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自适应稳健置信区间AI 解读

This paper studies the construction of adaptive confidence intervals under Huber’s contamination model when the contamination proportion is unknown. For the robust confidence interval of a Gaussian mean, we show that the optimal length of an adaptive interval must be exponentially wider than that of a nonadaptive one. An optimal construction is achieved through simultaneous uncertainty quantification of quantiles at all levels. The results are further extended beyond the…

张量对张量回归：黎曼优化、过参数化与统计计算鸿沟的相互作用AI 解读

We study the tensor-on-tensor regression, where the goal is to connect tensor responses to tensor covariates with a low Tucker rank parameter tensor/matrix without prior knowledge of its intrinsic rank. We propose the Riemannian gradient descent (RGD) and Riemannian Gauss–Newton (RGN) methods and cope with the challenge of unknown rank by studying the effect of rank over-parameterization. We provide the first convergence guarantee for the general tensor-on-tensor regression…

利用低阶多项式研究图函数估计的计算下界AI 解读

Graphon estimation has been one of the most fundamental problems in network analysis and has received considerable attention in the past decade. From the statistical perspective, the minimax error rate of graphon estimation has been established by (Ann. Statist. 43 (2015) 2624–2652) for both stochastic block model (SBM) and nonparametric graphon estimation. The statistical optimal estimators are based on constrained least squares and have computational complexity exponential…