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The problem of constructing confidence sets in the high-dimensional linear model with $n$ response variables and $p$ parameters, possibly $p\ge n$, is considered. Full honest adaptive inference is possible if the rate of sparse estimation…

In a meta-analysis, it is important to specify a model that adequately describes the effect-size distribution of the underlying population of studies. The conventional normal fixed-effect and normal random-effects models assume a normal…

Confidence intervals are an established means of portraying uncertainty about an inferred parameter and can be generated through the use of confidence distributions. For a confidence distribution to be ideal, it must maintain frequentist…

Insights into complex, high-dimensional data can be obtained by discovering features of the data that match or do not match a model of interest. To formalize this task, we introduce the "data selection" problem: finding a lower-dimensional…

With the growing adoption of Text-to-Image (TTI) systems, the social biases of these models have come under increased scrutiny. Herein we conduct a systematic investigation of one such source of bias for diffusion models: embedding spaces.…

Regularized M-estimators are used in diverse areas of science and engineering to fit high-dimensional models with some low-dimensional structure. Usually the low-dimensional structure is encoded by the presence of the (unknown) parameters…

The estimation of information measures of continuous distributions based on samples is a fundamental problem in statistics and machine learning. In this paper, we analyze estimates of differential entropy in $K$-dimensional Euclidean space,…

We consider the problem of setting confidence intervals on a parameter of interest from the maximum-likelihood fit of a physics model to a binned data set with a large number of bins, large event-counts per bin, and in the presence of…

We consider the statistical analysis of data on high-dimensional spheres and shape spaces. The work is of particular relevance to applications where high-dimensional data are available--a commonly encountered situation in many disciplines.…

Adequate uncertainty representation and quantification have become imperative in various scientific disciplines, especially in machine learning and artificial intelligence. As an alternative to representing uncertainty via one single…

A key sticking point of Bayesian analysis is the choice of prior distribution, and there is a vast literature on potential defaults including uniform priors, Jeffreys' priors, reference priors, maximum entropy priors, and weakly informative…

We consider the problem of constructing distribution-free prediction sets with finite-sample conditional guarantees. Prior work has shown that it is impossible to provide exact conditional coverage universally in finite samples. Thus, most…

We study sequential probability assignment in the Gaussian setting, where the goal is to predict, or equivalently compress, a sequence of real-valued observations almost as well as the best Gaussian distribution with mean constrained to a…

Scientists often use meta-analysis to characterize the impact of an intervention on some outcome of interest across a body of literature. However, threats to the utility and validity of meta-analytic estimates arise when scientists average…

We revisit the classical problem of universal prediction of stochastic sequences with a finite time horizon $T$ known to the learner. The question we investigate is whether it is possible to derive vanishing regret bounds that hold with…

Large language models (LLMs) exhibit strikingly conflicting behaviors: they can appear steadfastly overconfident in their initial answers whilst at the same time being prone to excessive doubt when challenged. To investigate this apparent…

Bayesian Deep Learning (BDL) gives access not only to aleatoric uncertainty, as standard neural networks already do, but also to epistemic uncertainty, a measure of confidence a model has in its own predictions. In this article, we show…

We consider a sparse linear regression model with unknown symmetric error under the high-dimensional setting. The true error distribution is assumed to belong to the locally $\beta$-H\"{o}lder class with an exponentially decreasing tail,…

Large language models (LLMs) are increasingly used to simulate human behavior, but common practices to use LLM-generated data are inefficient. Treating an LLM's output ("model choice") as a single data point underutilizes the information…

Large-scale empirical data, the sample size and the dimension are high, often exhibit various characteristics. For example, the noise term follows unknown distributions or the model is very sparse that the number of critical variables is…