Related papers: Geometry of the Minimum Volume Confidence Sets
Computation of confidence sets is central to data science and machine learning, serving as the workhorse of A/B testing and underpinning the operation and analysis of reinforcement learning algorithms. Among all valid confidence sets for…
Construction of tight confidence regions and intervals is central to statistical inference and decision making. This paper develops new theory showing minimum average volume confidence regions for categorical data. More precisely, consider…
Conformal prediction provides a principled framework for constructing predictive sets with finite-sample validity. While much of the focus has been on univariate response variables, existing multivariate methods either impose rigid…
We study the problem of learning a high-density region of an arbitrary distribution over $\mathbb{R}^d$. Given a target coverage parameter $\delta$, and sample access to an arbitrary distribution $D$, we want to output a confidence set $S…
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…
For a probability measure on a real separable Hilbert space, we are interested in "volume-based" approximations of the d-dimensional least squares error of it, i.e., least squares error with respect to a best fit d-dimensional affine…
Recent advances in statistics introduced versions of the central limit theorem for high-dimensional vectors, allowing for the construction of confidence regions for high-dimensional parameters. In this note, $s$-sparsely convex…
Consider the observation of n iid realizations of an experiment with d>1 possible outcomes, which corresponds to a single observation of a multinomial distribution M(n,p) where p is an unknown discrete distribution on {1,...,d}. In many…
Motivated by problems of uncertainty propagation and robust estimation we are interested in computing a polynomial sublevel set of fixed degree and minimum volume that contains a given semialgebraic set K. At this level of generality this…
Confidence intervals are a popular way to visualize and analyze data distributions. Unlike p-values, they can convey information both about statistical significance as well as effect size. However, very little work exists on applying…
This paper studies and critically discusses the construction of nonparametric confidence regions for density level sets. Methodologies based on both vertical variation and horizontal variation are considered. The investigations provide…
The goal of confidence-set learning in the binary classification setting is to construct two sets, each with a specific probability guarantee to cover a class. An observation outside the overlap of the two sets is deemed to be from one of…
We determine the minimal volume of a stable surface of rank one, and show that the surface attaining this minimum is unique up to isomorphism. This resolves a conjecture of Alexeev and the second author. Of independent interest, the…
Simultaneous confidence bands (SCBs) for percentiles in linear regression are valuable tools with many applications. In this paper, we propose a novel criterion for comparing SCBs for percentiles, termed the Minimum Area Confidence Set…
Linear combinations of multinomial probabilities, such as those resulting from contingency tables, are of use when evaluating classification system performance. While large sample inference methods for these combinations exist, small sample…
Large language models (LLMs) often exhibit a puzzling disconnect between their asserted confidence and actual problem-solving competence. We offer a mechanistic account of this decoupling by analyzing the geometry of internal states across…
Bounding volumes are an established concept in computer graphics and vision tasks but have seen little change since their early inception. In this work, we study the use of neural networks as bounding volumes. Our key observation is that…
Volumetry is one of the principal downstream applications of 3D medical image segmentation, for example, to detect abnormal tissue growth or for surgery planning. Conformal Prediction is a promising framework for uncertainty quantification,…
For classification tasks, the performance of a deep neural network is determined by the structure of its decision boundary, whose geometry directly affects essential properties of the model, including accuracy and robustness. Motivated by a…
We propose a cost volume-based neural network for depth inference from multi-view images. We demonstrate that building a cost volume pyramid in a coarse-to-fine manner instead of constructing a cost volume at a fixed resolution leads to a…