Bayesian deep learning

Insights in the Bayesian paradigm for deep learning

Master thesis (2023)

Authors

W.R. Schipper Electrical Engineering, Mathematics and Computer Science

Contributors

A.W. van der Vaart Statistics - EEMCS (mentor)
A. Heinlein Numerical Analysis - EEMCS (graduation committee member)
Faculty
Electrical Engineering, Mathematics and Computer Science, Electrical Engineering, Mathematics and Computer Science
Copyright: © 2023 Wieger Schipper
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Published Date

30-08-2023

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Abstract

In this thesis, we study a particle method for Bayesian deep learning. In particular, we look at the estimation of the parameters of an ensemble of Bayesian neural networks by means of this particle method, called Stein variational gradient descent (SVGD). This method iteratively updates a collection of parameters and it has the property that its update directions are chosen such that they optimally decrease the Kullback-Leibler divergence. We also study gradient flows of probability measures and show how gradient flows corresponding to functionals on the space of probability measures can induce particle flows. We formulate SVGD as a method in this space. In the regime of infinite particles we show results about convergence of SVGD. An existing convergence result for SVGD can be extended by showing that the probability measures, governing the collection of SVGD particles, are uniformly tight. We give conditions under which this holds.

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