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局部差分隐私下的渐近效率AI 解读

We develop a theory of asymptotic efficiency in regular parametric models when data confidentiality is ensured by local differential privacy (LDP). Even though efficient parameter estimation is a classical and well-studied problem in mathematical statistics, it leads to several nontrivial obstacles that need to be tackled when dealing with the LDP case. Starting from a regular parametric model P=(Pθ)θ∈Θ, Θ⊆Rp, for the i.i.d. unobserved sensitive data X1,…,Xn, we establish…

相位同步与正交群同步中谱方法的精确极小极大最优性AI 解读

We study the performance of the spectral method for the phase synchronization problem with additive Gaussian noises and incomplete data. The spectral method utilizes the leading eigenvector of the data matrix followed by a normalization step. We prove that it achieves the minimax lower bound of the problem with a matching leading constant under a squared ℓ2 loss. This shows that the spectral method has the same performance as more sophisticated procedures including maximum…

未知流形邻域中的密度估计：贝叶斯非参数方法AI 解读

We study the Bayesian density estimation of data living in the offset of an unknown submanifold of the Euclidean space. In this perspective, we introduce a new notion of anisotropic Hölder for the underlying density and obtain posterior rates that are minimax optimal and adaptive to the regularity of the density, to the intrinsic dimension of the manifold, and to the size of the offset, provided that the latter is not too small—while still allowed to go to zero. Our Bayesian…

通过置换增广回归构造线性模型的保形检验AI 解读

Permutation tests are widely recognized as robust alternatives to tests based on normal theory. Random permutation tests have been frequently employed to assess the significance of variables in linear models. Despite their widespread use, existing random permutation tests lack finite-sample and assumption-free guarantees for controlling type I error in partial correlation tests. To address this ongoing challenge, we have developed a conformal test through…

高维混杂下平均处理效应的去偏逆倾向得分加权AI 解读

We consider estimation of average treatment effects given observational data with high-dimensional pretreatment variables. Existing methods for this problem typically assume some form of sparsity for the regression functions. In this work, we introduce a debiased inverse propensity score weighting (DIPW) scheme for average treatment effect estimation that delivers n-consistent estimates when the propensity score follows a sparse logistic regression model; the outcome…

改进的协方差估计：重尾下的最优稳健性与次高斯保证AI 解读

We present an estimator of the covariance matrix Σ of random d-dimensional vector from an i.i.d. sample of size n. Our sole assumption is that this vector satisfies a bounded Lp−L2 moment assumption over its one-dimensional marginals, for some p≥4. Given this, we show that Σ can be estimated from the sample with the same high-probability error rates that the sample covariance matrix achieves in the case of Gaussian data. This holds even though we allow for very general…

基于核时序差分方法的最优策略评估AI 解读

We study nonparametric methods for estimating the value function of an infinite-horizon discounted Markov reward process (MRP). We analyze the kernel-based least-squares temporal difference (LSTD) estimate, which can be understood either as a nonparametric instrumental variables method, or as a projected approximation to the Bellman fixed point equation. Our analysis imposes no assumptions on the transition operator of the Markov chain, but rather only conditions on the…

依赖数据流的联合序贯检测与定位AI 解读

The problem of joint sequential detection and isolation is considered in the context of multiple, not necessarily independent, data streams. A multiple testing framework is proposed, where each hypothesis corresponds to a different subset of data streams, the sample size is a stopping time of the observations, and the probabilities of four kinds of error are controlled below distinct, user-specified levels. Two of these errors reflect the detection component of the…

样本分块相关矩阵的谱统计量AI 解读

A fundamental concept in multivariate statistics, the sample correlation matrix, is often used to infer the correlation/dependence structure among random variables, when the population mean and covariance are unknown. A natural block extension of it, the sample block correlation matrix, is proposed to take on the same role, when random variables are generalized to random subvectors. In this paper, we establish a spectral theory of the sample block correlation matrices and…

线性模型中高维回归系数的检验AI 解读

(2011) 260-274), and show that the ARE is always greater or equal to one under the local alternative studied in this paper. Our numerical studies imply that the proposed test with critical values derived from its asymptotical normal distribution may retain Type I error rate very well. Our numerical comparison demonstrates the proposed test performs better than existing ones in terms of powers. We further illustrate our proposed method with a real data example.

This paper investigates the stability of deep ReLU neural networks for nonparametric regression under the assumption that the noise has only a finite p-th moment. We unveil how the optimal rate of convergence depends on p, the degree of smoothness and the intrinsic dimension in a class of nonparametric regression functions with hierarchical composition structure when both the adaptive Huber loss and deep ReLU neural networks are used. This optimal rate of convergence cannot…

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一般数据集偏移下的高效且多重稳健风险估计AI 解读

. Despite extensive literature on dataset shift, limited works address how to efficiently use the auxiliary populations to improve the accuracy of risk evaluation for a given machine learning task in the target population. In this paper, we study the general problem of efficiently estimating target population risk under various dataset shift conditions, leveraging semiparametric efficiency theory. We consider a general class of dataset shift conditions, which includes three…

利用 Wasserstein–Fisher–Rao 梯度流学习高斯混合模型AI 解读

Gaussian mixture models form a flexible and expressive parametric family of distributions that has found a variety of applications. Unfortunately, fitting these models to data is a notoriously hard problem from a computational perspective. Currently, only moment-based methods enjoy theoretical guarantees while likelihood-based methods are dominated by heuristics such as Expectation-Maximization that are known to fail in simple examples. In this work, we propose a new…

高维加性回归的高效函数型 Lasso 核平滑AI 解读

Smooth backfitting has been proposed and proved as a powerful nonparametric estimation technique for additive regression models in various settings. Existing studies are restricted to cases with a moderate number of covariates and are not directly applicable to high dimensional settings. In this paper, we develop new kernel estimators based on the idea of smooth backfitting for high dimensional additive models. We introduce a novel penalization scheme, combining the idea of…

贝叶斯与频率学派反卷积模型中的 Wasserstein 收敛AI 解读

We study the multivariate deconvolution problem of recovering the distribution of a signal from independent and identically distributed observations additively contaminated with random errors having known distribution. For errors with ordinary smooth distribution, we recast the multidimensional problem as a one-dimensional problem leveraging the equivalence between the L1-Wasserstein and the max-sliced L1-Wasserstein metrics and derive an inversion inequality relating the…

Gromov–Wasserstein距离：熵正则化、对偶与样本复杂度AI 解读

The Gromov–Wasserstein (GW) distance, rooted in optimal transport (OT) theory, quantifies dissimilarity between metric measure spaces and provides a framework for aligning heterogeneous datasets. While computational aspects of the GW problem have been widely studied, a duality theory and fundamental statistical questions concerning empirical convergence rates remained obscure. This work closes these gaps for the quadratic GW distance over Euclidean spaces of different…

连续处理效应的非参数双重稳健检验AI 解读

The vast majority of literature on evaluating the significance of a treatment effect based on observational data has been confined to discrete treatments. These methods are not applicable to drawing inference for a continuous treatment, which arises in many important applications. To adjust for confounders when evaluating a continuous treatment, existing inference methods often rely on discretizing the treatment or using (possibly misspecified) parametric models for the…

稀疏序列多重检验的精确边界AI 解读

This work investigates multiple testing by considering minimax separation rates in the sparse sequence model, when the testing risk is measured as the sum FDR+FNR (False Discovery Rate plus False Negative Rate). First, using the popular beta-min separation condition, with all nonzero signals separated from 0 by at least some amount, we determine the sharp minimax testing risk asymptotically and thereby explicitly describe the transition from “achievable multiple testing with…

可微 Hilbert 空间值参数的一步估计AI 解读

rate estimators and corresponding confidence sets. These estimators correspond to generalizations of cross-fitted one-step estimators based on Hilbert-valued efficient influence functions. We give theoretical guarantees even when arbitrary estimators of nuisance functions are used, including those based on machine learning techniques. We show that these results naturally extend to Hilbert spaces that lack a reproducing kernel, as long as the parameter has an efficient…

广义Grenander型估计量的自助法辅助推断AI 解读

Westling and Carone (Ann. Statist. 48 (2020) 1001–1024) proposed a framework for studying the large sample distributional properties of generalized Grenander-type estimators, a versatile class of nonparametric estimators of monotone functions. The limiting distribution of those estimators is representable as the left derivative of the greatest convex minorant of a Gaussian process whose monomial mean can be of unknown order (when the degree of flatness of the function of…

长宽比发散时低秩矩阵估计的基本极限AI 解读

We consider the problem of estimating the factors of a low-rank n×d matrix, when this is corrupted by additive Gaussian noise. A special example of our setting corresponds to clustering mixtures of Gaussians with equal (known) covariances. Simple spectral methods do not take into account the distribution of the entries of these factors and are therefore often suboptimal. Here, we characterize the asymptotics of the minimum estimation error under the assumption that the…

重尾先验下的贝叶斯非参数自适应AI 解读

We propose a new Bayesian strategy for adaptation to smoothness in nonparametric models based on heavy-tailed series priors. We illustrate it in a variety of settings, showing in particular that the corresponding Bayesian posterior distributions achieve adaptive rates of contraction in the minimax sense (up to logarithmic factors) without the need to sample hyperparameters. Unlike many existing procedures, where a form of direct model (or estimator) selection is performed,…

高斯变分推断的近似精度AI 解读

The main computational challenge in Bayesian inference is to compute integrals against a high-dimensional posterior distribution. In the past decades, variational inference (VI) has emerged as a tractable approximation to these integrals, and a viable alternative to the more established paradigm of Markov chain Monte Carlo. However, little is known about the approximation accuracy of VI. In this work, we bound the TV error and the mean and covariance approximation error of…

利用t统计量的Edgeworth展开分析分批方法的高阶覆盖误差AI 解读

While batching methods have been widely used in simulation and statistics, their higher-order coverage behaviors and relative advantages in this regard remain open. We develop techniques to obtain higher-order coverage errors for batching methods by building Edgeworth-type expansions on t-statistics. The coefficients in these expansions are intricate analytically, but we provide algorithms to estimate the coefficients of the n−1 error terms via Monte Carlo simulation. We…