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Approximate Inference Turns Deep Networks into Gaussian Processes
Mohammad Emtiyaz Khan · Alexander Immer · Ehsan Abedi · Maciej Korzepa

Tue Dec 10 05:30 PM -- 07:30 PM (PST) @ East Exhibition Hall B + C #164

Deep neural networks (DNN) and Gaussian processes (GP) are two powerful models with several theoretical connections relating them, but the relationship between their training methods is not well understood. In this paper, we show that certain Gaussian posterior approximations for Bayesian DNNs are equivalent to GP posteriors. This enables us to relate solutions and iterations of a deep-learning algorithm to GP inference. As a result, we can obtain a GP kernel and a nonlinear feature map while training a DNN. Surprisingly, the resulting kernel is the neural tangent kernel. We show kernels obtained on real datasets and demonstrate the use of the GP marginal likelihood to tune hyperparameters of DNNs. Our work aims to facilitate further research on combining DNNs and GPs in practical settings.

Author Information

Emtiyaz Khan (RIKEN)

Emtiyaz Khan (also known as Emti) is a team leader at the RIKEN center for Advanced Intelligence Project (AIP) in Tokyo where he leads the Approximate Bayesian Inference Team. He is also a visiting professor at the Tokyo University of Agriculture and Technology (TUAT). Previously, he was a postdoc and then a scientist at Ecole Polytechnique Fédérale de Lausanne (EPFL), where he also taught two large machine learning courses and received a teaching award. He finished his PhD in machine learning from University of British Columbia in 2012. The main goal of Emti’s research is to understand the principles of learning from data and use them to develop algorithms that can learn like living beings. For the past 10 years, his work has focused on developing Bayesian methods that could lead to such fundamental principles. The approximate Bayesian inference team now continues to use these principles, as well as derive new ones, to solve real-world problems.

Alex Immer (EPFL, RIKEN)
Ehsan Abedi (EPFL)
Maciej Korzepa (Technical University of Denmark)

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