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 language||English (US)|
|Title of host publication||Proceedings of the 29th International Conference on Machine Learning, ICML 2012|
|Number of pages||8|
|State||Published - Oct 10 2012|