An Equivalence between Bayesian Priors and Penalties in Variational Inference

Pierre Wolinski, Guillaume Charpiat, Yann Ollivier

arXiv preprint, 2020 (presented at ISBA 2022)

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Abstract

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.

BibTeX

@misc{wolinski2020equivalence,
  title     = {An Equivalence between Bayesian Priors and Penalties in Variational Inference},
  author    = {Wolinski, Pierre and Charpiat, Guillaume and Ollivier, Yann},
  year      = {2020},
  eprint    = {2002.00178},
  archivePrefix = {arXiv}
}