Related papers: Generalized bootstrap in the Bures-Wasserstein spa…

Resampling methods such as the bootstrap have proven invaluable in the field of machine learning. However, the applicability of traditional bootstrap methods is limited when dealing with large streams of dependent data, such as time series…

Increasingly complex datasets pose a number of challenges for Bayesian inference. Conventional posterior sampling based on Markov chain Monte Carlo can be too computationally intensive, is serial in nature and mixes poorly between posterior…

Standard gradient descent methods yield point estimates with no measure of confidence. This limitation is acute in overparameterized and low-data regimes, where models have many parameters relative to available data and can easily overfit.…

Wasserstein barycenters define averages of probability measures in a geometrically meaningful way. Their use is increasingly popular in applied fields, such as image, geometry or language processing. In these fields however, the probability…

In this paper we study the applicability of the bootstrap to do inference on Manski's maximum score estimator under the full generality of the model. We propose three new, model-based bootstrap procedures for this problem and show their…

Bayesian inference typically requires the computation of an approximation to the posterior distribution. An important requirement for an approximate Bayesian inference algorithm is to output high-accuracy posterior mean and uncertainty…

Bootstrap inference is a powerful tool for obtaining robust inference for quantiles and difference-in-quantiles estimators. The computationally intensive nature of bootstrap inference has made it infeasible in large-scale experiments. In…

We propose of an improved version of the ubiquitous symmetrization inequality making use of the Wasserstein distance between a measure and its reflection in order to quantify the symmetry of the given measure. An empirical bound on this…

Confidence measures for the generalization error are crucial when small training samples are used to construct classifiers. A common approach is to estimate the generalization error by resampling and then assume the resampled estimator…

In this article, we present data-subsetting algorithms that allow for the approximate and scalable implementation of the Bayesian bootstrap. They are analogous to two existing algorithms in the frequentist literature: the bag of little…

This paper proposes asymptotically distribution-free inference methods for comparing a broad range of welfare indices across dependent samples, including those employed in inequality, poverty, and risk analysis. Two distinct situations are…

Fr\'echet regression, or conditional Barycenters, is a flexible framework for modeling relationships between covariates (usually Euclidean) and response variables on general metric spaces, e.g., probability distributions or positive…

Obtaining accurate estimates of machine learning model uncertainties on newly predicted data is essential for understanding the accuracy of the model and whether its predictions can be trusted. A common approach to such uncertainty…

In this paper we introduce the concept of bootstrapped pivots for the sample and the population means. This is in contrast to the classical method of constructing bootstrapped confidence intervals for the population mean via estimating the…

Randomized clinical trials are considered the gold standard for estimating causal effects. Nevertheless, in studies that are aimed at examining adverse effects of interventions, such trials are often impractical because of ethical and…

Reliable forward uncertainty quantification in engineering requires methods that account for aleatory and epistemic uncertainties. In many applications, epistemic effects arising from uncertain parameters and model form dominate prediction…

In this paper we study a bootstrap strategy for estimating the variance of a mean taken over large multifactor crossed random effects data sets. We apply bootstrap reweighting independently to the levels of each factor, giving each…

Let $X_{1},\ldots,X_{n}$ be i.i.d. sample in $\mathbb{R}^{p}$ with zero mean and the covariance matrix $\mathbf{\Sigma}$. The problem of recovering the projector onto an eigenspace of $\mathbf{\Sigma}$ from these observations naturally…

Finkelstein-Schoenfeld, Buyse, Pocock, and other authors have developed generalizations of the Mann-Whitney test that allow for pairwise patient comparisons to include a hierarchy of measurements. Various authors present either asymptotic…

Modern problems in statistics tend to include estimators of high computational complexity and with complicated distributions. Statistical inference on such estimators usually relies on asymptotic normality assumptions, however, such…