Walsh-Hadamard Variational Inference for Bayesian Deep Learning
This addresses the problem of scalable Bayesian inference for deep learning models, offering a novel method to mitigate over-regularization, though it appears incremental as it builds on existing kernel method strategies.
The paper tackles the challenge of Bayesian inference for over-parameterized models like DeepNets and ConvNets, which suffer from over-regularization in variational inference, by proposing Walsh-Hadamard Variational Inference (WHVI) that uses Walsh-Hadamard-based factorization to reduce parameterization and accelerate computations, resulting in considerable speedups and model reductions compared to other techniques.
Over-parameterized models, such as DeepNets and ConvNets, form a class of models that are routinely adopted in a wide variety of applications, and for which Bayesian inference is desirable but extremely challenging. Variational inference offers the tools to tackle this challenge in a scalable way and with some degree of flexibility on the approximation, but for over-parameterized models this is challenging due to the over-regularization property of the variational objective. Inspired by the literature on kernel methods, and in particular on structured approximations of distributions of random matrices, this paper proposes Walsh-Hadamard Variational Inference (WHVI), which uses Walsh-Hadamard-based factorization strategies to reduce the parameterization and accelerate computations, thus avoiding over-regularization issues with the variational objective. Extensive theoretical and empirical analyses demonstrate that WHVI yields considerable speedups and model reductions compared to other techniques to carry out approximate inference for over-parameterized models, and ultimately show how advances in kernel methods can be translated into advances in approximate Bayesian inference.