aiqbench analysis
GEMSS introduces a novel variational mixture approach designed to extract multiple distinct, sparse solutions from underdetermined regression and classification tasks where standard methods often yield arbitrary single results. By incorporating built-in repulsion between mixture components, the method effectively navigates high-dimensional spaces with collinearities to provide domain experts with statistically plausible alternative explanations rather than just one model output. This advancement addresses a critical gap in interpretability for scenarios like $n \ll p$, offering open-source tools that outperform existing baselines in recovering diverse feature subsets from real-world datasets.
GEMSS: A Variational Method for Discovering Multiple Sparse Solutions in Classification and Regression Problems
arXiv:2602.08913v3 Announce Type: replace 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.
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 (this http URL) and democratized through a free online application at this http URL.
Machine Learning (cs.LG); Machine Learning (stat.ML)
arXiv:2602.08913 [cs.LG]
(or arXiv:2602.08913v3 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2602.08913 Focus to learn more arXiv-issued DOI via DataCite
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Full text under the publisher's open licence · 305 words
