The Phylogenetic Indian Buffet Process: A Non-Exchangeable Nonparametric Prior for Latent Features
This work addresses the need for more flexible non-exchangeable priors in Bayesian modeling for applications where exchangeability is inappropriate, offering a domain-specific improvement for fields like phylogenetics and choice modeling.
The authors tackled the problem of modeling non-exchangeable dependencies in nonparametric Bayesian latent feature models by introducing the Phylogenetic Indian Buffet Process, which uses a tree structure to express relationships between objects, and demonstrated its application to probabilistic choice modeling with computational efficiency nearly matching exchangeable counterparts.
Nonparametric Bayesian models are often based on the assumption that the objects being modeled are exchangeable. While appropriate in some applications (e.g., bag-of-words models for documents), exchangeability is sometimes assumed simply for computational reasons; non-exchangeable models might be a better choice for applications based on subject matter. Drawing on ideas from graphical models and phylogenetics, we describe a non-exchangeable prior for a class of nonparametric latent feature models that is nearly as efficient computationally as its exchangeable counterpart. Our model is applicable to the general setting in which the dependencies between objects can be expressed using a tree, where edge lengths indicate the strength of relationships. We demonstrate an application to modeling probabilistic choice.