NDLI: A Spectral Algorithm for Learning Mixtures of Spherical Gaussians by MASSA CHUSETTS INSTITUTE

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A Spectral Algorithm for Learning Mixtures of Spherical Gaussians by MASSA CHUSETTS INSTITUTE

Content Provider	Semantic Scholar
Author	Grant Wang Theses
Abstract	Mixtures of Gaussians are a fundamental model in statistics and learning theory, and the task of learning such mixtures is a problem of both practical and theoretical interest. While there are many notions of learning, in this thesis we will consider the following notion: given m points sampled from the mixture, classify the points according to the Gaussian from which they were sampled. While there are algorithms for learning mixtures of Gaussians used in practice, such as the EM algorithm, very few provide any guarantees. For instance, it is known that the EM algorithm can fail to converge. Recently, polynomial-time algorithms have been developed that provably learn mixtures of spherical Gaussians when assumptions are made on the separation between the Gaussians. A spherical Gaussian distribution is a Gaussian distribution in which the variance is the same in every direction. In this thesis, we develop a polynomial-time algorithm to learn a mixture of k spherical Gaussians in W" when the separation depends polynomially on k and log n. Previous works provided algorithms that learn mixtures of Gaussians when the separation between the Gaussians grows polynomially in n. We also show how the algorithm can be modified slightly to learn mixtures of spherical Gaussians when the separation is essentially the least possible, in exponential-time. The main tools we use to develop this algorithm are the singular value decomposition and distance concentration. While distance concentration has been used to learn Gaussians in previous works, the application of singular value decomposition is a new technique that we believe can be applied to learning mixtures of non-spherical Gaussians.
File Format	PDF HTM / HTML
Alternate Webpage(s)	http://dspace.mit.edu/bitstream/handle/1721.1/87899/54863801-MIT.pdf?sequence=2
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article

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