Pré-Publication, Document De Travail Année : 2024

An Equivalence between Bayesian Priors and Penalties in Variational Inference

Résumé

In machine learning, it is common to optimize the parameters of a probabilistic model, modulated by an ad hoc regularization term that penalizes some values of the parameters. Regularization terms appear naturally in Variational Inference, a tractable way to approximate Bayesian posteriors: the loss to optimize contains a Kullback-Leibler divergence term between the approximate posterior and a Bayesian prior. We fully characterize the regularizers that can arise according to this procedure, and provide a systematic way to compute the prior corresponding to a given penalty. Such a characterization can be used to discover constraints over the penalty function, so that the overall procedure remains Bayesian.

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Dates et versions

hal-02466702 , version 1 (04-02-2020)
hal-02466702 , version 2 (24-02-2026)

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Pierre Wolinski, Guillaume Charpiat, Yann Ollivier. An Equivalence between Bayesian Priors and Penalties in Variational Inference. 2024. ⟨hal-02466702v2⟩
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