Paper proposes a robust test for high-dimensional models with large covariates and instruments.
problem Testing high-dimensional linear instrumental variable models with large covariates and instruments.
method Introduces a test based on the maximum norm of multiple parameters and a power-enhanced test.
result The proposed test is robust to heteroskedastic errors and has higher power than existing tests.
The statistical analysis of discrete data has been the subject of extensive statistical research dating back to the work of Pearson. In this survey we review some recently developed methods for testing hypotheses about high-dimensional multinomials. Traditional tests like the χ2 test and the likelihood ratio test ca…
Paper develops a new test for high-dimensional matrix-valued data.
problem Hypothesis testing for mean of matrix-valued data in high-dimensional settings.
method Proposes a new test statistic for high-dimensional matrix rank testing.
result Develops a novel approach for sparse singular value decomposition (SVD) estimation.
New test for comparing high-dimensional text data.
problem Testing equality of multinomial distributions in high dimensions.
method Proposed a test statistic with asymptotic normality under null.
result Achieves optimal detection boundary across parameter space.
GTBO uses group testing to optimize high-dimensional functions efficiently.
problem Challenges in optimizing high-dimensional, expensive functions due to the curse of dimensionality.
method GTBO combines testing and optimization phases to identify active variables and guide efficient optimization.
result GTBO outperforms state-of-the-art methods on high-dimensional optimization tasks.
E-C2ST uses E-values for high-dimensional data two-sample tests.
problem Statistical testing for high-dimensional data.
method Combines split likelihood ratio tests and predictive independence tests, using E-values for anytime-valid sequential tests.
result E-C2ST achieves enhanced statistical power by partitioning datasets into multiple batches.
Novel tests for genetic independence in high-dimensional data.
problem Testing independence in genetics studies with many variables.
method Defining premetric structures on genetic data support spaces.
result Solid theoretical framework and computationally-efficient implementations.
diproperm tests differences in HDLSS data with binary classifiers.
problem Testing differences in HDLSS data with binary classifiers.
method DiProPerm test for binary linear classifiers.
result Validates the DiProPerm test on real-world data.
The paper presents new metrics to quantify and test for (i) the equality of distributions and (ii) the independence between two high-dimensional random vectors. We show that the energy distance based on the usual Euclidean distance cannot completely characterize the homogeneity of two high-dimensional distributions in …
New tests for high-dimensional data improve on existing methods.
problem Testing mean vectors in high-dimensional data.
method Generalized multivariate sign transformation, using different norm functions.
result Tests using generalized signs have higher power than existing tests.
Testing independence is of significant interest in many important areas of large-scale inference. Using extreme-value form statistics to test against sparse alternatives and using quadratic form statistics to test against dense alternatives are two important testing procedures for high-dimensional independence. However…
New method tests CMI using deep neural networks for high-dimensional data.
problem Testing conditional mean independence in high-dimensional settings.
method Population CMI measure and bootstrap-based testing with deep generative neural networks.
result Strong empirical performance and versatility in various scenarios.
New KNN test improves association analysis of high-dimensional sequencing data.
problem Challenges in using neural networks for high-dimensional sequencing data analysis.
method Kernel-based neural network (KNN) test for complex association analysis.
result KNN test outperforms SKAT in detecting non-linear and interaction effects.
GTBO uses group testing to optimize high-dimensional functions efficiently.
problem Optimizing expensive, high-dimensional functions with limited data.
method Group testing to identify active dimensions, then guide optimization.
result GTBO outperforms state-of-the-art methods on high-dimensional benchmarks.
We consider the problem of uncertainty assessment for low dimensional components in high dimensional models. Specifically, we propose a decorrelated score function to handle the impact of high dimensional nuisance parameters. We consider both hypothesis tests and confidence regions for generic penalized M-estimators. U…
We consider the hypothesis testing problem of detecting a shift between the means of two multivariate normal distributions in the high-dimensional setting, allowing for the data dimension p to exceed the sample size n. Specifically, we propose a new test statistic for the two-sample test of means that integrates a rand…
Enhances power of covariance matrix tests for high-dimensional data.
problem Testing large covariance matrices in high-dimensional data.
method Proposes a new Fisher's combined probability test for quadratic form and maximum form statistics.
result Boosts power against more general alternatives.
In analyzing high-dimensional models, sparsity of the model parameter is a common but often undesirable assumption. In this paper, we study the following two-sample testing problem: given two samples generated by two high-dimensional linear models, we aim to test whether the regression coefficients of the two linear mo…
Statistical query algorithms and low-degree tests are nearly equivalent in high-dimensional hypothesis testing.
problem High-dimensional hypothesis testing and information-computation gaps.
method Analysis of statistical query framework and low-degree polynomials.
result Statistical query algorithms and low-degree polynomials are almost equivalent in power under mild conditions.
High-dimensional U-statistics show surprising phase transitions, impacting kernel-based tests.
problem Understanding phase transitions in high-dimensional U-statistics.
method Proved a convergence theorem for U-statistics of degree two in high dimensions.
result High-dimensional U-statistics can have non-Gaussian limits with larger variance and asymmetry.
Efficient tests achieve best error rates in high-dimensional hypothesis testing.
problem Achieving optimal error rates in computationally efficient hypothesis testing.
method Linear spectral statistics and low-degree likelihood ratio analysis.
result An efficient test achieves the best possible error rates among all computationally efficient tests.
Nonparametric two sample testing is a decision theoretic problem that involves identifying differences between two random variables without making parametric assumptions about their underlying distributions. We refer to the most common settings as mean difference alternatives (MDA), for testing differences only in firs…
The package High-dimensional Metrics (\Rpackage{hdm}) is an evolving collection of statistical methods for estimation and quantification of uncertainty in high-dimensional approximately sparse models. It focuses on providing confidence intervals and significance testing for (possibly many) low-dimensional subcomponents…
Study improves predictive performance testing for high-dimensional data using exhaustive nested cross-validation.
problem Reproducibility issues in K-fold cross-validation for high-dimensional data. method Proposes a novel predictive performance test based on exhaustive nested cross-validation, addressing computational complexity with a closed-form expression.
result Demonstrates the effectiveness of Ridge-based methods in high-dimensional predictive performance testing.
New method improves feature importance assessment in random forests.
problem Improving feature importance measures for random forests.
method Hypothesis testing via self-normalized feature-residual correlation test (FACT).
result The method provides theoretically justified feature importance tests with controlled type I error and appealing power.
This article develops a framework for testing general hypothesis in high-dimensional models where the number of variables may far exceed the number of observations. Existing literature has considered less than a handful of hypotheses, such as testing individual coordinates of the model parameter. However, the problem o…
This paper investigates the utilization of maximum and average distance correlations for multivariate independence testing. We characterize their consistency properties in high-dimensional settings with respect to the number of marginally dependent dimensions, compare the advantages of each test statistic, examine thei…
The paper tackles high-dimensional mixed linear regression with unknown parameters and proposes methods for estimation, confidence intervals, and hypothesis testing.
problem High-dimensional mixed linear regression with unknown parameters and covariance structure.
method Iterative high-dimensional EM algorithm for estimating regression vectors, debiased estimators for individual coordinates, and large-scale multiple testing procedure.
result Asymptotic normality of debiased estimators and FDR control for hypothesis testing.
Proposes counterfactual explanations for deep two-sample tests on high-dimensional data.
problem Limited interpretability of deep two-sample tests on high-dimensional data.
method Combines diffusion autoencoder and pretrained deep two-sample test model to generate counterfactuals.
result Counterfactual transformations increase p-values, indicating closer distribution similarity.
A new framework for paired-sample testing in high-dimensional data.
problem Challenges in standard paired-sample testing for high-dimensional data.
method Develops a two-step testing procedure using scoring functions and Wilcoxon signed-rank test.
result Substantial performance gains in testing accuracy compared to traditional methods.
A new, fast kernel test for large data.
problem Efficient kernel two-sample tests for high-dimensional, large-scale data.
method A new kernel-based test that is computationally efficient and robust to high dimensions.
result The new test performs well across various alternatives and dimensions.
This paper proposes a decorrelation-based approach to test hypotheses and construct confidence intervals for the low dimensional component of high dimensional proportional hazards models. Motivated by the geometric projection principle, we propose new decorrelated score, Wald and partial likelihood ratio statistics. Wi…
Generalizes causal inference to high-dimensional outcomes.
problem Limited causal inference methods for multivariate outcomes.
method Formulates causal discrepancy tests for nominal variables, uses conditional independence tests.
result Causal CDcorr method improves finite sample validity and power.
Nonparametric two sample testing deals with the question of consistently deciding if two distributions are different, given samples from both, without making any parametric assumptions about the form of the distributions. The current literature is split into two kinds of tests - those which are consistent without any a…
In this article the package High-dimensional Metrics (\texttt{hdm}) is introduced. It is a collection of statistical methods for estimation and quantification of uncertainty in high-dimensional approximately sparse models. It focuses on providing confidence intervals and significance testing for (possibly many) low-dim…
High-dimensional k-sample comparison is a common applied problem. We construct a class of easy-to-implement nonparametric distribution-free tests based on new tools and unexplored connections with spectral graph theory. The test is shown to possess various desirable properties along with a characteristic exploratory fl…
New framework tests mean-variance spanning in high dimensions.
problem Testing mean-variance spanning in high-dimensional asset spaces.
method Robust Student-t statistic based on batch-mean method, combined using Cauchy combination test.
result Advantages of diversification vary by economic conditions and cross-country.
This paper presents a multi-dimensional computational method to predict the spatial variation data inside and across multiple dies of a wafer. This technique is based on tensor computation. A tensor is a high-dimensional generalization of a matrix or a vector. By exploiting the hidden low-rank property of a high-dimens…
Tensor networks improve integration accuracy for high-dimensional problems.
problem Integration of high-dimensional functions with exponential convergence.
method Regression-free tensor network representations for integration.
result Exponential convergence achieved for non-analytic integrands.
We solve a high-dimensional model where nonlinear autoencoders detect hidden structure missed by PCA.
problem Hidden structure in high-dimensional data not detected by PCA.
method Tractable spiked model with two latent factors, one visible and one uncorrelated.
result Nonlinear autoencoders can extract hidden structure missed by PCA, even if reconstruction loss is higher.
Kernel test detects manifold data differences with high-dimensional noise.
problem Detecting differences between manifold data samples.
method Kernel-based two-sample test statistic related to MMD for manifold data.
result The test power exceeds a threshold depending on manifold dimensionality, Hölder order, and squared divergence.
New method detects changes in high-dimensional Gaussian data streams.
problem Detecting changes in high-dimensional data streams.
method Likelihood ratio tests across scales and coordinates.
result Patience (null rejection rate) at desired level, response delay under alternative.
Proposes a method to estimate and infer networks from multiple high-dimensional point processes.
problem Estimating and inferring networks from multiple high-dimensional point processes with shared and unique structures.
method Joint estimation procedure for networks of high-dimensional point processes incorporating weights to encourage similarity.
result Powerful hierarchical multiple testing procedure for edges of all estimated networks, controlling family-wise error rate.
Measuring conditional dependence is an important topic in statistics with broad applications including graphical models. Under a factor model setting, a new conditional dependence measure based on projection is proposed. The corresponding conditional independence test is developed with the asymptotic null distribution …
Hypothesis tests in models whose dimension far exceeds the sample size can be formulated much like the classical studentized tests only after the initial bias of estimation is removed successfully. The theory of debiased estimators can be developed in the context of quantile regression models for a fixed quantile value…
Paper develops robust methods for large-scale testing without tuning parameters.
problem Heavy-tailed data in high-dimensional settings.
method Revisits Hodges-Lehmann estimator for robust inference without tuning parameters.
result Develops confidence intervals and controls false discovery proportion.
We propose a novel class of time-varying nonparanormal graphical models, which allows us to model high dimensional heavy-tailed systems and the evolution of their latent network structures. Under this model, we develop statistical tests for presence of edges both locally at a fixed index value and globally over a range…
Conditional independence testing is a fundamental problem underlying causal discovery and a particularly challenging task in the presence of nonlinear and high-dimensional dependencies. Here a fully non-parametric test for continuous data based on conditional mutual information combined with a local permutation scheme …