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ℓ∞ 扰动下对抗训练估计量的渐近行为AI 解读

Adversarial training has been proposed to protect machine learning models against adversarial attacks. This paper focuses on adversarial training under 𝓁∞-perturbation, which has recently attracted much research attention. The asymptotic behavior of the adversarial training estimator is investigated in the generalized linear model. The results imply that the asymptotic distribution of the adversarial training estimator under 𝓁∞-perturbation could put a positive probability…

伯努利网格中最长显著游程长度的分布及应用AI 解读

We consider the length of the longest significance run in a (two-dimensional) Bernoulli net and derive its asymptotic limit distribution. Our results can be considered as generalizations of known theorems in significance runs. We give three types of theoretical results: (1) reliability-style lower and upper bounds, (2) Erdös–Rényi law, and (3) the asymptotic limit distribution. To understand the rate of convergence to the asymptotic distributions, we carry out numerical…

均匀随机点背景中丝状结构的自适应多尺度检测AI 解读

We are given a set of n points that might be uniformly distributed in the unit square [0,1]2. We wish to test whether the set, although mostly consisting of uniformly scattered points, also contains a small fraction of points sampled from some (a priori unknown) curve with Cα-norm bounded by β. An asymptotic detection threshold exists in this problem; for a constant T−(α,β)>0, if the number of points sampled from the curve is smaller than T−(α,β)n1/(1+α), reliable detection…