Efficient Support Recovery of Mixtures of Sparse Linear Classifiers with Less Measurements

Abstract:The support recovery problem in mixture of linear classifiers intends to identify which features actually matter when data is generated by a mixture of several linear decision rules. In particular, the aim is to recover the support (nonzero coordinates) of $l$ unknown $k$-sparse vectors from sign measurements. Each measurement is generated by selecting one of the $l$ vectors uniformly at random, and returning the sign of its inner product with a chosen measurement vector. In this paper, we propose adaptive and non-adaptive schemes that significantly improve upon prior results by reducing the number of measurements and achieving sublinear decoding time simultaneously. In particular, our adaptive constructions substantially reduce measurements compared to existing approaches, while also lowering decoding complexity from super-quadratic to sublinear in the ambient dimension. We further provide a non-adaptive scheme that improves previous measurement bounds while maintaining efficient decoding. Overall, our approach yields a more efficient trade-off between sample complexity and decoding time for support recovery in mixture models than previously known methods.

Machine Learning (cs.LG); Data Structures and Algorithms (cs.DS)

arXiv:2609.32176 [cs.LG]

(or arXiv:2609.32176v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.32176 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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