Orthogonalized Design Matrices Speed-ups of Bayesian Semiparametric Regression

2026-07-09

AI Summary

This work addresses the computational inefficiency in Bayesian semiparametric regression arising from complex design matrix structures. To mitigate this challenge, the authors propose an orthogonalization preprocessing step applied to the design日晚间 matrix prior to iterative inference, combined with a hybrid algorithm integrating Gibbs sampling and coordinate ascent variational inference. This approach reduces computational complexity to quadratic in the number of covariates, substantially accelerating both model fitting and posterior inference. Empirical evaluations across diverse experimental settings demonstrate speedups ranging from 5× to 60× compared to conventional methods, effectively alleviating the computational bottleneck induced by high-dimensional covariates.

Abstract

We explain how important classes of Bayesian semiparametric regression fitting and inference procedures can be sped up, significantly, via the use of orthogonalized design matrices. Typically, design matrices in semiparametric regression contain predictor observations and basis functions of such data. In Bayesian semiparametric regression, loop-type approaches such as Gibbs sampling and coordinate ascent variational inference typically are required. We show that pre-loop reformulation of Bayesian semiparametric regression models involving orthogonalized design matrices lead to two orders of magnitude, with respect to column dimension, computational reduction. Our computer experiments reveal that this simple paradigm results in approximately 5- to 60-fold speed-ups.

Problem

• Bayesian semiparametric regression
• computational speed-up
• orthogonalized design matrices
• Gibbs sampling
• variational inference

Innovation

• orthogonalized design matrices
• Bayesian semiparametric regression
• computational speed-up
• Gibbs sampling
• variational inference