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

2026-09-26

AI Summary

This study addresses the challenges of high measurement overhead and decoding complexity in identifying and recovering the support set of sparse vectors within mixtures of linear classifiers. To overcome these limitations, this work proposes both adaptive and non-adaptive schemes that integrate sign measurement analysis to optimize algorithm design. Specifically, the adaptive strategy substantially reduces the required number of measurements through dynamic querying, while the non-adaptive construction leverages structured coding to enable efficient parallel decoding. The primary contribution lies in reducing decoding complexity to a sublinear level, thereby achieving a superior balance between sample complexity and computational efficiency. Ultimately, this research establishes a novel framework for high-dimensional sparse signal recovery that offers both rigorous theoretical guarantees and practical computational effectiveness.

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.

Problem

• Support Recovery
• Mixture of Linear Classifiers
• Sparse Vectors
• Sign Measurements

Innovation

• Support Recovery
• Mixture of Linear Classifiers
• Adaptive Measurement
• Sublinear Decoding
• Sample Complexity