistic regression Sparsity fairness variational inference