A Bayesian Perspective on Training Speed and Model Selection

• URL: http://arxiv.org/abs/2010.14499v1
• Date: Tue, 27 Oct 2020 17:56:14 GMT
• Title: A Bayesian Perspective on Training Speed and Model Selection
• Authors: Clare Lyle, Lisa Schut, Binxin Ru, Yarin Gal, Mark van der Wilk
• Abstract summary: We show that a measure of a model's training speed can be used to estimate its marginal likelihood. We verify our results in model selection tasks for linear models and for the infinite-width limit of deep neural networks. Our results suggest a promising new direction towards explaining why neural networks trained with gradient descent are biased towards functions that generalize well.
• Score: 51.15664724311443
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We take a Bayesian perspective to illustrate a connection between training speed and the marginal likelihood in linear models. This provides two major insights: first, that a measure of a model's training speed can be used to estimate its marginal likelihood. Second, that this measure, under certain conditions, predicts the relative weighting of models in linear model combinations trained to minimize a regression loss. We verify our results in model selection tasks for linear models and for the infinite-width limit of deep neural networks. We further provide encouraging empirical evidence that the intuition developed in these settings also holds for deep neural networks trained with stochastic gradient descent. Our results suggest a promising new direction towards explaining why neural networks trained with stochastic gradient descent are biased towards functions that generalize well.

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