Interpreting a Penalty as the Influence of a Bayesian Prior

Pierre Wolinski (1) , Guillaume Charpiat (1) , Yann Ollivier (2, 3)

1 TAU - TAckling the Underspecified
2 FAIR - Facebook AI Research [Paris]
3 LRI - Laboratoire de Recherche en Informatique

In machine learning, it is common to optimize the parameters of a probabilistic model, modulated by a somewhat ad hoc regularization term that penalizes some values of the parameters. Regularization terms appear naturally in Variational Inference (VI), 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 which regularizers can arise this way, and provide a systematic way to compute the corresponding prior. This viewpoint also provides a prediction for useful values of the regularization factor in neural networks. We apply this framework to regularizers such as L1 or group-Lasso.

Domaines: Machine Learning [stat.ML]; Apprentissage [cs.LG]; Réseau de neurones [cs.NE]

Pierre Wolinski, Guillaume Charpiat, Yann Ollivier. Interpreting a Penalty as the Influence of a Bayesian Prior. 2020. ⟨hal-02466702⟩