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星形约束下稳健次高斯均值估计的信息论极限AI 解读

We obtain the minimax rate for a mean location model with a bounded star-shaped set K⊆Rn constraint on the mean, in an adversarially corrupted data setting with Gaussian noise. We assume an unknown fraction ϵ≤1/2−κ for some fixed κ∈(0,1/2] of N observations are arbitrarily corrupted. We obtain a minimax risk up to proportionality constants under the squared ℓ2 loss of max(η∗2,σ2ϵ2)∧d2 with η∗=sup{η≥0:Nη2 σ2≤logMKloc(η,c)}, where logMKloc(η,c) denotes the local entropy of the…

半监督 U 统计量AI 解读

Semi-supervised datasets are ubiquitous across diverse domains where obtaining fully labeled data is costly or time-consuming. The prevalence of such datasets has consistently driven the demand for new tools and methods that exploit the potential of unlabeled data. Responding to this demand, we introduce semi-supervised U-statistics enhanced by the abundance of unlabeled data, and investigate their statistical properties. We show that the proposed approach is asymptotically…

条件独立性的局部置换检验AI 解读

In this paper, we investigate local permutation tests for testing conditional independence between two random vectors X and Y given Z. The local permutation test determines the significance of a test statistic by locally shuffling samples, which share similar values of the conditioning variables Z, and it forms a natural extension of the usual permutation approach for unconditional independence testing. Despite its simplicity and empirical support, the theoretical…

极小极大最优的条件独立性检验AI 解读

We consider the problem of conditional independence testing of X and Y given Z where X,Y and Z are three real random variables and Z is continuous. We focus on two main cases—when X and Y are both discrete, and when X and Y are both continuous. In view of recent results on conditional independence testing [Ann. Statist. 48 (2020) 1514–1538], one cannot hope to design nontrivial tests, which control the type I error for all absolutely continuous conditionally independent…

高维 Ising 模型中的图性质检验AI 解读

This paper explores the information-theoretic limitations of graph property testing in zero-field Ising models. Instead of learning the entire graph structure, sometimes testing a basic graph property such as connectivity, cycle presence or maximum clique size is a more relevant and attainable objective. Since property testing is more fundamental than graph recovery, any necessary conditions for property testing imply corresponding conditions for graph recovery, while custom…

图模型的组合推断AI 解读

We propose a new family of combinatorial inference problems for graphical models. Unlike classical statistical inference where the main interest is point estimation or parameter testing, combinatorial inference aims at testing the global structure of the underlying graph. Examples include testing the graph connectivity, the presence of a cycle of certain size, or the maximum degree of the graph. To begin with, we study the information-theoretic limits of a large family of…