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

2013

Article

ei


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 View the MathML source 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) 1612–1619].

Author(s): Sra, S. and Karp, DB.
Journal: Journal of Multivariate Analysis
Volume: 114
Pages: 256-269
Year: 2013
Month: February
Day: 0

Department(s): Empirical Inference
Bibtex Type: Article (article)

Digital: 0
DOI: 10.1016/j.jmva.2012.08.010

Links: Web

BibTex

@article{SraK2012,
  title = {The multivariate Watson distribution: Maximum-likelihood estimation and other aspects},
  author = {Sra, S. and Karp, DB.},
  journal = {Journal of Multivariate Analysis},
  volume = {114},
  pages = {256-269},
  month = feb,
  year = {2013},
  month_numeric = {2}
}