# Stability of Sequential and Parallel Coordinate Ascent Variational Inference

arXiv: https://arxiv.org/abs/2603.20929 · HTML: https://mlsanity.com/paper/2603.20929/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 25 references that are in the map.
- First posted on arXiv 21 Mar 2026.

## Builds on (most cited first, 15 of 15)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Concentration of tempered posteriors and of their variational approximations](https://mlsanity.com/paper/1706.09293/) (2017)
- [Frequentist Consistency of Variational Bayes](https://mlsanity.com/paper/1705.03439/) (2017)
- [Variational Bayes for high-dimensional linear regression with sparse priors](https://mlsanity.com/paper/1904.07150/) (2019)
- [Bayesian linear regression with sparse priors](https://mlsanity.com/paper/1403.0735/) (2014)
- [On Statistical Optimality of Variational Bayes](https://mlsanity.com/paper/1712.08983/) (2017)
- [Theoretical and Computational Guarantees of Mean Field Variational Inference for Community Detection](https://mlsanity.com/paper/1710.11268/) (2017)
- [On the Convergence of Coordinate Ascent Variational Inference](https://mlsanity.com/paper/2306.01122/) (2023)
- [Local convexity of the TAP free energy and AMP convergence for Z2-synchronization](https://mlsanity.com/paper/2106.11428/) (2021)
- [Convergence of coordinate ascent variational inference for log-concave measures via optimal transport](https://mlsanity.com/paper/2404.08792/) (2024)
- [An Instability in Variational Inference for Topic Models](https://mlsanity.com/paper/1802.00568/) (2018)
- [A Variational Algorithm for Bayesian Variable Selection](https://mlsanity.com/paper/1602.07640/) (2016)
- [Statistical optimality and stability of tangent transform algorithms in logit models](https://mlsanity.com/paper/2010.13039/) (2020)
- [An Approximate Bayesian Approach to Covariate-dependent Graphical Modeling](https://mlsanity.com/paper/2303.08979/) (2023)
- [A Variational Spike-and-Slab Approach for Group Variable Selection](https://mlsanity.com/paper/2309.16855/) (2023)

## Built on by (most cited first, 1 of 1)

- [Wasserstein Contraction of Coordinate Ascent Variational Inference](https://mlsanity.com/paper/2605.30253/) (2026)

## Abstract (arXiv)

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.