Bayesian inference on principal component analysis using reversible jump Markov chain Monte Carlo

Authors:
Zhihua Zhang;Kap Luk Chan;James T. Kwok;Dit-Yan Yeung
Affiliations:
Department of Computer Science, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong;School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore;Department of Computer Science, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong;Department of Computer Science, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong
Venue:
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
Year:
2004

Citing 5
Cited 2

Bayesian radial basis functions of variable dimension

Neural Computation
Bayesian PCA

Proceedings of the 1998 conference on Advances in neural information processing systems II
Model selection by MCMC computation

Signal Processing - Special section on Markov Chain Monte Carlo (MCMC) methods for signal processing
Minimum-Entropy Data Partitioning Using Reversible Jump Markov Chain Monte Carlo

IEEE Transactions on Pattern Analysis and Machine Intelligence
Bayesian Learning for Neural Networks

Bayesian Learning for Neural Networks

Variational Bayesian functional PCA

Computational Statistics & Data Analysis
Automatic model selection by cross-validation for probabilistic PCA

Neural Processing Letters

Quantified Score

Hi-index	0.00

Visualization

Abstract

Based on the probabilistic reformulation of principal component analysis (PCA), we consider the problem of determining the number of principal components as a model selection problem. We present a hierarchical model for probabilistic PCA and construct a Bayesian inference method for this model using reversible jump Markov chain Monte Carlo (MCMC). By regarding each principal component as a point in a one-dimensional space and employing only birth-death moves in our reversible jump methodology, our proposed method is simple and capable of automatically determining the number of principal components and estimating the parameters simultaneously under the same disciplined framework. Simulation experiments are performed to demonstrate the effectiveness of our MCMC method.