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通过随机扰动与矩估计实现 β 模型的边差分隐私估计AI 解读

A standing challenge in data privacy is the trade-off between the level of privacy and the efficiency of statistical inference. Here, we conduct an in-depth study of this trade-off for parameter estimation in the β-model (Ann. Appl. Probab. 21 (2011) 1400–1435) for edge differentially private network data released via jittering (J. R. Stat. Soc. Ser. C. Appl. Stat. 66 (2017) 481–500). Unlike most previous approaches based on maximum likelihood estimation for this network…

利用光滑 Fisher 一致替代损失寻找最优动态治疗方案AI 解读

Large health care data repositories such as electronic health records (EHR) open new opportunities to derive individualized treatment strategies for complicated diseases such as sepsis. In this paper, we consider the problem of estimating sequential treatment rules tailored to a patient’s individual characteristics, often referred to as dynamic treatment regimes (DTRs). Our main objective is to find the optimal DTR that maximizes a discontinuous value function through direct…

函数均值估计的迁移学习：相变与自适应算法AI 解读

This paper studies transfer learning for estimating the mean of random functions based on discretely sampled data, where in addition to observations from the target distribution, auxiliary samples from similar but distinct source distributions are available. The paper considers both common and independent designs and establishes the minimax rates of convergence for both designs. The results reveal an interesting phase transition phenomenon under the two designs and…

This paper takes a different look on the problem of testing the mutual independence of the components of a high-dimensional vector. Instead of testing if all pairwise associations (e.g., all pairwise Kendall’s τ) between the components vanish, we are interested in the (null) hypothesis that all pairwise associations do not exceed a certain threshold in absolute value. The consideration of these hypotheses is motivated by the observation that in the high-dimensional regime,…

通过双向MOSUM对高维时间序列变点进行ℓ2推断AI 解读

We propose an inference method for detecting multiple change points in high-dimensional time series, targeting dense or spatially clustered signals. Our method aggregates moving sum (MOSUM) statistics cross-sectionally by an ℓ2-norm and maximizes them over time. We further introduce a novel Two-Way MOSUM, which utilizes spatial-temporal moving regions to search for breaks, with the added advantage of enhancing testing power when breaks occur in only a few groups. The…

发现的边缘：控制拒绝边界上的局部错误发现率AI 解读

Despite the popularity of the false discovery rate (FDR) as an error control metric for large-scale multiple testing, its close Bayesian counterpart the local false discovery rate (lfdr), defined as the posterior probability that a particular null hypothesis is false, is a more directly relevant standard for justifying and interpreting individual rejections. However, the lfdr is difficult to work with in small samples, as the prior distribution is typically unknown. We…

量化非平稳函数值过程结构假设偏离的一般框架AI 解读

We present a general theory to quantify the uncertainty from imposing structural assumptions on the second-order structure of nonstationary Hilbert space-valued processes, which can be measured via functionals of time-dependent spectral density operators. The second-order dynamics are well known to be elements of the space of trace class operators, the latter is a Banach space of type 1 and of cotype 2, which makes the development of statistical inference tools more…

基于低频观测的扩散过程一致推断AI 解读

Let (Xt) be a reflected diffusion process in a bounded convex domain in Rd, solving the stochastic differential equation dXt=∇f(Xt)dt+ 2f(Xt)dWt,t≥0, with Wt a d-dimensional Brownian motion. The data X0,XD,…,XND consist of discrete measurements and the time interval D between consecutive observations is fixed so that one cannot ‘zoom’ into the observed path of the process. The goal is to infer the diffusivity f and the associated transition operator Pt,f. We prove…

高维线性模型中 L2-boosting 的早停AI 解读

Increasingly high-dimensional data sets require that estimation methods do not only satisfy statistical guarantees but also remain computationally feasible. In this context, we consider L2-boosting via orthogonal matching pursuit in a high-dimensional linear model and analyze a data-driven early stopping time τ of the algorithm, which is sequential in the sense that its computation is based on the first τ iterations only. This approach is much less costly than established…

灵活函数库下斜切回归树的收敛速度AI 解读

We develop a theoretical framework for the analysis of oblique decision trees, where the splits at each decision node occur at linear combinations of the covariates (as opposed to conventional tree constructions that force axis-aligned splits involving only a single covariate). While this methodology has garnered significant attention from the computer science and optimization communities since the mid-80s, the advantages they offer over their axis-aligned counterparts…

对抗训练中的过度参数化之弊：随机特征回归的稳健泛化分析AI 解读

Successful deep learning models often involve training neural network architectures that contain more parameters than the number of training samples. Such overparametrized models have recently been extensively studied, and the virtues of overparametrization have been established from both the statistical perspective, via the double-descent phenomenon, and the computational perspective via the structural properties of the optimization landscape. Despite this success, it is…

动态处理效应的高维推断AI 解读

Estimating dynamic treatment effects is a crucial endeavor in causal inference, particularly when confronted with high-dimensional confounders. Doubly robust (DR) approaches have emerged as promising tools for estimating treatment effects due to their flexibility. However, we showcase that the traditional DR approaches that only focus on the DR representation of the expected outcomes may fall short of delivering optimal results. In this paper, we propose a novel DR…

异质性因果效应估计的极小极大收敛率AI 解读

Estimation of heterogeneous causal effects - i.e., how effects of policies and treatments vary across subjects - is a fundamental task in causal inference. Many methods for estimating conditional average treatment effects (CATEs) have been proposed in recent years, but questions surrounding optimality have remained largely unanswered. In particular, a minimax theory of optimality has yet to be developed, with the minimax rate of convergence and construction of rate-optimal…

度量统计：利用距离剖面探索随机对象并进行推断AI 解读

This article provides an overview on the statistical modeling of complex data as increasingly encountered in modern data analysis. It is argued that such data can often be described as elements of a metric space that satisfies certain structural conditions and features a probability measure. We refer to the random elements of such spaces as random objects and to the emerging field that deals with their statistical analysis as metric statistics. Metric statistics provides…

缺失数据下异方差主成分分析的统计推断AI 解读

This paper studies how to construct confidence regions for principal component analysis (PCA) in high dimension, a problem that has been vastly underexplored. While computing measures of uncertainty for nonlinear/nonconvex estimators is in general difficult in high dimension, the challenge is further compounded by the prevalent presence of missing data and heteroskedastic noise. We propose a novel approach to performing valid inference on the principal subspace, on the basis…

凸函数极小点与最小值的估计和推断：最优性、自适应性与不确定性原理AI 解读

Optimal estimation and inference for both the minimizer and minimum of a convex regression function under the white noise and nonparametric regression models are studied in a nonasymptotic local minimax framework, where the performance of a procedure is evaluated at individual functions. Fully adaptive and computationally efficient algorithms are proposed and sharp minimax lower bounds are given for both the estimation accuracy and expected length of confidence intervals for…

自适应变分贝叶斯：最优性、计算与应用AI 解读

In this paper, we explore adaptive inference based on variational Bayes. Although several studies have been conducted to analyze the contraction properties of variational posteriors, there is still a lack of a general and computationally tractable variational Bayes method that performs adaptive inference. To fill this gap, we propose a novel adaptive variational Bayes framework, which can operate on a collection of models. The proposed framework first computes a variational…

基于经验 Copula 的高维独立性检验AI 解读

Testing for pairwise independence for the case where the number of variables may be of the same size or even larger than the sample size has received increasing attention in the recent years. We contribute to this branch of the literature by considering tests that allow to detect higher-order dependencies. The proposed methods are based on connecting the problem to copulas and making use of the Moebius transformation of the empirical copula process; an approach that is…

监督式同质性融合：一种组合方法AI 解读

Fusing regression coefficients into homogeneous groups can unveil those coefficients that share a common value within each group. Such groupwise homogeneity reduces the intrinsic dimension of the parameter space and unleashes sharper statistical accuracy. We propose and investigate a new combinatorial grouping approach called L0-Fusion that is amenable to mixed integer optimization (MIO). On the statistical aspect, we identify a fundamental quantity called MSE grouping…

高维多参考对齐问题的估计速率AI 解读

We study the continuous multireference alignment model of estimating a periodic function on the circle from noisy and circularly-rotated observations. Motivated by analogous high-dimensional problems that arise in cryo-electron microscopy, we establish minimax rates for estimating generic signals that are explicit in the dimension K. In a high-noise regime with noise variance σ2≳K, for signals with Fourier coefficients of roughly uniform magnitude, the rate scales as σ6 and…

基于模型的离线强化学习样本复杂度AI 解读

This paper is concerned with offline reinforcement learning (RL), which learns using precollected data without further exploration. Effective offline RL would be able to accommodate distribution shift and limited data coverage. However, prior results either suffer from suboptimal sample complexities or incur high burn-in cost to reach sample optimality, thus posing an impediment to efficient offline RL in sample-starved applications. We demonstrate that the model-based (or…

情境多臂老虎机中的迁移学习AI 解读

Motivated by a range of applications, we study in this paper the problem of transfer learning for nonparametric contextual multi-armed bandits under the covariate shift model, where we have data collected from source bandits before the start of the target bandit learning. The minimax rate of convergence for the cumulative regret is established and a novel transfer learning algorithm that attains the minimax regret is proposed. The results quantify the contribution of the…

利用秩指标检验两个高维向量的独立性AI 解读

To test independence between two high-dimensional random vectors, we propose three tests based on the rank-based indices derived from Hoeffding’s D, Blum–Kiefer–Rosenblatt’s R and Bergsma–Dassios–Yanagimoto’s τ∗. Under the null hypothesis of independence, we show that the distributions of the proposed test statistics converge to normal ones if the dimensions diverge arbitrarily with the sample size. We further derive an explicit rate of convergence. Thanks to the monotone…

具有错误发现率保证的自适应新异检测AI 解读

This paper studies the semisupervised novelty detection problem where a set of “typical” measurements is available to the researcher. Motivated by recent advances in multiple testing and conformal inference, we propose AdaDetect, a flexible method that is able to wrap around any probabilistic classification algorithm and control the false discovery rate (FDR) on detected novelties in finite samples without any distributional assumption other than exchangeability. In contrast…