Premium
Exact dimensionality selection for Bayesian PCA
Author(s) -
Bouveyron Charles,
Latouche Pierre,
Mattei PierreAlexandre
Publication year - 2020
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12424
Subject(s) - marginal likelihood , frequentist inference , curse of dimensionality , hyperparameter , model selection , principal component analysis , bayesian probability , dimensionality reduction , computer science , context (archaeology) , bayesian hierarchical modeling , bayes factor , selection (genetic algorithm) , prior probability , artificial intelligence , mathematics , bayesian inference , paleontology , biology
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 nonasymptotic frameworks, we show on simulated data that this exact dimensionality selection approach is competitive with both Bayesian and frequentist state‐of‐the‐art methods.