Related papers: Data-intrinsic approximation in metric spaces

We propose an computational framework for real-time risk assessment and prioritizing for random outcomes without prior information on probability distributions. The basic model is built based on satisficing measure (SM) which yields a…

Statistical uncertainties complicate engineering design -- confounding regulated design approaches, and degrading the performance of reliability efforts. The simplest means to tackle this uncertainty is double loop simulation; a nested…

Modern inference and learning often hinge on identifying low-dimensional structures that approximate large scale data. Subspace clustering achieves this through a union of linear subspaces. However, in contemporary applications data is…

Empirically, Deep Learning (DL) has demonstrated unprecedented success in practical applications. However, DL remains by and large a mysterious "black-box", spurring recent theoretical research to build its mathematical foundations. In this…

In this paper we revisit the classical method of partitioning classification and study its convergence rate under relaxed conditions, both for observable (non-privatised) and for privatised data. We consider the problem of classification in…

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…

Inverse problems are inherently ill-posed and therefore require regularization techniques to achieve a stable solution. While traditional variational methods have well-established theoretical foundations, recent advances in machine learning…

Accurate uncertainty estimation is crucial for deploying neural networks in risk-sensitive applications such as medical diagnosis. Monte Carlo Dropout is a widely used technique for approximating predictive uncertainty by performing…

Most of the existing methods for estimating the local intrinsic dimension of a data distribution do not scale well to high-dimensional data. Many of them rely on a non-parametric nearest neighbors approach which suffers from the curse of…

The performance of a machine learning system is usually evaluated by using i.i.d.\ observations with true labels. However, acquiring ground truth labels is expensive, while obtaining unlabeled samples may be cheaper. Stratified sampling can…

Teramoto et al. defined a new measure called the gap ratio that measures the uniformity of a finite point set sampled from $\cal S$, a bounded subset of $\mathbb{R}^2$. We generalize this definition of measure over all metric spaces by…

The most widely used internal measure for clustering evaluation is the silhouette coefficient, whose naive computation requires a quadratic number of distance calculations, which is clearly unfeasible for massive datasets. Surprisingly,…

Differential privacy is a leading protection setting, focused by design on individual privacy. Many applications, in medical / pharmaceutical domains or social networks, rather posit privacy at a group level, a setting we call integral…

We construct a structure preserving non-conforming finite element approximation scheme for the bi-harmonic wave maps into spheres equation. It satisfies a discrete energy law and preserves the non-convex sphere constraint of the continuous…

To model modern large-scale datasets, we need efficient algorithms to infer a set of $P$ unknown model parameters from $N$ noisy measurements. What are fundamental limits on the accuracy of parameter inference, given finite signal-to-noise…

Appropriately representing elements in a database so that queries may be accurately matched is a central task in information retrieval; recently, this has been achieved by embedding the graphical structure of the database into a manifold in…

Cross-modality distillation arises as an important topic for data modalities containing limited knowledge such as depth maps and high-quality sketches. Such techniques are of great importance, especially for memory and privacy-restricted…

The clustering of bounded data presents unique challenges in statistical analysis due to the constraints imposed on the data values. This paper introduces a novel method for model-based clustering specifically designed for bounded data.…

Robust inference for stochastic dynamical systems is often hampered by sparse sampling and the absence of closed-form likelihoods. We introduce a Monte Carlo path-inference framework that leverages full-path statistics and bridge processes…

Many clustering algorithms when the data are curves or functions have been recently proposed. However, the presence of contamination in the sample of curves can influence the performance of most of them. In this work we propose a robust,…