Predictive Complexity Priors

• URL: http://arxiv.org/abs/2006.10801v3
• Date: Wed, 21 Oct 2020 15:56:55 GMT
• Title: Predictive Complexity Priors
• Authors: Eric Nalisnick, Jonathan Gordon, Jos\'e Miguel Hern\'andez-Lobato
• Abstract summary: We propose 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. We apply our predictive complexity prior to high-dimensional regression, reasoning over neural network depth, and sharing of statistical strength for few-shot learning.
• Score: 3.5547661483076998
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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