发表机构
Halıcıoğlu Data Science Institute, University of California, San Diego（加州大学圣地亚哥分校哈利奇奥卢数据科学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对混合线性分类器的支持恢复问题，提出自适应与非自适应方案，在减少测量次数的同时将解码时间降至亚线性，实现更优的样本复杂度与解码效率权衡。
AI 中文摘要
混合线性分类器中的支持恢复问题旨在当数据由多个线性决策规则的混合生成时，识别哪些特征真正起作用。具体而言，目标是从符号测量中恢复$l$个未知$k$-稀疏向量的支持（非零坐标）。每次测量通过均匀随机选择$l$个向量中的一个，并返回其与所选测量向量内积的符号来生成。在本文中，我们提出了自适应和非自适应方案，通过减少测量次数并同时实现亚线性解码时间，显著改进了先前的结果。特别是，我们的自适应构造相比现有方法大幅减少了测量次数，同时将解码复杂度从环境维度上的超二次降低到亚线性。我们进一步提供了一种非自适应方案，在保持高效解码的同时改进了先前的测量界限。总体而言，我们的方法在混合模型的支持恢复中，相比已知方法实现了样本复杂度和解码时间之间更高效的权衡。
英文摘要
The support recovery problem in mixture of linear classifiers aims to identify the features relevant to the underlying decision rules when data is generated by a mixture of several linear decision rules. In particular, the goal 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 simultaneously reducing the number of measurements and achieving sublinear decoding time. 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 compared to previously known methods.
