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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https://hal.archives-ouvertes.fr/hal-01484099
Contributor : Pierre-Alexandre Mattei <>
Submitted on : Monday, May 20, 2019 - 6:16:38 PM
Last modification on : Friday, December 6, 2019 - 9:40:31 AM

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  • HAL Id : hal-01484099, version 2
  • ARXIV : 1703.02834

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Charles Bouveyron, Pierre Latouche, Pierre-Alexandre Mattei. Exact Dimensionality Selection for Bayesian PCA. Scandinavian Journal of Statistics, Wiley, In press. ⟨hal-01484099v2⟩

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