Sparse online variational Bayesian regression

• URL: http://arxiv.org/abs/2102.12261v1
• Date: Wed, 24 Feb 2021 12:49:42 GMT
• Title: Sparse online variational Bayesian regression
• Authors: Kody J. H. Law and Vitaly Zankin
• Abstract summary: variational Bayesian inference as an inexpensive and scalable alternative to a fully Bayesian approach. For linear models the method requires only the iterative solution of deterministic least squares problems. For large p an approximation is able to achieve promising results for a cost of O(p) in both computation and memory.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This work considers variational Bayesian inference as an inexpensive and scalable alternative to a fully Bayesian approach in the context of sparsity-promoting priors. In particular, the priors considered arise from scale mixtures of Normal distributions with a generalized inverse Gaussian mixing distribution. This includes the variational Bayesian LASSO as an inexpensive and scalable alternative to the Bayesian LASSO introduced in [56]. It also includes priors which more strongly promote sparsity. For linear models the method requires only the iterative solution of deterministic least squares problems. Furthermore, for $n\rightarrow \infty$ data points and p unknown covariates the method can be implemented exactly online with a cost of O(p$^3$) in computation and O(p$^2$) in memory. For large p an approximation is able to achieve promising results for a cost of O(p) in both computation and memory. Strategies for hyper-parameter tuning are also considered. The method is implemented for real and simulated data. It is shown that the performance in terms of variable selection and uncertainty quantification of the variational Bayesian LASSO can be comparable to the Bayesian LASSO for problems which are tractable with that method, and for a fraction of the cost. The present method comfortably handles n = p = 131,073 on a laptop in minutes, and n = 10$^5$, p = 10$^6$ overnight.

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