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arXiv · 1703.02834

Exact Dimensionality Selection for Bayesian PCA

Charles Bouveyron·Pierre Latouche·Pierre-Alexandre Mattei
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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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Charles Bouveyron, Pierre Latouche, Pierre-Alexandre Mattei. 2017-03-08. Exact Dimensionality Selection for Bayesian PCA. https://arxiv.org/abs/1703.02834

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