A Birth-Death Process for Feature Allocation
Konstantina Palla, David Knowles, Zoubin Ghahramani
Abstract
We propose a Bayesian nonparametric prior over feature allocations for sequential data, the birth-death feature allocation process (BDFP). The BDFP models the evolution of the feature allocation of a set of N objects across a covariate (e.g.~time) by creating and deleting features. A BDFP is exchangeable, projective, stationary and reversible, and its equilibrium distribution is given by the Indian buffet process (IBP). We show that the Beta process on an extended space is the de Finetti mixing distribution underlying the BDFP. Finally, we present the finite approximation of the BDFP, the Beta Event Process (BEP), that permits simplified inference. The utility of the BDFP as a prior is demonstrated on real world dynamic genomics and social network data.
BibTeX
@InProceedings{pmlr-v70-palla17a,
title = {A Birth-Death Process for Feature Allocation},
author = {Konstantina Palla and David Knowles and Zoubin Ghahramani},
booktitle = {Proceedings of the 34th International Conference on Machine Learning},
pages = {2751--2759},
year = {2017},
editor = {Precup, Doina and Teh, Yee Whye},
volume = {70},
series = {Proceedings of Machine Learning Research},
month = {06--11 Aug},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v70/palla17a/palla17a.pdf},
url = {https://proceedings.mlr.press/v70/palla17a.html},
abstract = {We propose a Bayesian nonparametric prior over feature allocations for sequential data, the birth-death feature allocation process (BDFP). The BDFP models the evolution of the feature allocation of a set of N objects across a covariate (e.g.~time) by creating and deleting features. A BDFP is exchangeable, projective, stationary and reversible, and its equilibrium distribution is given by the Indian buffet process (IBP). We show that the Beta process on an extended space is the de Finetti mixing distribution underlying the BDFP. Finally, we present the finite approximation of the BDFP, the Beta Event Process (BEP), that permits simplified inference. The utility of the BDFP as a prior is demonstrated on real world dynamic genomics and social network data.}
}