Exploring Deep Learning Parameter Space with a-GPS: Approximate Gaussian Proposal Sampler

Fabian Meyer Bull, Geir Storvik, Arnt B. Salberg, Anne Schistad Solberg

Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)

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Keywords: sgmcmc, bayesian deep learning, uncertainty, sampling, UQ

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TL;DR: A sampler that dynamically fits a Gaussian to the modes and can jump between modes.

Abstract: To trust the predictions provided by deep neural networks we need to quantify the uncertainty. This can be done with Bayesian neural networks. However, they require a trade-off between exactness and effectiveness. This paper introduces a new sampling framework: Adaptive Proposal Sampling (APS). APS is a mode seeking sampler that adapts the proposal to match a posterior mode. When modes overlap, APS will adapt to a new mode if it draws a sample that belongs to a new mode. A variant of APS is the approximate Gaussian Proposal Sampler (a-GPS). We show that it becomes a perfect sampler if it has the same score function as the posterior. With a warm-start of a pretrained model, combined with stochastic gradients it scales up to deep learning. Results show that a-GPS 1) proposes samples that are proportional to a mode, 2) explores multi-modal landscapes, 3) has fast computations, 4) scales to big data. Immediate results suggest that this framework may be a step towards having both exactness and effectiveness.

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Submission Number: 5473