Related papers: A projection pursuit framework for testing general…
We derive a new class of statistical tests for generalized linear models based on thresholding point estimators. These tests can be employed whether the model includes more parameters than observations or not. For linear models, our tests…
The paper concerns inference in the ill-conditioned functional response model, which is a part of functional data analysis. In this regression model, the functional response is modeled using several independent scalar variables. To verify…
We consider a novel Bayesian approach to estimation, uncertainty quantification, and variable selection for a high-dimensional linear regression model under sparsity. The number of predictors can be nearly exponentially large relative to…
Inference for the parameters indexing generalised linear models is routinely based on the assumption that the model is correct and a priori specified. This is unsatisfactory because the chosen model is usually the result of a data-adaptive…
Approximate inference via information projection has been recently introduced as a general-purpose approach for efficient probabilistic inference given sparse variables. This manuscript goes beyond classical sparsity by proposing efficient…
Rapid advancements in data science require us to have fundamentally new frameworks to tackle prevalent but highly non-trivial "irregular" inference problems, to which the large sample central limit theorem does not apply. Typical examples…
In this paper, we present a novel and effective inference approach to conduct both finite- and large-sample inference for high-dimensional linear regression models. This approach is developed under the so-called repro samples framework, in…
In this paper, we study inference for high-dimensional data characterized by small sample sizes relative to the dimension of the data. In particular, we provide an infinite-dimensional framework to study statistical models that involve…
Fitting high-dimensional statistical models often requires the use of non-linear parameter estimation procedures. As a consequence, it is generally impossible to obtain an exact characterization of the probability distribution of the…
We introduce a general framework for testing goodness-of-fit for Gaussian graphical models in both the low- and high-dimensional settings. This framework is based on a novel algorithm for generating exchangeable copies by conditioning on…
In recent years, there has been considerable theoretical development regarding variable selection consistency of penalized regression techniques, such as the lasso. However, there has been relatively little work on quantifying the…
Variable selection for high-dimensional, highly correlated data has long been a challenging problem, often yielding unstable and unreliable models. We propose a resample-aggregate framework that exploits diffusion models' ability to…
An important challenge in statistical analysis lies in controlling the bias of estimators due to the ever-increasing data size and model complexity. Approximate numerical methods and data features like censoring and misclassification often…
Ensuring robust model performance in diverse real-world scenarios requires addressing generalizability across domains with covariate shifts. However, no formal procedure exists for statistically evaluating generalizability in machine…
Uncertainty estimation aims to evaluate the confidence of a trained deep neural network. However, existing uncertainty estimation approaches rely on low-dimensional distributional assumptions and thus suffer from the high dimensionality of…
Sparse feature selection is necessary when we fit statistical models, we have access to a large group of features, don't know which are relevant, but assume that most are not. Alternatively, when the number of features is larger than the…
For a high-dimensional linear model with a finite number of covariates measured with error, we study statistical inference on the parameters associated with the error-prone covariates, and propose a new corrected decorrelated score test and…
We introduce a new framework for dimension reduction in the context of high-dimensional regression. Our proposal is to aggregate an ensemble of random projections, which have been carefully chosen based on the empirical regression…
We study high-dimensional two-sample mean comparison and address the curse of dimensionality through data-adaptive projections. Leveraging the low-dimensional and localized signal structures commonly seen in single-cell genomics data, our…
Motivated by the prevalence of high dimensional low sample size datasets in modern statistical applications, we propose a general nonparametric framework, Direction-Projection-Permutation (DiProPerm), for testing high dimensional…