On the Convergence of Bound Optimization Algorithms

Many practitioners who use EM and related algorithms complain that they are sometimes slow. When does this happen, and what can be done about it? In this paper, we study the general class of bound optimization algorithms – including EM, Iterative Scaling, Non-negative Matrix Factorization, CCCP – and their relationship to direct optimization algorithms such as gradientbased methods for parameter learning. We derive a general relationship between the updates performed by bound optimization methods and those of gradient and second-order methods and identify analytic conditions under which bound optimization algorithms exhibit quasi-Newton behavior, and conditions under which they possess poor, first-order convergence. Based on this analysis, we consider several specific algorithms, interpret and analyze their convergence properties and provide some recipes for preprocessing input to these algorithms to yield faster convergence behavior. We report empirical results supporting our a...

• Type: Conference
• Year: 2003
• Where: UAI
• Authors: Ruslan Salakhutdinov, Sam T. Roweis, Zoubin Ghahramani
• Keywords: Bound Optimization, Bound Optimization Algorithms, Bound Optimization Methods, UAI 2003, UAI 2008