Asymptotic Test for Dimensionality in Probabilistic Principal Component Analysis with Missing Values



Park, Chong-sun

  • 발행 : 2004.04.01


In this talk we proposed an asymptotic test for dimensionality in the latent variable model for probabilistic principal component analysis with missing values at random. Proposed algorithm is a sequential likelihood ratio test for an appropriate Normal latent variable model for the principal component analysis. Modified EM-algorithm is used to find MLE for the model parameters. Results from simulations and real data sets give us promising evidences that the proposed method is useful in finding necessary number of components in the principal component analysis with missing values at random.


Probabilistic Principal Component Analysis;Dimension Reduction;Latent Variable Model;Missing Values


  1. Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability v.Ⅴ pp.111-150 Statistical Inference in Factor Anaysis Anderson,T.W.;Rubin,H.;J,Newman(ed.)
  2. Psychometrika v.6 no.1 pp.49-53 Maximum Likehood Estimation and Factor Analysis Young,G.
  3. Journal of Educational Psychology v.24 pp.417-441 Ananlysis of a Complex of Statistical Variables into Principal Components Hotelling,H.
  4. Annals of Mathematical Statistics v.34 pp.122-148 Asymptotic Theory for Principal Component Analysis Anderson,T.W.
  5. Analysis of Incomplete Multivariate Data by Simulation Schafer,L.
  6. Journal of the Royal Statistical Society,Series B v.61 pp.611-622 Probabilistic Principal Component Analysis Tipping,M.E.;Bishop,C.M.
  7. Annals of Eugenics v.7 pp.179-188 The use of multiple measurements in taxonomic problems Fisher,R.A.
  8. Principal Component Analysis Jolliffe,I.T.
  9. Uppsala Symposium on Psychological Factor Analysis,Number 3 in Nordisk Psykologi Monograph Series, 35-42 A Modified Method of Estimation in Factor Analysis and Some Large Sample Results Lawley,D.N.
  10. Applied Multivariate Statistical Analysis Johnson,R.A.;Wichern,R.A.
  11. Skamdinavisk Aktuarietidskrift v.36 pp.223-239 On Principal Components and Least Square Methods of Factor Analysis Whittle,P.
  12. Statistical Analysis with Missing Data Little,R.;Rubin,D.
  13. Journal of the Royal Statistical Society,Series B v.52 pp.443-452 On Use of the EM Algorithm for Penalized Likelihood Estimation Green,P.J.