Lévy measure decompositions for the beta and gamma processes

Yingjian Wang, Lawrence Carin

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Scopus citations

Abstract

We develop new representations for the Lévy measures of the beta and gamma processes. These representations are manifested in terms of an infinite sum of well-behaved (proper) beta and gamma distributions. Further, we demonstrate how these infinite sums may be truncated in practice, and explicitly characterize truncation errors. We also perform an analysis of the characteristics of posterior distributions, based on the proposed decompositions. The decompositions provide new insights into the beta and gamma processes (and their generalizations), and we demonstrate how the proposed representation unifies some properties of the two. This paper is meant to provide a rigorous foundation for and new perspectives on Lévy processes, as these are of increasing importance in machine learning. Copyright 2012 by the author(s)/owner(s).
Original languageEnglish (US)
Title of host publicationProceedings of the 29th International Conference on Machine Learning, ICML 2012
Pages73-80
Number of pages8
StatePublished - Oct 10 2012
Externally publishedYes

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