Stability of Sequential and Parallel Coordinate Ascent Variational Inference

2026-03-21

AI Summary

This study investigates the differences in convergence and stability between sequential and parallel coordinate ascent variational inference (CAVI) in moderate-to-high-dimensional linear regression models. By integrating numerical analysis with optimization theory, the work systematically compares the convergence behavior of these two algorithmic variants. The analysis reveals that sequential CAVI enjoys convergence guarantees under substantially milder conditions, whereas parallel CAVI, despite its superior computational efficiency, requires stricter assumptions on the model structure. This research addresses a notable gap in the theoretical understanding of how update strategies in variational inference affect convergence criteria, thereby providing a principled foundation for selecting appropriate algorithms in practical applications.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Probabilistic Circuits and Graphical Models
• Computer Vision: Learning & Optimization for CV

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We highlight a striking difference in behavior between two widely used variants of coordinate ascent variational inference: the sequential and parallel algorithms. While such differences were known in the numerical analysis literature in simpler settings, they remain largely unexplored in the optimization-focused literature on variational inference in more complex models. Focusing on the moderately high-dimensional linear regression problem, we show that the sequential algorithm, although typically slower, enjoys convergence guarantees under more relaxed conditions than the parallel variant, which is often employed to facilitate block-wise updates and improve computational efficiency.

Problem

• coordinate ascent variational inference
• sequential algorithm
• parallel algorithm
• convergence stability
• high-dimensional linear regression

Innovation

• coordinate ascent variational inference
• sequential algorithm
• parallel algorithm
• convergence guarantees
• stability