Related papers: Catoni-style confidence sequences for heavy-tailed…
We consider the problem of adaptive inference on a regression function at a point under a multivariate nonparametric regression setting. The regression function belongs to a H\"older class and is assumed to be monotone with respect to some…
The problem of stopping stochastic gradient descent (SGD) in an online manner, based solely on the observed trajectory, is a challenging theoretical problem with significant consequences for applications. While SGD is routinely monitored as…
Skewness and kurtosis are fundamental statistical moments commonly used to quantify asymmetry and tail behavior in probability distributions. Despite their widespread application in statistical mechanics, condensed matter physics, and…
Catoni proposed a robust M-estimator and gave the deviation inequality for one fixed test function. The present paper is devoted to the uniform concentration inequality for a family of test functions. As an application, we consider…
In a sparse stochastic block model with two communities of unequal sizes we derive two posterior concentration inequalities, that imply (1) posterior (almost-)exact recovery of the community structure under sparsity bounds comparable to…
Conformal prediction (CP) has been a popular method for uncertainty quantification because it is distribution-free, model-agnostic, and theoretically sound. For forecasting problems in supervised learning, most CP methods focus on building…
We propose a new method to construct confidence intervals for quantities that are associated with a stationary time series, which avoids direct estimation of the asymptotic variances. Unlike the existing tuning-parameter-dependent…
Self-consistency (SC) is a widely used test-time inference technique for improving performance in chain-of-thought reasoning. It involves generating multiple responses, or samples from a large language model (LLM) and selecting the most…
In this paper, we present new high-probability PAC-Bayes bounds for different types of losses. Firstly, for losses with a bounded range, we recover a strengthened version of Catoni's bound that holds uniformly for all parameter values. This…
We propose new confidence sets (CSs) for the regression discontinuity parameter in fuzzy designs. Our CSs are based on local linear regression, and are bias-aware, in the sense that they take possible bias explicitly into account. Their…
Reproducibility is imperative for any scientific discovery. More often than not, modern scientific findings rely on statistical analysis of high-dimensional data. At a minimum, reproducibility manifests itself in stability of statistical…
We consider a linear regression model, with the parameter of interest a specified linear combination of the regression parameter vector. We suppose that, as a first step, a data-based model selection (e.g. by preliminary hypothesis tests or…
We present an efficient method of calculating exact confidence intervals for the hypergeometric parameter representing the number of "successes," or "special items," in the population. The method inverts minimum-width acceptance intervals…
We consider clinical trials in which an experimental treatment is compared with a control in pre-specified patient subpopulations. In such settings, adaptive enrichment designs allow the enrolled population to be modified at an interim…
The problem is in the estimation of the fraction of population with a sensitive characteristic. We consider the Item Count Technique an indirect method of questioning designed to protect respondents' privacy. The exact confidence interval…
Assurance cases (ACs) are prepared to argue that a system has satisfied critical quality attributes. Many methods exist to assess confidence in ACs, including quantitative methods that represent confidence numerically. While quantitative…
Model selection is critical in the modern statistics and machine learning community. However, most existing works do not apply to heavy-tailed data, which are commonly encountered in real applications, such as the single-cell multiomics…
A sampling-based method is introduced to approximate the Gittins index for a general family of alternative bandit processes. The approximation consists of a truncation of the optimization horizon and support for the immediate rewards, an…
We propose a robust optimization approach for constructing confidence bands for stochastic processes using a finite number of simulated sample paths. Our approach can be used to quantify uncertainty in realizations of stochastic processes…
Bootstrap smoothed (bagged) estimators have been proposed as an improvement on estimators found after preliminary data-based model selection. Efron, 2014, derived a widely applicable formula for a delta method approximation to the standard…