Related papers: Geometry of the Minimum Volume Confidence Sets
This paper introduces Least Volume (LV)--a simple yet effective regularization method inspired by geometric intuition--that reduces the number of latent dimensions required by an autoencoder without prior knowledge of the dataset's…
We develop confidence sets which provide spatial uncertainty guarantees for the output of a black-box machine learning model designed for image segmentation. To do so we adapt conformal inference to the imaging setting, obtaining thresholds…
We provide lower error bounds for randomized algorithms that approximate integrals of functions depending on an unrestricted or even infinite number of variables. More precisely, we consider the infinite-dimensional integration problem on…
Embeddings are a basic initial feature extraction step in many machine learning models, particularly in natural language processing. An embedding attempts to map data tokens to a low-dimensional space where similar tokens are mapped to…
Metric embedding has become a common technique in the design of algorithms. Its applicability is often dependent on how high the embedding's distortion is. For example, embedding finite metric space into trees may require linear distortion…
The high energy physics unfolding problem is an important statistical inverse problem in data analysis at the Large Hadron Collider (LHC) at CERN. The goal of unfolding is to make nonparametric inferences about a particle spectrum from…
The task of approximating a function of d variables from its evaluations at a given number of points is ubiquitous in numerical analysis and engineering applications. When d is large, this task is challenged by the so-called curse of…
Given a network property or a data structure, a local certification is a labeling that allows to efficiently check that the property is satisfied, or that the structure is correct. The quality of a certification is measured by the size of…
The equations of motion of a mechanical system subjected to nonholonomic linear constraints can be formulated in terms of a linear almost Poisson structure in a vector bundle. We study the existence of invariant measures for the system in…
Volume of metric balls relates to rate-distortion theory and packing bounds on codes. In this paper, the volume of balls in complex Grassmann manifolds is evaluated for an arbitrary radius. The ball is defined as a set of hyperplanes of a…
We consider interval estimation of the difference between two binomial proportions. Several methods of constructing such an interval are known. Unfortunately those confidence intervals have poor coverage probability: it is significantly…
Persistence diagrams, combining geometry and topology for an effective shape description used in pattern recognition, have already proven to be an effective tool for shape representation with respect to a certainfiltering function.…
Interesting data often concentrate on low dimensional smooth manifolds inside a high dimensional ambient space. Random projections are a simple, powerful tool for dimensionality reduction of such data. Previous works have studied bounds on…
The main goal of this paper is to present a series of inequalities connecting the surface area measure of a convex body and surface area measure of its projections and sections. We present a solution of a question from S. Campi, P.…
Neural volume rendering became increasingly popular recently due to its success in synthesizing novel views of a scene from a sparse set of input images. So far, the geometry learned by neural volume rendering techniques was modeled using a…
In this paper, we study a fixed-confidence, fixed-tolerance formulation of a class of stochastic bi-level optimization problems, where the upper-level problem selects from a finite set of systems based on a performance metric, and the…
Finding correspondences between 3D shapes is a crucial problem in computer vision and graphics, which is for example relevant for tasks like shape interpolation, pose transfer, or texture transfer. An often neglected but essential property…
Transductive conformal prediction addresses the simultaneous prediction for multiple data points. Given a desired confidence level, the objective is to construct a prediction set that includes the true outcomes with the prescribed…
This paper examines asymptotic properties of local M-estimators under three sets of high-level conditions. These conditions are sufficiently general to cover the minimum volume predictive region, conditional maximum score estimator for a…
We develop a numerical method for the computation of a minimal convex and compact set, $\mathcal{B}\subset\mathbb{R}^N$, in the sense of mean width. This minimisation is constrained by the requirement that $\max_{b\in\mathcal{B}}\langle b ,…