Efficient Approximate Inference with Walsh-Hadamard Variational Inference
This addresses a bottleneck in scalable Bayesian inference for models like Bayesian neural networks, though it appears incremental as it builds on existing kernel method strategies.
The paper tackles the challenge of over-regularization in variational inference for over-parameterized models by proposing Walsh-Hadamard Variational Inference, which uses Walsh-Hadamard-based factorization to reduce parameterization, accelerate computations, and increase posterior expressiveness.
Variational inference offers scalable and flexible tools to tackle intractable Bayesian inference of modern statistical models like Bayesian neural networks and Gaussian processes. For largely over-parameterized models, however, the over-regularization property of the variational objective makes the application of variational inference challenging. 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, which uses Walsh-Hadamard-based factorization strategies to reduce model parameterization, accelerate computations, and increase the expressiveness of the approximate posterior beyond fully factorized ones.