Towards Understanding Mixtures of Gaussians: Spectral Methods and Polynomial Time Learning with No Separation
主 题: Towards Understanding Mixtures of Gaussians: Spectral Methods and Polynomial Time Learning with No Separation
报告人: Dr. Mikhail Belkin (The Ohio State University)
时 间: 2009-06-24 上午10:00 - 11:30
地 点: 理科一号楼 1418
Mixtures of Gaussian distributions is an important tool in machine learning and statistics, widely used in numerous appplications, such as speech recognition and computer vision. In recent years there has been considerable progress toward theoretical understanding of the complexity of estimating mixture distribution, especially in high dimensions. However, commonly used methods, such as Expectation Maximization suffer from several shortcomings, particularly their sensitivity
to initialization and the inability to estimate the number of components required. In my talk I will discuss two recent lines of woks on mixtures of Gaussians. In our joint work with Tao Shi and Bin Yu we develop a class of spectral methods based on eigenvectors of certain kernel matrices and provide theoretical analyses and experimental showing that these methods may overcome some of the shortcomings of Expectation Maximization. I will also discuss some interesting connections to spectral clustering. In the second part of the talk I will discuss some recent joint work with Kaushik Sinha showing the first polynomial time algorithm for learning mixtures of Gaussians in high dimension with arbitrarily small separation between components.
