The multivariate Watson distribution: Maximum-likelihood estimation and other aspects

JOURNAL OF MULTIVARIATE ANALYSIS

卷:114

Article

Sra, Suvrit¹  Karp, Dmitrii² 

[1] Max Planck Inst Intelligent Syst, Tubingen, Germany

[2] Far Eastern Fed Univ, Chair Business Informat, Vladivostok 690950, Russia

关键词: Watson distribution;    Kummer function;    Confluent hypergeometric;    Directional statistics;    Diametrical clustering;    Special function;    Hypergeometric identities;   

DOI  :  10.1016/j.jmva.2012.08.010

来源: Elsevier

【 摘 要 】

This paper studies fundamental aspects of modelling data using multivariate Watson distributions. Although these distributions are natural for modelling axially symmetric data (i.e., unit vectors where +/- x are equivalent), for high-dimensions using them can be difficult-largely because for Watson distributions even basic tasks such as maximum-likelihood are numerically challenging. To tackle the numerical difficulties some approximations have been derived. But these are either grossly inaccurate in high-dimensions [K.V. Mardia, P. Jupp, Directional Statistics, second ed., John Wiley & Sons, 2000] or when reasonably accurate [A. Bijral, M. Breitenbach, G.Z. Grudic, Mixture of Watson distributions: a generative model for hyperspherical embeddings, in: Artificial Intelligence and Statistics, AISTATS 2007, 2007, pp. 35-42], they lack theoretical justification. We derive new approximations to the maximum-likelihood estimates; our approximations are theoretically well-defined, numerically accurate, and easy to compute. We build on our parameter estimation and discuss mixture-modelling with Watson distributions; here we uncover a hitherto unknown connection to the diametrical clustering algorithm of Dhillon et al. [I.S. Dhillon, E.M. Marcotte, U. Roshan, Diametrical clustering for identifying anticorrelated gene clusters, Bioinformatics 19 (13) (2003) 1612-16191. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free