This paper establishes a precise high-dimensional asymptotic theory for
boosting on separable data, taking statistical and computational perspectives.
We consider a high-dimensional setting where the number of features (weak
learners) $p$ scales with the sample size $n$, in an overparametrized regime.
Under a class of statistical models, we provide an exact analysis of the
generalization error of boosting when the algorithm interpolates the training
data and maximizes the empirical $\ell_1$-margin. Further, we explicitly pin
down the relation between the boosting test error and the optimal Bayes error,
as well as the proportion of active features at interpolation (with zero
initialization). In turn, these precise characterizations answer certain
questions raised in \cite{breiman1999prediction, schapire1998boosting}
surrounding boosting, under assumed data generating processes. At the heart of
our theory lies an in-depth study of the maximum-$\ell_1$-margin, which can be
accurately described by a new system of non-linear equations; to analyze this
margin, we rely on Gaussian comparison techniques and develop a novel uniform
deviation argument. Our statistical and computational arguments can handle (1)
any finite-rank spiked covariance model for the feature distribution and (2)
variants of boosting corresponding to general $\ell_q$-geometry, $q \in [1,
2]$. As a final component, via the Lindeberg principle, we establish a
universality result showcasing that the scaled $\ell_1$-margin (asymptotically)
remains the same, whether the covariates used for boosting arise from a
non-linear random feature model or an appropriately linearized model with
matching moments.

本文建立了一个精确的高维渐近理论，探讨了分离数据上的 Boosting 的统计和计算方法。在考虑特征（弱学习器）数量 $p$ 与样本大小 $n$ 比例过大的高维情况下，提供了一种统计模型的确切分析，探讨了 Boosting 在插值训练数据并最大化经验 l1-margin 时的泛化误差，解答了 Boosting 的相关问题。同时，文章研究了最大 l1-margin，引入了新的非线性方程和高斯比较技术和均匀偏差论证。