Exact Dimensionality Selection for Bayesian PCA
Methodology
2019-05-22 v2 Statistics Theory
Machine Learning
Statistics Theory
Abstract
We present a Bayesian model selection approach to estimate the intrinsic dimensionality of a high-dimensional dataset. To this end, we introduce a novel formulation of the probabilisitic principal component analysis model based on a normal-gamma prior distribution. In this context, we exhibit a closed-form expression of the marginal likelihood which allows to infer an optimal number of components. We also propose a heuristic based on the expected shape of the marginal likelihood curve in order to choose the hyperparameters. In non-asymptotic frameworks, we show on simulated data that this exact dimensionality selection approach is competitive with both Bayesian and frequentist state-of-the-art methods.
Cite
@article{arxiv.1703.02834,
title = {Exact Dimensionality Selection for Bayesian PCA},
author = {Charles Bouveyron and Pierre Latouche and Pierre-Alexandre Mattei},
journal= {arXiv preprint arXiv:1703.02834},
year = {2019}
}