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Journal Articles Scandinavian Journal of Statistics Year : 2020

Exact Dimensionality Selection for Bayesian PCA


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.
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Dates and versions

hal-01484099 , version 1 (06-03-2017)
hal-01484099 , version 2 (20-05-2019)



Charles Bouveyron, Pierre Latouche, Pierre-Alexandre Mattei. Exact Dimensionality Selection for Bayesian PCA. Scandinavian Journal of Statistics, 2020, ⟨10.1111/sjos.12424⟩. ⟨hal-01484099v2⟩
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