Feature Selection and Junta Testing are Statistically Equivalent

Lorenzo Beretta; Nathaniel Harms; Caleb Koch

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arXiv · 2505.04604

Feature Selection and Junta Testing are Statistically Equivalent

Lorenzo Beretta·Nathaniel Harms·Caleb Koch

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Abstract

For a function $f \colon \{0,1\}^n \to \{0,1\}$, the junta testing problem asks whether $f$ depends on only $k$ variables. If $f$ depends on only $k$ variables, the feature selection problem asks to find those variables. We prove that these two tasks are statistically equivalent. Specifically, we show that the ``brute-force'' algorithm, which checks for any set of $k$ variables consistent with the sample, is simultaneously sample-optimal for both problems, and the optimal sample size is \[ \Theta\left(\frac 1 \varepsilon \left( \sqrt{2^k \log {n \choose k}} + \log {n \choose k}\right)\right). \]

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Lorenzo Beretta, Nathaniel Harms, Caleb Koch. 2025-05-07. Feature Selection and Junta Testing are Statistically Equivalent. https://arxiv.org/abs/2505.04604

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