A Reparameterization of Mixtures of Truncated Basis Functions and its Applications

Mixtures of truncated basis functions (MoTBFs) are a popular tool within the context of hybrid Bayesian networks, mainly because they are compatible with efficient 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 benefiting from existing likelihood-based mixture estimation methods like the EM algorithm. Furthermore, the standard parameterization does not facilitate the definition 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.