Polynomial Learning of Distribution Families

Abstract--The question of polynomial learnability of probability distributions, particularly Gaussian mixture distributions, has recently received significant attention in theoretical computer science and machine learning. However, despite major progress, the general question of polynomial learnability of Gaussian mixture distributions still remained open. The current work resolves the question of polynomial learnability for Gaussian mixtures in high dimension with an arbitrary fixed number of components. Specifically, we show that parameters of a Gaussian mixture distribution with fixed number of components can be learned using a sample whose size is polynomial in dimension and all other parameters. The result on learning Gaussian mixtures relies on an analysis of distributions belonging to what we call "polynomial families" in low dimension. These families are characterized by their moments being polynomial in parameters and include almost all common probability distributio...

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Mikhail Belkin, Kaushik Sinha
• Keywords: CORR 2010, Education, Gaussian Mixture Distribution, Gaussian Mixtures, Polynomial