Semiparametric principal component analysis

Fang Han, Han Liu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

12 Scopus citations

Abstract

We propose two new principal component analysis methods in this paper utilizing a semiparametric model. The according methods are named Copula Component Analysis (COCA) and Copula PCA. The semiparametric model assumes that, after unspecified marginally monotone transformations, the distributions are multi-variate Gaussian. The COCA and Copula PCA accordingly estimate the leading eigenvectors of the correlation and covariance matrices of the latent Gaussian distribution. The robust nonparametric rank-based correlation coefficient estimator, Spearman's rho, is exploited in estimation. We prove that, under suitable conditions, although the marginal distributions can be arbitrarily continuous, the COCA and Copula PCA estimators obtain fast estimation rates and are feature selection consistent in the setting where the dimension is nearly exponentially large relative to the sample size. Careful numerical experiments on the synthetic and real data are conducted to back up the theoretical results. We also discuss the relationship with the transelliptical component analysis proposed by Han and Liu (2012).

Original languageEnglish (US)
Title of host publicationAdvances in Neural Information Processing Systems 25
Subtitle of host publication26th Annual Conference on Neural Information Processing Systems 2012, NIPS 2012
Pages171-179
Number of pages9
StatePublished - Dec 1 2012
Event26th Annual Conference on Neural Information Processing Systems 2012, NIPS 2012 - Lake Tahoe, NV, United States
Duration: Dec 3 2012Dec 6 2012

Publication series

NameAdvances in Neural Information Processing Systems
Volume1
ISSN (Print)1049-5258

Other

Other26th Annual Conference on Neural Information Processing Systems 2012, NIPS 2012
CountryUnited States
CityLake Tahoe, NV
Period12/3/1212/6/12

All Science Journal Classification (ASJC) codes

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing

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  • Cite this

    Han, F., & Liu, H. (2012). Semiparametric principal component analysis. In Advances in Neural Information Processing Systems 25: 26th Annual Conference on Neural Information Processing Systems 2012, NIPS 2012 (pp. 171-179). (Advances in Neural Information Processing Systems; Vol. 1).