A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Proves a theorem for Assouad dimension with applications to distance sets and radial projections.
Introduces Grassmann Distance Complexity to measure algebraic set nearest point problems.
Study geodesic distances and convexity in contact sets.
Distance function to a finite set is a topological Morse function.
Study shows singular set of distance functions is delta-convex.
Study shows continuous evolution of curves in Fréchet distance.
This paper introduces a new distance metric for filtered A-infinity categories, focusing on Lagrangian submanifolds.
Study entropic regularization of Gaussian measures and processes on Hilbert space.
New tools for estimating and inferring Wasserstein distance in topic models.
We consider the problem of allocating samples to a finite set of discrete distributions in order to learn them uniformly well in terms of four common distance measures: , , -divergence, and separation distance. To present a unified treatment of these distances, we first propose a general optimistic…
Simple algorithm achieves distance to calibration error of at most 2√T+1.
New method improves robust point matching under probabilistic settings.
We define a new notion---the sub-index of a critical point of a distance function. We show how sub-index affects the homotopy type of sublevel sets of distance functions.
New distances for comparing multivariate normal distributions.
New topologies for star-shaped sets without boundedness.
A new robust metric compares distributions more accurately than existing methods.
Quantum Earth Mover's distance improves stability and efficiency in quantum learning.
On a complete, connected, locally compact, non-compact geodesic space , we assign each compact set a distance-like function. With the help of these functions, we obtain a pseudo-metric on the space of (non-empty) compact subsets of which is less than the Hausdorff distance. The quotient metric space is close…
Paper proposes a method to recover point configurations from noisy distance data.
The paper examines convergence of distances in Lipschitz structures on manifolds.
Extends Mahalanobis distance to Banach spaces for anomaly detection.
We construct a compact metric space that has any other compact metric space as a tangent, with respect to the Gromov-Hausdorff distance, at all points. Furthermore, we give examples of compact sets in the Euclidean unit cube, that have almost any other compact set of the cube as a tangent at all points or just in a den…
We consider the setting of Reeb graphs of piecewise linear functions and study distances between them that are stable, meaning that functions which are similar in the supremum norm ought to have similar Reeb graphs. We define an edit distance for Reeb graphs and prove that it is stable and universal, meaning that it pr…
The aim of this article is to generalize the notion of the cut locus and to get the structure theorem for it. For this purpose, we first introduce a class of 1-Lipschitz functions, each member of which is called an {\it almost distance function}. Typical examples of an almost distance function are the distance function…
For many machine learning problem settings, particularly with structured inputs such as sequences or sets of objects, a distance measure between inputs can be specified more naturally than a feature representation. However, most standard machine models are designed for inputs with a vector feature representation. In th…
Study of -neighbors in Riemannian manifolds, proving infinite set of distances.
The Sinkhorn "distance", a variant of the Wasserstein distance with entropic regularization, is an increasingly popular tool in machine learning and statistical inference. However, the time and memory requirements of standard algorithms for computing this distance grow quadratically with the size of the data, making th…
The paper studies the distance from calibration in sequential prediction, proving upper and lower bounds.
Transportation distances have been used for more than a decade now in machine learning to compare histograms of features. They have one parameter: the ground metric, which can be any metric between the features themselves. As is the case for all parameterized distances, transportation distances can only prove useful in…
A framework for measuring differences in categorical data.
Geodesic distance matrices can reveal shape properties that are largely invariant to non-rigid deformations, and thus are often used to analyze and represent 3-D shapes. However, these matrices grow quadratically with the number of points. Thus for large point sets it is common to use a low-rank approximation to the di…
Research explores Lorentzian distances on a specific geometric plane.
Given a pair of planar curves, one can define its generalized area distance, a concept that generalizes the area distance of a single curve. In this paper, we show that the generalized area distance of a pair of planar curves is an improper indefinite affine spheres with singularities, and, reciprocally, every indefini…
Connects robust optimization to conformal prediction for uncertainty sets.
We study the level sets of the distance function from a boundary point of a convex set in Euclidean space. We provide a lower bound for the range of connectivity of the level sets, in terms of the critical points of the distance function in the sense of Grove-Shiohama-Gromov-Cheeger.
Person re-identification (Re-ID) aims at matching images of the same person across disjoint camera views, which is a challenging problem in multimedia analysis, multimedia editing and content-based media retrieval communities. The major challenge lies in how to preserve similarity of the same person across video footag…
The paper introduces a new Wasserstein distance for approximating posteriors in inverse problems.
We show that if the Hempel distance of a Heegaard splitting is larger than three then the mapping class group of the Heegaard splitting is isomorphic to a subgroup of the mapping class group of the ambient 3-manifold. This implies that given two handlebody sets in the curve complex for a surface that are distance at le…
Many modern data-intensive computational problems either require, or benefit from distance or similarity data that adhere to a metric. The algorithms run faster or have better performance guarantees. Unfortunately, in real applications, the data are messy and values are noisy. The distances between the data points are …
In high dimension, low sample size (HDLSS)settings, the simple average distance classifier based on the Euclidean distance performs poorly if differences between the locations get masked by the scale differences. To rectify this issue, modifications to the average distance classifier was proposed by Chan and Hall (2009…
The main object of study in the paper is the distance from a point to a line in the Riemannian manifold associated with the Heston model. We reduce the problem of computing such a distance to certain minimization problems for functions of one variable over finite intervals. One of the main ideas in this paper is to use…
Lorentzian distances to Cauchy surfaces fail to be locally equi-Lipschitz.
The paper studies convexity of products of squared Euclidean distances.
Metric learning has the aim to improve classification accuracy by learning a distance measure which brings data points from the same class closer together and pushes data points from different classes further apart. Recent research has demonstrated that metric learning approaches can also be applied to trees, such as m…
Distance metric learning is a successful way to enhance the performance of the nearest neighbor classifier. In most cases, however, the distribution of data does not obey a regular form and may change in different parts of the feature space. Regarding that, this paper proposes a novel local distance metric learning met…
Unlike the case of surfaces of topologically finite type, there are several different Teichmüller spaces that are associated to a surface of topological infinite type. These Teichmüller spaces first depend (set-theoretically) on whether we work in the hyperbolic category or in the conformal category. They also depend, …
The notion of task similarity is at the core of various machine learning paradigms, such as domain adaptation and meta-learning. Current methods to quantify it are often heuristic, make strong assumptions on the label sets across the tasks, and many are architecture-dependent, relying on task-specific optimal parameter…
Study on Frechet distance properties for paths and graphs.