A Utsugi | PubMed Health

PubMed2001

Bayesian analysis of mixtures of factor analyzers.

For Bayesian inference on the mixture of factor analyzers, natural conjugate priors on the parameters are introduced, and then a Gibbs sampler that generates parameter samples following the posterior is constructed. In addition, a deterministic estimation algorithm is derived by taking modes instead of samples from the conditional posteriors used in the Gibbs sampler. This is regarded as a maximum a posteriori estimation algorithm with hyperparameter search. The behaviors of the Gibbs sampler and the deterministic algorithm are compared on a simulation experiment.

Algorithms↗

PubMed1998

Density estimation by mixture models with smoothing priors

In the statistical approach for self-organizing maps (SOMs), learning is regarded as an estimation algorithm for a gaussian mixture model with a gaussian smoothing prior on the centroid parameters. The values of the hyperparameters and the topological structure are selected on the basis of a statistical principle. However, since the component selection probabilities are fixed to a common value, the centroids concentrate on areas with high data density. This deforms a coordinate system on an extracted manifold and makes smoothness evaluation for the manifold inaccurate. In this article, we study an extended SOM model whose component selection probabilities are variable. To stabilize the estimation, a smoothing prior on the component selection probabilities is introduced. An estimation algorithm for the parameters and the hyperparameters based on empirical Bayesian inference is obtained. The performance of density estimation by the new model and the SOM model is compared via simulation experiments.

Journal Article↗