Related papers: The HulC: Confidence Regions from Convex Hulls

In econometrics, many parameters of interest can be written as ratios of expectations. The main approach to construct confidence intervals for such parameters is the delta method. However, this asymptotic procedure yields intervals that may…

In statistical inference, it is rarely realistic that the hypothesized statistical model is well-specified, and consequently it is important to understand the effects of misspecification on inferential procedures. When the hypothesized…

Conformal prediction, and split conformal prediction as a specific implementation, offer a distribution-free approach to estimating prediction intervals with statistical guarantees. Recent work has shown that split conformal prediction can…

If you are predicting the label $y$ of a new object with $\hat y$, how confident are you that $y = \hat y$? Conformal prediction methods provide an elegant framework for answering such question by building a $100 (1 - \alpha)\%$ confidence…

This paper investigates the post-hoc calibration of confidence for "exploratory" machine learning classification problems. The difficulty in these problems stems from the continuing desire to push the boundaries of which categories have…

We introduce a Hamiltonian Monte Carlo (HMC) methodology based on a randomized selection of integration times, referred to as eHMC, where "e" stands for empirical. The approach relies on an offline calibration phase that leverages…

In this paper, we consider the polyhedral structure of the unit commitment polytope. In particular, we provide the convex hull results for the problem under the following different settings: 1) the convex hulls for the integrated…

We introduce two data-driven procedures for optimal estimation and inference in nonparametric models using instrumental variables. The first is a data-driven choice of sieve dimension for a popular class of sieve two-stage least squares…

Although a few methods have been developed recently for building confidence intervals after model selection, how to construct confidence sets for joint post-selection inference is still an open question. In this paper, we develop a new…

We address the challenge of performing Targeted Maximum Likelihood Estimation (TMLE) after an initial Highly Adaptive Lasso (HAL) fit. Existing approaches that utilize the data-adaptive working model selected by HAL-such as the relaxed HAL…

Given a random sample of points from some unknown distribution, we propose a new data-driven method for estimating its probability support $S$. Under the mild assumption that $S$ is $r$-convex, the smallest $r$-convex set which contains the…

Manual estimation of fetal Head Circumference (HC) from Ultrasound (US) is a key biometric for monitoring the healthy development of fetuses. Unfortunately, such measurements are subject to large inter-observer variability, resulting in low…

Using Quadrics as the object representation has the benefits of both generality and closed-form projection derivation between image and world spaces. Although numerous constraints have been proposed for dual quadric reconstruction, we found…

Upper and lower bounds are derived for the Gaussian mean width of the intersection of a convex hull of $M$ points with an Euclidean ball of a given radius. The upper bound holds for any collection of extreme point bounded in Euclidean norm.…

We address functional uncertainty quantification for ill-posed inverse problems where it is possible to evaluate a possibly rank-deficient forward model, the observation noise distribution is known, and there are known parameter…

Hyperdimensional Computing (HDC) offers a computationally efficient paradigm for neuromorphic learning. Yet, it lacks rigorous uncertainty quantification, leading to open decision boundaries and, consequently, vulnerability to outliers,…

The Euclid mission, designed to map the geometry of the dark Universe, presents an unprecedented opportunity for advancing our understanding of the cosmos through its photometric galaxy cluster survey. This paper focuses on enhancing the…

We propose a general method for constructing hypothesis tests and confidence sets that have finite sample guarantees without regularity conditions. We refer to such procedures as "universal." The method is very simple and is based on a…

Considering the increasing size of available data, the need for statistical methods that control the finite sample bias is growing. This is mainly due to the frequent settings where the number of variables is large and allowed to increase…

Estimating the maximum mean finds a variety of applications in practice. In this paper, we study estimation of the maximum mean using an upper confidence bound (UCB) approach where the sampling budget is adaptively allocated to one of the…