On learning statistical mixtures maximizing the complete likelihood

摘要

Statistical mixtures arc scmi-paramctric models ubiquitously met in data scicncc sincc they can universally model smooth densities arbitrarily closcly. Finite mixtures arc usually inferred from data using the celebrated Expcctation-Maximization framework that locally itcrativcly maximizes the incomplete likelihood by assigning softly data to mixture components. In this paper, wc present a novel methodology to infer mixtures by transforming the learning problem into a sequcncc of gcomctric ccntcr-bascd hard clustering problems that provably maximizes monotonically the complete likelihood. Our versatile method is fast and uses low memory footprint: The corc inner steps can be implemented using various generalized k-mcans type hcuristics. Thus wc can leverage rcccnt results on clustering to mixture learning. In particular, for mixtures of singly-paramctric distributions including for example the Raylcigh, Wcibull, or Poisson distributions, wc show how to use dynamic programming to solve cxactly the inner gcomctric clustering problems. Wc discuss on several extensions of the methodology.