arXiv:2602.16568v2 Announce Type: replace-cross Abstract: Sparse recovery is among the most well-studied problems in learning theory and high-dimensional statistics. In this work, we investigate the statistical and computational landscapes of sparse recovery with $\ell_\infty$ error guarantees. This variant of the problem is motivated by \emph{variable selection} tasks, where the goal is to estimate the support of a $k$-sparse signal in $\mathbb{R}^d$. Our main contribution is a provable separation between the \emph{oblivious} (``for each'') and \emph{adaptive} (``for all'') models of $\ell_\i
This research is published as AI and machine learning models are becoming increasingly complex and critical, highlighting foundational mathematical challenges in feature selection.
Improving sparse recovery and variable selection is crucial for developing more efficient, interpretable, and robust AI models, impacting diverse applications from scientific discovery to engineering.
New theoretical bounds and separations between adaptive and oblivious models contribute to a deeper understanding of the fundamental limits and capabilities of sparse learning algorithms.
- · Machine learning researchers
- · Data scientists
- · AI algorithm developers
- · Practitioners relying on suboptimal feature selection methods
Improved theoretical understanding of variable selection problems in high-dimensional data.
Development of more efficient and provably accurate algorithms for sparse learning.
Enhanced performance and interpretability of AI systems in areas requiring precise feature identification.
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Read at arXiv cs.LG