Prior Hyperparameters in Bayesian PCA
Bayesian PCA (BPCA) provides a Bayes inference for probabilistic PCA, in which several prior distributions have been devised; for example, automatic relevance determination (ARD) is used for determining the dimensionality. However, there is arbitrariness in prior setting; different prior settings result in different estimations. This article aims at presenting a standard setting of prior distribution for BPCA. We first define a general hierarchical prior for BPCA and show an exact predictive distribution. We show that several of the already proposed priors can be regarded as special cases of the general prior. By comparing various priors, we show that BPCA with nearly non-informative hierarchical priors exhibits the best performance.