日期精度：到日 5104 篇 · 到月 0 篇 · 到年 0 篇
爬山聚类的一致性结果
We consider several hill-climbing approaches to clustering as formulated by Fukunaga and Hostetler (IEEE Trans. Inf. Theory IT-21 (1975) 32–40) in the 1970s. We study both continuous-space and discrete-space (i.e., medoid) variants and establish their consistency.
灵活应对赢家诅咒的推断方法
Across science and policy, decision-makers often need to draw conclusions about the best candidate among competing alternatives. For instance, researchers may seek to infer the effectiveness of the most successful treatment or determine which demographic group benefits most from a specific treatment. Similarly, in machine learning, practitioners are often interested in the population performance of the model that performs best empirically. However, cherry-picking the best…
半监督 U 统计量
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…
高维经验 Copula 过程：Stute 表示及其应用
The empirical copula process, a fundamental tool for copula inference, is studied in the high dimensional regime where the dimension is allowed to grow to infinity exponentially in the sample size. Under natural, weak smoothness assumptions on the underlying copula, it is shown that Stute’s representation is valid in the following sense: all low-dimensional margins of fixed dimension of the empirical copula process can be approximated by a functional of the low-dimensional…
网络干扰下基于平均场方法的因果效应估计
We study causal effect estimation from observational data under interference. The interference pattern is captured by an observed network. We adopt the chain graph framework of (J. Amer. Statist. Assoc. 116 (2021) 833–844), which allows (i) interaction among the outcomes of distinct study units connected along the graph and (ii) long range interference, whereby the outcome of an unit may depend on the treatments assigned to distant units connected along the interference…
非参数隐马尔可夫与独立同分布模型中的聚类风险
We conduct an in-depth analysis of the Bayes risk of clustering in the context of hidden Markov and i.i.d. models. In both settings, we identify the situations where this risk is comparable to the Bayes risk of classification and those where its minimizer, the Bayes clusterer, can be derived from the Bayes classifier. While we demonstrate that clustering based on the Bayes classifier does not always match the optimal Bayes clusterer, we show that this difference is primarily…
序贯实验中的反事实推断
We consider after-study statistical inference for sequentially designed experiments wherein multiple units are assigned treatments for multiple time points using treatment policies that adapt over time. Our goal is to provide inference guarantees for the counterfactual mean at the smallest possible scale—mean outcome under different treatments for each unit and each time—with minimal assumptions on the adaptive treatment policy. Without any structural assumptions on the…
分位数回归的渐近精确选择后推断
In modern data analysis, it is common to select a model before performing statistical inference. Selective inference tools make adjustments for the model selection process in order to ensure reliable inference post selection. In this paper, we introduce an asymptotic pivot to infer about the effects of selected variables on conditional quantile functions. Utilizing estimators from smoothed quantile regression, our proposed pivot is easy to compute and yields…
自适应线性回归中的近最优推断
When data is collected in an adaptive manner, even simple methods like ordinary least squares can exhibit non-normal asymptotic behavior. As an undesirable consequence, hypothesis tests and confidence intervals based on asymptotic normality can lead to erroneous results. We propose a family of online debiasing estimators to correct these distributional anomalies in least squares estimation. Our proposed methods take advantage of the covariance structure present in the…
通过协变量调整消除因果目标选择偏差的共同原因原则
Average treatment effects (ATEs) may be subject to selection bias when they are estimated among only a nonrepresentative subset of the target population. Selection bias can sometimes be eliminated by conditioning on a “sufficient adjustment set” of covariates, even for some forms of missingness not at random (MNAR). Without requiring full specification of the causal structure, we consider sufficient adjustment sets to allow nonparametric identification of conditional ATEs in…
函数值空间过程的谱密度估计
The spectral density function describes the second-order properties of a stationary stochastic process on Rd. This paper considers the nonparametric estimation of the spectral density of a continuous-time stochastic process taking values in a separable Hilbert space. Our estimator is based on kernel smoothing and can be applied to a wide variety of spatial sampling schemes including those in which data are observed at irregular spatial locations. Thus, it finds immediate…
通过神经对抗不变性学习从异质环境中追寻因果关系
Pursuing causality from data is a fundamental problem in scientific discovery, treatment intervention, and transfer learning. This paper introduces a novel algorithmic method for addressing nonparametric invariance and causality learning in regression models across multiple environments, where the joint distribution of response variables and covariates varies, but the conditional expectations of outcome given an unknown set of quasi-causal variables are invariant. The…
基于样本协方差矩阵的完全随机缺失检验
We study the problem of testing whether the missing values of a potentially high-dimensional dataset are Missing Completely at Random (MCAR). We relax the problem of testing MCAR to the problem of testing the compatibility of a collection of covariance matrices, motivated by the fact that this procedure is feasible when the dimension grows with the sample size. Our first contributions are to define a natural measure of the incompatibility of a collection of correlation…
鞅的 Yurinskii 耦合
Yurinskii’s coupling is a popular theoretical tool for nonasymptotic distributional analysis in mathematical statistics and applied probability, offering a Gaussian strong approximation with an explicit error bound under easily verifiable conditions. Originally stated in ℓ2-norm for sums of independent random vectors, it has recently been extended both to the ℓp-norm, for 1≤p≤∞, and to vector-valued martingales in ℓ2-norm, under some strong conditions. We present as our main…
It is well-known that trimmed sample means are robust against heavy tails and data contamination. This paper analyzes the performance of trimmed means and related methods in two novel contexts. The first one consists of estimating expectations of functions in a given family, with uniform error bounds; this is closely related to the problem of estimating the mean of a random vector under a general norm. The second problem considered is that of regression with quadratic loss.…
强化学习中稳健策略评估的在线估计与推断
Reinforcement learning has emerged as one of the prominent topics attracting attention in modern statistical learning, with policy evaluation being a key component. Unlike the traditional machine learning literature on this topic, our work emphasizes statistical inference for the model parameters and value functions of reinforcement learning algorithms. While most existing analyses assume random rewards to follow standard distributions, we embrace the concept of robust…
离散观测数据的函数主成分分析理论
Functional data analysis is an important research field in statistics which treats data as random functions drawn from some infinite-dimensional functional space, and functional principal component analysis (FPCA) based on eigen-decomposition plays a central role for data reduction and representation. After nearly three decades of research, there remains a key problem unsolved, namely, the perturbation analysis of covariance operator for diverging number of eigencomponents…
Plackett–Luce 模型中似然估计量的统一分析
The Plackett–Luce model has been extensively used for rank aggregation in social choice theory. A central statistical question in this model concerns estimating the utility vector that governs the model’s likelihood. In this paper, we investigate the asymptotic theory of utility vector estimation by maximizing different types of likelihood, such as full, marginal, and quasi-likelihood. Starting from interpreting the estimating equations of these estimators to gain some…
对称性：非参数回归中的一般结构
In this paper, we present the framework of symmetry in nonparametric regression. This generalises the framework of covariate sparsity, where the regression function f:[0,1]d→R depends only on at most s
高维广义线性模型的贝叶斯模型选择一致性进展
Uncovering genuine relationships between a response variable and a large collection of covariates is a fundamental and practically important problem. In the context of Gaussian linear models, both the Bayesian and non-Bayesian literature is well-developed and there are no substantial differences in the model selection consistency results available from the two schools. For generalized linear models (GLMs), however, Bayesian model selection consistency results are lacking in…
分布式强化学习中的估计与统计推断
In this paper, we study distributional reinforcement learning from the perspective of statistical efficiency. We investigate distributional policy evaluation, aiming to estimate the complete return distribution (denoted $η^π$) attained by a given policy $π$. We use the certainty-equivalence method to construct our estimator $\hatη^π$, given a generative model is available. In this circumstance we need a dataset of size $\widetilde O\left(\frac{|\mathcal{S}||\mathcal{A}|}{\varepsilon^{2p}(1-γ)^{2p+2}}\right)$…
矩阵情境在线决策中的统计推断
The study of online decision-making problems that leverage contextual information has drawn notable attention due to their significant applications in fields ranging from healthcare to autonomous systems. In modern applications, contextual information can be rich and is often represented as a matrix. Moreover, while existing online decision algorithms mainly focus on reward maximization, less attention has been devoted to statistical inference. To address these gaps, in this…
任意元素依赖下的结构化矩阵学习与马尔可夫转移核估计
The problem of structured matrix estimation has been studied mostly under strong noise dependence assumptions. This paper considers a general framework of noisy low-rank-plus-sparse matrix recovery, where the noise matrix may come from any joint distribution with arbitrary dependence across entries. We propose an incoherent-constrained least-square estimator and prove its tightness both in the sense of deterministic lower bound and matching minimax risks under various noise…
连锁不平衡评分回归及跨祖源扩展的高维统计推断
Linkage disequilibrium score regression (LDSC) has emerged as an essential tool for genetic and genomic analyses of complex traits, utilizing high-dimensional data derived from genome-wide association studies (GWAS). LDSC computes the linkage disequilibrium (LD) scores using an external reference panel, and integrates the LD scores with only summary data from the original GWAS. In this paper, we investigate LDSC within a fixed-effect data integration framework, underscoring…