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arXiv · 2602.08913

GEMSS: A Variational Method for Discovering Multiple Sparse Solutions in Classification and Regression Problems

Kateřina Henclová·Václav Šmídl
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Abstract

In underdetermined regression and classification problems, multiple feature subsets often yield equivalent predictive performance. In applied settings, especially with $n \ll p$, high dimension or collinearities, it is valuable to provide a domain expert with a menu of statistically plausible explanations, rather than one arbitrary solution. This creates the need for appropriate methods. We present Gaussian Ensemble for Multiple Sparse Solutions (GEMSS), a method that uses a single variational mixture to approximate the corresponding multimodal posterior. Its evidence lower bound contains a built-in repulsion between the mixture's components, enabling the model to simultaneously produce several distinct sparse solutions. We evaluate GEMSS on a novel, reusable benchmark. The ground-truth solution set and its structure are known by construction and set-level recovery metrics are evaluated. GEMSS consistently outperforms dedicated multiplicity methods (Enumeration LASSO, ALFESE), two strong sampling baselines that approximate the same posterior (Randomized-LASSO ensemble, BB-SSL), and naive iterative masking. As solutions' overlap increases, the gap widens and additional ensemble restarts cannot close it. Only ALFESE proves competitive. Further, GEMSS is validated on real-world datasets, producing multiple distinct and highly predictive solutions: the practical goal that existing methods struggle to meet. The open-source Python package 'gemss' is available (github.com/kat-er-ina/gemss) and democratized through a free online application at huggingface.co/spaces/kat-er-ina/gemss.

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Kateřina Henclová, Václav Šmídl. 2026-07-30. GEMSS: A Variational Method for Discovering Multiple Sparse Solutions in Classification and Regression Problems. https://arxiv.org/abs/2602.08913

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