An Equivalence between Bayesian Priors and Penalties in Variational Inference
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.
- Publication:
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arXiv e-prints
- Pub Date:
- February 2020
- DOI:
- 10.48550/arXiv.2002.00178
- arXiv:
- arXiv:2002.00178
- Bibcode:
- 2020arXiv200200178W
- Keywords:
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- Computer Science - Machine Learning;
- Mathematics - Statistics Theory;
- Statistics - Machine Learning