A hierarchical Bayesian choice model with visibility

We extend the standard choice model of multinomial logit model (MLM) into a hierarchical Bayesian model to simultaneously estimate the preferences of customers and the visibility of items from purchasing history. We say that an item has high visibility when customers well consider that item as a candidate before making a choice. We design two algorithms for estimating the parameters of the proposed choice model. One algorithm estimates the posterior distribution with the Gibbs sampling, and the other approximately performs the maximum a posteriori estimation. Our experimental results show that we can estimate the preferences of customers from their purchasing history without the prior knowledge of the choice set. The existing approaches to estimating the preferences of customers rely on the explicit knowledge of the choice set.