Title: Transformed scaled process priors for generalized Indian Buffet processes
Authors: Mario Beraha - Università di Torino (Italy) [presenting]
Abstract: In trait allocation models, each observation displays a collection of traits corresponding to a (usually nonnegative integer) association level. In the Bayesian nonparametric framework, data are modeled as conditionally i.i.d. stochastic processes (termed generalized Indian buffet processes) whose law depends on a random measure. Traditionally, completely random measures are employed as prior, but, as shown previously, this leads to a rather simplistic predictive structure. Namely, the probability of a new observation displaying new (unobserved) traits depends on the observed sample only through its cardinality. In the context of latent feature models, this problem was faced recently by proposing to use scaled processes as priors instead of completely random measures. We extend this framework to the more general latent trait models. The proposal is based on a suitable transformation of SPs and which are recovered as a special case. We characterize the marginal, posterior, and predictive distribution induced by the proposed class of prior processes in trait allocation models, showing in particular that this choice leads to a richer predictive structure. We consider the case of Bernoulli, Poisson, and negative binomial distributed traits as examples.