We provide matching upper and lower bounds of order $\sigma^2/\log(d/n)$ for the prediction error of the minimum $\ell_1$-norm interpolator, a.k.a. basis pursuit. Our result is tight up to negligible terms when $d \gg n$, and is the first to imply asymptotic consistency of noisy minimum-norm interpolation for isotropic features and sparse ground truths. Our work complements the literature on "benign overfitting" for minimum $\ell_2$-norm interpolation, where asymptotic consistency can be achieved only when the features are effectively low-dimensional.
翻译：我们为最小 $\ ell_ 1$\\\\\\\\\ d/n. brog (d/n) 排序提供了匹配的上限和下限 $sigma\\\\\\\\\\\\\\\\\\ d/n) log(d/n), 用于预测最小 $\ ell_ 1$- norm interpolator, a.k. a. basic 追求的错误。 我们的结果紧凑到当$\ gg n$ 美元时可忽略不计的值, 并且第一个意味着杂音的最低- norm interpoint 和稀有的地面事实。 我们的工作补充了关于最小 $\ ell_ 2 $- Norm interpologation 的“ 居居居居居多” 的文献, 只有这些特征实际上低维度时, 才能实现无症状的一致性。
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