# Adaptive mixture variational inference for spike-and-slab regression

arXiv: https://arxiv.org/abs/2609.38656 · HTML: https://mlsanity.com/paper/2609.38656/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 20 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Builds on (most cited first, 11 of 11)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Rank-normalization, folding, and localization: An improved widehatR for assessing convergence of MCMC](https://mlsanity.com/paper/1903.08008/) (2019)
- [Variational Bayes for high-dimensional linear regression with sparse priors](https://mlsanity.com/paper/1904.07150/) (2019)
- [Covariances, Robustness, and Variational Bayes](https://mlsanity.com/paper/1709.02536/) (2017)
- [Variational Boosting: Iteratively Refining Posterior Approximations](https://mlsanity.com/paper/1611.06585/) (2016)
- [A Unified Perspective on Natural Gradient Variational Inference with Gaussian Mixture Models](https://mlsanity.com/paper/2209.11533/) (2022)
- [Boosting Black Box Variational Inference](https://mlsanity.com/paper/1806.02185/) (2018)
- [Trust-Region Variational Inference with Gaussian Mixture Models](https://mlsanity.com/paper/1907.04710/) (2019)
- [Variational Inference for Uncertainty Quantification: an Analysis of Trade-offs](https://mlsanity.com/paper/2403.13748/) (2024)
- [Flexible mean field variational inference using mixtures of non-overlapping exponential families](https://mlsanity.com/paper/2010.06768/) (2020)
- [GEMSS: A Variational Method for Discovering Multiple Sparse Solutions in Classification and Regression Problems](https://mlsanity.com/paper/2602.08913/) (2026)

## Abstract (arXiv)

Correlated predictors can support competing sparse explanations with similar predictions, making joint uncertainty about variable inclusion difficult to capture with mean-field approximations. We develop an adaptive fitting procedure for mixtures of product distributions in Gaussian regression with a point-mass spike-and-slab prior. It minimizes reverse Kullback-Leibler divergence directly on inclusion indicators and active coefficients, jointly refining component parameters and weights as the mixture grows. This avoids an additional divergence penalty on unused latent coefficients under independent augmentation. Our analysis relates approximation accuracy to mixture size, support coverage and dependence within supports, and establishes contraction, selection consistency and a Bernstein-von Mises approximation under explicit conditions on the prior, posterior concentration and variational error. On all 250 simulated datasets with exact posterior references, mixtures reduce errors in inclusion probabilities, grouped support probabilities and coefficient covariance relative to multistart mean field. Comparisons at fixed mixture size and common initialization favor direct joint refinement over augmented or restricted refinement in posterior divergence. Complete stagewise fitting can nevertheless be more accurate near collinearity. The results support direct joint refinement for posterior approximation while showing that local gains do not ensure superiority of the full adaptive search.