Horseshoe Regularization for Machine Learning in Complex and Deep Models
This is an incremental review that expands the scope of horseshoe regularization for researchers in machine learning dealing with complex models.
The paper reviews the application of horseshoe regularization beyond linear Gaussian models, addressing methodological and computational challenges in nonlinear, non-Gaussian, multivariate, and deep neural network contexts to broaden its utility in machine learning.
Since the advent of the horseshoe priors for regularization, global-local shrinkage methods have proved to be a fertile ground for the development of Bayesian methodology in machine learning, specifically for high-dimensional regression and classification problems. They have achieved remarkable success in computation, and enjoy strong theoretical support. Most of the existing literature has focused on the linear Gaussian case; see Bhadra et al. (2019b) for a systematic survey. The purpose of the current article is to demonstrate that the horseshoe regularization is useful far more broadly, by reviewing both methodological and computational developments in complex models that are more relevant to machine learning applications. Specifically, we focus on methodological challenges in horseshoe regularization in nonlinear and non-Gaussian models; multivariate models; and deep neural networks. We also outline the recent computational developments in horseshoe shrinkage for complex models along with a list of available software implementations that allows one to venture out beyond the comfort zone of the canonical linear regression problems.