Related papers: $\epsilon$-Kernel Coresets for Stochastic Points

Radial basis function neural networks (\emph{RBFNN}) are {well-known} for their capability to approximate any continuous function on a closed bounded set with arbitrary precision given enough hidden neurons. In this paper, we introduce the…

We provide improved error bounds for kernel-based numerical differentiation in terms of growth functions when kernels are of a finite smoothness, such as polyharmonic splines, thin plate splines or Wendland kernels. In contrast to existing…

Approximation/interpolation from spaces of positive definite or conditionally positive definite kernels is an increasingly popular tool for the analysis and synthesis of scattered data, and is central to many meshless methods. For a set of…

Regression tasks, notably in safety-critical domains, require proper uncertainty quantification, yet the literature remains largely classification-focused. In this light, we introduce a family of measures for total, aleatoric, and epistemic…

Despite a large corpus of recent work on scaling up Gaussian processes, a stubborn trade-off between computational speed, prediction and uncertainty quantification accuracy, and customizability persists. This is because the vast majority of…

We develop a rigorous framework for deterministic coreset construction in empirical risk minimization (ERM). Our central contribution is the Adaptive Deterministic Uniform-Weight Trimming (ADUWT) algorithm, which constructs a coreset by…

A coreset (or core-set) of a dataset is its semantic compression with respect to a set of queries, such that querying the (small) coreset provably yields an approximate answer to querying the original (full) dataset. In the last decade,…

We study how to utilize (possibly erroneous) predictions in a model for computing under uncertainty in which an algorithm can query unknown data. Our aim is to minimize the number of queries needed to solve the minimum spanning tree…

Despite the ubiquity of the Gaussian process regression model, few theoretical results are available that account for the fact that parameters of the covariance kernel typically need to be estimated from the dataset. This article provides…

Probabilistic convolutional neural networks, which predict distributions of predictions instead of point estimates, led to recent advances in many areas of computer vision, from image reconstruction to semantic segmentation. Besides state…

Neural Stochastic Differential Equations (NSDEs) model the drift and diffusion functions of a stochastic process as neural networks. While NSDEs are known to make accurate predictions, their uncertainty quantification properties have been…

Critical points mark locations in the domain where the level-set topology of a scalar function undergoes fundamental changes and thus indicate potentially interesting features in the data. Established methods exist to locate and relate such…

Estimating expected polynomials of density functions from samples is a basic problem with numerous applications in statistics and information theory. Although kernel density estimators are widely used in practice for such functional…

Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…

Descriptive statistics for parametric models are currently highly sensative to departures, gross errors, and/or random errors. Here, leveraging the structures of parametric distributions and their central moment kernel distributions, a…

Depth measures are powerful tools for defining level sets in emerging, non--standard, and complex random objects such as high-dimensional multivariate data, functional data, and random graphs. Despite their favorable theoretical properties,…

Due to the growing adoption of deep neural networks in many fields of science and engineering, modeling and estimating their uncertainties has become of primary importance. Despite the growing literature about uncertainty quantification in…

In many real-world applications we are interested in approximating costly functions that are analytically unknown, e.g. complex computer codes. An emulator provides a fast approximation of such functions relying on a limited number of…

Low-discrepancy designs play a central role in quasi-Monte Carlo methods and are increasingly influential in other domains such as machine learning, robotics and computer graphics, to name a few. In recent years, one such low-discrepancy…

Interpolation and approximation of functionals with conditionally positive definite kernels is considered on sets of centers that are not determining for polynomials. It is shown that polynomial consistency is sufficient in order to define…