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成对依赖马尔可夫随机场中的虚假关联AI 解读

Summary identified the issue of ′nonsense correlations’ in time series data, where dependence within each of two random vectors causes overdispersion, i.e., variance inflation, for measures of dependence between the two. Since then much has been written about nonsense correlations, but nearly all of it confined to the time series literature. In this paper we provide the first, to our knowledge, rigorous study of this phenomenon for other forms of (positive) dependence,…

Estimation of the average treatment effect (ATE) is a central problem in causal inference. In recent times, inference for the ATE in the presence of high-dimensional covariates has been extensively studied. Among the diverse approaches that have been proposed, augmented inverse probability weighting (AIPW) with cross-fitting has emerged a popular choice in practice. In this work, we study this cross-fit AIPW estimator under well-specified outcome regression and propensity…

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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…

双重机器学习估计量速率双重稳健性的弱假设证伪检验AI 解读

The class of doubly robust (DR) functionals studied by Rotnitzky et al. (2021) is of central importance in economics and biostatistics. It strictly includes both (i) the class of mean-square continuous functionals that can be written as an expectation of an affine functional of a conditional expectation studied by Chernozhukov et al. (2022b) and the class of functionals studied by Robins et al. (2008). The present state-of-the-art estimators for DR functionals ψ are…

Ising 模型下针对稀疏备择的全局检验AI 解读

In this paper, we study the effect of dependence on detecting sparse signals. In particular, we focus on global testing against sparse alternatives for the means of binary outcomes following an Ising model, and establish how the interplay between the strength and sparsity of a signal determines its detectability under various notions of dependence. The profound impact of dependence is best illustrated under the Curie–Weiss model where we observe the effect of a…

稀疏图 β 模型中的信号检测阈值AI 解读

In this paper, we study sharp thresholds for detecting sparse signals in $\beta$-models for potentially sparse random graphs. The results demonstrate interesting interplay between graph sparsity, signal sparsity and signal strength. In regimes of moderately dense signals, irrespective of graph sparsity, the detection thresholds mirror corresponding results in independent Gaussian sequence problems. For sparser signals, extreme graph sparsity implies that all tests are…

结构化高维模型中泛函的极小极大估计AI 解读

We introduce a new method of estimation of parameters in semiparametric and nonparametric models. The method employs $U$-statistics that are based on higher-order influence functions of the parameter of interest, which extend ordinary linear influence functions, and represent higher derivatives of this parameter. For parameters for which the representation cannot be perfect the method often leads to a bias-variance trade-off, and results in estimators that converge at a…

扰乱几何网数值积分的渐近正态性AI 解读

In a very recent work, Basu and Owen [Found. Comput. Math. 17 (2017) 467–496] propose the use of scrambled geometric nets in numerical integration when the domain is a product of $s$ arbitrary spaces of dimension $d$ having a certain partitioning constraint. It was shown that for a class of smooth functions, the integral estimate has variance $O(n^{-1-2/d}(\log n)^{s-1})$ for scrambled geometric nets compared to $O(n^{-1})$ for ordinary Monte Carlo. The main idea of this…

遗传关联研究中检验 SNP 集合效应的广义 Higher CriticismAI 解读

It is of substantial interest to study the effects of genes, genetic pathways, and networks on the risk of complex diseases. These genetic constructs each contain multiple SNPs, which are often correlated and function jointly, and might be large in number. However, only a sparse subset of SNPs in a genetic construct is generally associated with the disease of interest. In this article, we propose the generalized higher criticism (GHC) to test for the association between an…

高维稀疏二元回归的假设检验AI 解读

In this paper, we study the detection boundary for minimax hypothesis testing in the context of high-dimensional, sparse binary regression models. Motivated by genetic sequencing association studies for rare variant effects, we investigate the complexity of the hypothesis testing problem when the design matrix is sparse. We observe a new phenomenon in the behavior of detection boundary which does not occur in the case of Gaussian linear regression. We derive the detection…