Exact Dimensionality Selection for Bayesian PCA

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.
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Contributeur : Pierre-Alexandre Mattei <>
Soumis le : lundi 6 mars 2017 - 17:59:38
Dernière modification le : vendredi 1 février 2019 - 15:50:13
Document(s) archivé(s) le : mercredi 7 juin 2017 - 16:00:23


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  • HAL Id : hal-01484099, version 1
  • ARXIV : 1703.02834


Charles Bouveyron, Pierre Latouche, Pierre-Alexandre Mattei. Exact Dimensionality Selection for Bayesian PCA. 2017. 〈hal-01484099〉



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