High-dimensional group inference is an essential part of statistical methods for analysing complex data sets, including hierarchical testing, tests of interaction, detection of heterogeneous treatment effects and inference for local heritability. Group inference in regression models can be measured with respect to a weighted quadratic functional of the regression sub-vector corresponding to the group. Asymptotically unbiased estimators of these weighted quadratic functionals are constructed and a novel procedure using these estimators for inference is proposed. We derive its asymptotic Gaussian distribution which enables the construction of asymptotically valid confidence intervals and tests which perform well in terms of length or power. The proposed test is computationally efficient even for a large group, statistically valid for any group size and achieving good power performance for testing large groups with many small regression coefficients. We apply the methodology to several interesting statistical problems and demonstrate its strength and usefulness on simulated and real data.
Cognitive Diagnosis Models (CDMs) are a special family of discrete latent variable models widely used in educational, psychological and social sciences. In many applications of CDMs, certain hierarchical structures among the latent attributes are assumed by researchers to characterize their dependence structure. Specifically, a directed acyclic graph is used to specify hierarchical constraints on the allowable configurations of the discrete latent attributes. In this paper, we consider the important yet unaddressed problem of testing the existence of latent hierarchical structures in CDMs. We …
Hierarchical inference in (generalized) regression problems is powerful for finding significant groups or even single covariates, especially in high-dimensional settings where identifiability of the entire regression parameter vector may be ill-posed. The general method proceeds in a fully data-driven and adaptive way from large to small groups or singletons of covariates, depending on the signal strength and the correlation structure of the design matrix. We propose a novel hierarchical multiple testing adjustment that can be used in combination with any significance test for a group of covar…
Clustering is part of unsupervised analysis methods that consist in grouping samples into homogeneous and separate subgroups of observations also called clusters. To interpret the clusters, statistical hypothesis testing is often used to infer the variables that significantly separate the estimated clusters from each other. However, data-driven hypotheses are considered for the inference process, since the hypotheses are derived from the clustering results. This double use of the data leads traditional hypothesis test to fail to control the Type I error rate particularly because of uncertainty…
Permutation methods are commonly used to test significance of regressors of interest in general linear models (GLMs) for functional (image) data sets, in particular for neuroimaging applications as they rely on mild assumptions. Permutation inference for GLMs typically consists of three parts: choosing a relevant test statistic, computing pointwise permutation tests and applying a multiple testing correction. We propose new multiple testing methods as an alternative to the commonly used maximum value of test statistics across the image. The new methods improve power and robustness against inho…
This paper presents a selective survey of recent developments in statistical inference and multiple testing for high-dimensional regression models, including linear and logistic regression. We examine the construction of confidence intervals and hypothesis tests for various low-dimensional objectives such as regression coefficients and linear and quadratic functionals. The key technique is to generate debiased and desparsified estimators for the targeted low-dimensional objectives and estimate their uncertainty. In addition to covering the motivations for and intuitions behind these statistica…
Concept Drift Detection and Adaptation with Hierarchical Hypothesis Testing
University of Florida（佛罗里达大学）；Robert Bosch Research and Technology Center（罗伯特·博世研究与技术中心）；University of Illinois at Chicago（伊利诺伊大学芝加哥分校）；MZ Inc.（MZ公司）；Central China Normal University（华中师范大学）
Statistical analysis of multimodal imaging data is a challenging task, since the data involves high-dimensionality, strong spatial correlations and complex data structures. In this paper, we propose rigorous statistical testing procedures for making inferences on the complex dependence of multimodal imaging data. Motivated by the analysis of multi-task fMRI data in the Human Connectome Project (HCP) study, we particularly address three hypothesis testing problems: (a) testing independence among imaging modalities over brain regions, (b) testing independence between brain regions within imaging…
Statistical testing is classically used as an exploratory tool to search for association between a phenotype and many possible explanatory variables. This approach often leads to multiple testing under dependence. We assume a hierarchical structure between tests via an Ornstein-Uhlenbeck process on a tree. The process correlation structure is used for smoothing the p-values. We design a penalized estimation of the mean of the Ornstein-Uhlenbeck process for p-value computation. The performances of the algorithm are assessed via simulations. Its ability to discover new associations is demonstrat…
The problems of large-scale multiple testing are often encountered in modern scientific researches. Conventional multiple testing procedures usually suffer considerable loss of testing efficiency due to the lack of consideration of correlations among tests. In fact, the appropriate use of correlation information not only enhances the efficacy of multiple testing but also improves the interpretability of the results. Since the disease- or trait-related single nucleotide polymorphisms (SNPs) often tend to be clustered and exhibit serial correlations, the hidden Markov model (HMM) based multiple …
Non-linear hierarchical models are commonly used in many disciplines. However, inference in the presence of non-nested effects and on large datasets is challenging and computationally burdensome. This paper provides two contributions to scalable and accurate inference. First, I derive a new mean-field variational algorithm for estimating binomial logistic hierarchical models with an arbitrary number of non-nested random effects. Second, I propose "marginally augmented variational Bayes" (MAVB) that further improves the initial approximation through a step of Bayesian post-processing. I prove t…
Background: The nucleus of eukaryotic cells spatially packages chromosomes into a hierarchical and distinct segregation that plays critical roles in maintaining transcription regulation. High-throughput methods of chromosome conformation capture, such as Hi-C, have revealed topologically associating domains (TADs) that are defined by biased chromatin interactions within them. Results: Here, we introduce a novel method, HiCKey, to decipher hierarchical TAD structures in Hi-C data and compare them across samples. We first derive a generalized likelihood-ratio (GLR) test for detecting change-poin…
Calibrating hierarchical Bayesian domain inference for a proportion
Continuing Academic Specialist Center for Statistical Training and Consulting, Michigan State University（密歇根州立大学统计培训与咨询中心继续教育学术专员）；Institute for Social Research, University of Michigan（密歇根大学社会研究所）
Classical tests for a difference in means control the type I error rate when the groups are defined a priori. However, when the groups are instead defined via clustering, then applying a classical test yields an extremely inflated type I error rate. Notably, this problem persists even if two separate and independent data sets are used to define the groups and to test for a difference in their means. To address this problem, in this paper, we propose a selective inference approach to test for a difference in means between two clusters. Our procedure controls the selective type I error rate by a…
We combine Bayesian prediction and weighted inference as a unified approach to survey inference. The general principles of Bayesian analysis imply that models for survey outcomes should be conditional on all variables that affect the probability of inclusion. We incorporate the weighting variables under the framework of multilevel regression and poststratification, as a byproduct generating model-based weights after smoothing. We investigate deep interactions and introduce structured prior distributions for smoothing and stability of estimates. The computation is done via Stan and implemented …
Hierarchical Semi-Implicit Variational Inference with Application to Diffusion Model Acceleration
Peking University（北京大学）；Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）；Beijing Academy of Artificial Intelligence（北京人工智能研究院）；Megvii Technology Inc.（旷视科技有限公司）
Variable selection methods with nonlocal priors have been widely studied in linear regression models, and their theoretical and empirical performances have been reported. However, the crucial model selection properties for hierarchical nonlocal priors in high-dimensional generalized linear regression have rarely been investigated. In this paper, we consider a hierarchical nonlocal prior for high-dimensional logistic regression models and investigate theoretical properties of the posterior distribution. Specifically, a product moment (pMOM) nonlocal prior is imposed over the regression coeffici…
This paper presents recent methodological advances to perform simulation-based inference (SBI) of a general class of Bayesian hierarchical models (BHMs), while checking for model misspecification. Our approach is based on a two-step framework. First, the latent function that appears as second layer of the BHM is inferred and used to diagnose possible model misspecification. Second, target parameters of the trusted model are inferred via SBI. Simulations used in the first step are recycled for score compression, which is necessary to the second step. As a proof of concept, we apply our framewor…
Sampling-Based Accuracy Testing of Posterior Estimators for General Inference
Mila – Quebec AI Institute（米拉-魁北克人工智能研究所）；Université de Montréal（蒙特利尔大学）；CIELA Institute（CIELA研究所）；Flatiron Institute Center for Computational Mathematics（弗拉蒂龙研究所计算数学中心）
本文提出 TARP 覆盖率测试，通过随机点与采样估计生成式后验估计器的覆盖概率，无需后验评估，可在高维空间中识别现有方法无法发现的不准确推断。
Inference of Hierarchical Core-Periphery Structure in Temporal Networks
University of California, Los Angeles（加州大学洛杉矶分校）；University of Michigan（密歇根大学）；KTH Royal Institute of Technology（瑞典皇家理工学院）；Stockholm University（斯德哥尔摩大学）；Uppsala University（乌普萨拉大学）；Santa Fe Institute（圣塔菲研究所）
