Related papers: Curvature of high-dimensional data

$Anomaly$ $detection$ problems (also called $change$-$point$ $detection$ problems) have been studied in data mining, statistics and computer science over the last several decades in applications such as medical condition monitoring and…

Diffusion models can unintentionally memorize training samples, raising concerns about privacy and copyright. While recent methods can detect memorization, they often rely on global or model-specific signals and provide limited insight into…

Combining information both within and across trajectories, we propose a simple estimator for the local regularity of the trajectories of a stochastic process. Independent trajectories are measured with errors at randomly sampled time…

Kernel density estimators with circular data have been studied extensively for decades, as they allow flexible estimations even when the shape of the underlying density is complex. Many recent studies have examined bias correction methods;…

In this work some advances in the theory of curvature of two-dimensional probability manifolds corresponding to families of distributions are proposed. It is proved that location-scale distributions are hyperbolic in the Information…

The manifold hypothesis says that natural high-dimensional data lie on or around a low-dimensional manifold. The recent success of statistical and learning-based methods in very high dimensions empirically supports this hypothesis,…

We study the query complexity of geodesically convex (g-convex) optimization on a manifold. To isolate the effect of that manifold's curvature, we primarily focus on hyperbolic spaces. In a variety of settings (smooth or not; strongly…

Estimating normals for noisy point clouds is a persistent challenge in 3D geometry processing, particularly for end-to-end oriented normal estimation. Existing methods generally address relatively clean data and rely on supervised priors to…

The global dimensionality of a neural representation manifold provides rich insight into the computational process underlying both artificial and biological neural networks. However, all existing measures of global dimensionality are…

Variational representations of divergences and distances between high-dimensional probability distributions offer significant theoretical insights and practical advantages in numerous research areas. Recently, they have gained popularity in…

We study nonparametric covariance function estimation for functional data observed with noise at discrete locations on a $d$-dimensional domain. Estimating the covariance function from discretely observed data is a challenging nonparametric…

We introduce a novel technique for neural point cloud consolidation which learns from only the input point cloud. Unlike other point upsampling methods which analyze shapes via local patches, in this work, we learn from global subsets. We…

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…

A new vision in multidimensional statistics is proposed impacting severalareas of application. In these applications, a set of noisy measurementscharacterizing the repeatable response of a process is known as a realizationand can be seen as…

The concept of biased data is well known and its practical applications range from social sciences and biology to economics and quality control. These observations arise when a sampling procedure chooses an observation with probability that…

We give a metric characterization of the scalar curvature of a smooth Riemannian manifold, analyzing the maximal distance between $(n+1)$ points in infinitesimally small neighborhoods of a point. Since this characterization is purely in…

We show that the theory of varifolds can be suitably enriched to open the way to applications in the field of discrete and computational geometry. Using appropriate regularizations of the mass and of the first variation of a varifold we…

We prove various inequalities measuring how far from an isometry a local map from a manifold of high curvature to a manifold of low curvature must be. We consider the cases of volume-preserving, conformal and quasi-conformal maps. The…

Object parsing and segmentation from point clouds are challenging tasks because the relevant data is available only as thin structures along object boundaries or other features, and is corrupted by large amounts of noise. To handle this…

This paper presents a novel self-supervised approach to reconstruct human shape and pose from noisy point cloud data. Relying on large amount of dataset with ground-truth annotations, recent learning-based approaches predict correspondences…