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arXiv · 2006.10801

Predictive Complexity Priors

Eric Nalisnick·Jonathan Gordon·José Miguel Hernández-Lobato
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Abstract

Specifying a Bayesian prior is notoriously difficult for complex models such as neural networks. Reasoning about parameters is made challenging by the high-dimensionality and over-parameterization of the space. Priors that seem benign and uninformative can have unintuitive and detrimental effects on a model's predictions. For this reason, we propose predictive complexity priors: a functional prior that is defined by comparing the model's predictions to those of a reference model. Although originally defined on the model outputs, we transfer the prior to the model parameters via a change of variables. The traditional Bayesian workflow can then proceed as usual. We apply our predictive complexity prior to high-dimensional regression, reasoning over neural network depth, and sharing of statistical strength for few-shot learning.

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Eric Nalisnick, Jonathan Gordon, José Miguel Hernández-Lobato. 2020-06-18. Predictive Complexity Priors. https://arxiv.org/abs/2006.10801

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