Uncertainty in Deep Learning
Deep learning has attracted tremendous attention from researchers in various fields of information engineering such as AI, computer vision, and language processing [Kalchbrenner and Blunsom, 2013; Krizhevsky et al. 2012; Mnih et al. 2013] but also from more traditional sciences such as physics, biology, and manufacturing [Anjos et al. 2015; Baldi et al. 2014; Bergmann et al. 2014] Neural networks, image processing tools such as convolutional neural networks, sequence processing models such as recurrent neural networks, and regularisation tools such as dropout, are used extensively. However, fields such as physics, biology, and manufacturing are ones in which representing model uncertainty is of crucial importance [Ghahramani, 2015; Krzywinski and Altman, 2013] With the recent shift in many of these fields towards the use of Bayesian uncertainty [Herzog and Ostwald, 2013; Nuzzo, 2014; Trafimow and Marks, 2015] new needs arise from deep learning. In this work we develop tools to obtain practical uncertainty estimates in deep learning, casting recent deep learning tools as Bayesian models without changing either the models or the optimisation. In the first part of this thesis we develop the theory for such tools, providing applications and illustrative examples. We tie approximate inference in Bayesian models to dropout and other stochastic regularisation techniques, and assess the approximations empirically. We give example applications arising from this connection between modern deep learning and Bayesian modelling such as active learning of image data and data efficient deep reinforcement learning. We further demonstrate the method's practicality through a survey of recent applications making use of the suggested tools in language applications, medical diagnostics, bioinformatics, image processing, and autonomous driving. In the second part of the thesis we explore its theoretical implications, and the insights stemming from the link between Bayesian modelling and deep learning. We discuss what determines model uncertainty properties, analyse the approximate inference analytically in the linear case, and theoretically examine various priors such as spike and slab priors.