  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.
