Levy Measure Decompositions for the Beta and Gamma Processes
Levy Measure Decompositions for the Beta and Gamma Processes
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发表时间：
2012-06
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通讯作者：
Yingjian Wang;L. Carin
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作者：
Yingjian Wang;L. Carin
我们开发了新的表示的Levy措施的beta和gamma过程。这些表示表现为行为良好的（适当的）beta和gamma分布的无限总和。此外，我们演示了如何在实践中截断这些无限的总和，并明确表征截断误差。我们还进行了分析的后验分布的特点，建议的分解的基础上。的分解提供了新的见解的beta和gamma过程（及其推广），我们演示了如何提出的表示统一的两个的一些属性。本文旨在为Levy过程提供严格的基础和新的视角，因为这些过程在机器学习中越来越重要。
We develop new representations for the Levy 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 Levy processes, as these are of increasing importance in machine learning.