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[2602.16568] Separating Oblivious and Adaptive Models of Variable Selection
Summary
This paper explores the differences between oblivious and adaptive models in variable selection, revealing significant implications for sparse recovery in statistics and machine learning.
Why It Matters
Understanding the distinctions between oblivious and adaptive models is crucial for improving variable selection methods in high-dimensional statistics. The findings can influence algorithm design and efficiency in machine learning applications, particularly in sparse recovery scenarios.
Key Takeaways
- Oblivious models achieve optimal error rates in near-linear time with fewer samples than adaptive models.
- Adaptive models require significantly more samples to reach similar performance levels, highlighting a critical trade-off.
- The study contrasts the behavior of $ ext{l}_ ext{infty}$ and $ ext{l}_ ext{2}$ models in sparse recovery tasks.
- A partially-adaptive model shows promise for achieving variable selection with fewer measurements.
- These insights can guide future research and practical applications in machine learning and statistics.
Mathematics > Statistics Theory arXiv:2602.16568 (math) [Submitted on 18 Feb 2026] Title:Separating Oblivious and Adaptive Models of Variable Selection Authors:Ziyun Chen, Jerry Li, Kevin Tian, Yusong Zhu View a PDF of the paper titled Separating Oblivious and Adaptive Models of Variable Selection, by Ziyun Chen and 3 other authors View PDF HTML (experimental) 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 $\ell_\infty$ sparse recovery. We show that under an oblivious model, the optimal $\ell_\infty$ error is attainable in near-linear time with $\approx k\log d$ samples, whereas in an adaptive model, $\gtrsim k^2$ samples are necessary for any algorithm to achieve this bound. This establishes a surprising contrast with the standard $\ell_2$ setting, where $\approx k \log d$ samples suffice even for adaptive sparse recovery. We conclude with a preliminary examination of a \emph{partially-adaptive} model, where we show nontrivial variable selection guarantees are possible with $\approx k\...
