nips nips2004 nips2004-163 nips2004-163-reference knowledge-graph by maker-knowledge-mining
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Author: Sajama Sajama, Alon Orlitsky
Abstract: We present a semi-parametric latent variable model based technique for density modelling, dimensionality reduction and visualization. Unlike previous methods, we estimate the latent distribution non-parametrically which enables us to model data generated by an underlying low dimensional, multimodal distribution. In addition, we allow the components of latent variable models to be drawn from the exponential family which makes the method suitable for special data types, for example binary or count data. Simulations on real valued, binary and count data show favorable comparison to other related schemes both in terms of separating different populations and generalization to unseen samples. 1
[1] M. Tipping and C. Bishop. Probabilistic principal component analysis. Journal of the Royal Statistical Society, Series B, 61(3):611–622, 1999.
[2] David J. Bartholomew and Martin Knott. Latent variable models and Factor analysis, volume 7 of Kendall’s Library of Statistics. Oxford University Press, 2nd edition, 1999.
[3] A. Kaban and M. Girolami. A combined latent class and trait model for the analysis and visualization of discrete data. IEEE Transaction on Pattern Analysis and Machine Intelligence, 23(8):859–872, August 2001.
[4] M. Collins, S. Dasgupta, and R. E. Schapire. A generalization of principal components analysis to the exponential family. In Advances in Neural Information Processing Systems 14, 2002.
[5] P. McCullagh and J. A. Nelder. Generalized Linear Models. Monographs on Statistics and Applied Probability. Chapman and Hall, 1983.
[6] B. G. Lindsay. The geometry of mixture likelihoods : A general theory. The Annals of Statistics, 11(1):86–04, 1983.
[7] Sajama and A. Orlitsky. Semi-parametric exponential family PCA : Reducing dimensions via non-parametric latent distribution estimation. Technical Report CS2004-0790, University of California at San Diego, http://cwc.ucsd.edu/∼ sajama, 2004.
[8] C. F. J. Wu. On the convergence properties of the EM algorithm. Annals of Statistics, 11(1):95– 103, 1983.
[9] J. Kiefer and J. Wolfowitz. Consistency of the maximum likelihood estimator in the presence of in£nitely many incidental parameters. The Annals of Mathematical Statistics, 27:887–906, 1956.
[10] R. Tibshirani. Principal curves revisited. Statistics and Computation, 2:183–190, 1992.