A Reparameterization of Mixtures of Truncated Basis Functions and its Applications

Abstract

Mixtures of truncated basis functions (MoTBFs) are a popular tool within the context of hybrid Bayesian networks, mainly because they are compatible with e_cient probabilistic inference schemes. However, their standard parameterization allows the presence of negative mixture weights as well as non-normalized mixture terms, which prevents them from bene_ting from existing likelihood-based mixture estimation methods like the EM algorithm. Furthermore, the standard parameterization does not facilitate the de_nition of a Bayesian framework ideally allowing conjugate analysis. In this paper we show how MoTBFs can be reparameterized applying a strategy already used in the literature for Gaussian mixture models with negative terms. We exemplify how the new parameterization is compatible with the EM algorithm and conjugate analysis