High-dimensional singular marginal-likelihood asymptotics

Extend the asymptotic log-marginal-likelihood expansions for probabilistic principal component analysis to high-dimensional regimes in which the dimension grows and model singularities are present.

Background

The paper derives complete fixed-dimension, large-sample asymptotics for marginal likelihoods in probabilistic principal component analysis using singular learning theory. In high-dimensional covariance estimation, however, the dimension may grow with the sample size, and standard Laplace-approximation arguments require regularity conditions that fail at PPCA singularities. The authors identify obtaining corresponding high-dimensional asymptotics as an unresolved direction.