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.

翻译：在机器学习中，通常通过调节一个针对特定参数值进行惩罚的专用正则化项来优化概率模型的参数。在变分推断（一种近似贝叶斯后验的可行方法）中，正则化项自然出现：优化目标包含近似后验与贝叶斯先验之间的库尔贝克-莱布勒散度项。我们完整刻画了通过该流程可能产生的正则化函数，并提供了从给定惩罚项系统计算对应先验的方法。这种刻画可用于发现惩罚函数的约束条件，从而确保整体流程保持贝叶斯性质。