arXiv research

Sharp error bounds derived for bidirectional GANs without restrictive assumptions.

Extends Optimal Transport to multiple agents, aiming for equitable and optimal distribution.

This paper proves a generalization bound for complex-valued neural networks scaling with spectral complexity.

The paper develops generalization bounds for deep compound Gaussian neural networks.

Improved neural network reconstruction from sparse measurements with theoretical guarantees.

We consider the problem of online nonparametric regression with arbitrary deterministic sequences. Using ideas from the chaining technique, we design an algorithm that achieves a Dudley-type regret bound similar to the one obtained in a non-constructive fashion by Rakhlin and Sridharan (2014). Our regret bound is expre…

We study the problem of reconstructing an unknown matrix M of rank r and dimension d using O(rd poly log d) Pauli measurements. This has applications in quantum state tomography, and is a non-commutative analogue of a well-known problem in compressed sensing: recovering a sparse vector from a few of its Fourier coeffic…

Study shows depth improves generalization in deep learning models.

Bounding the generalization error of learning algorithms has a long history, which yet falls short in explaining various generalization successes including those of deep learning. Two important difficulties are (i) exploiting the dependencies between the hypotheses, (ii) exploiting the dependence between the algorithm'…

MSRL learns a representation maximizing mutual info with response variables.

New framework controls generalization for heavy-tailed data in RLHF and SGLD.

Unified framework for robust clustering under various dissimilarity measures.

The paper analyzes how machine learning models perform under covariate shift, especially when the feature shift in $x$ is larger than that in $y$.

The paper tightens bounds on distances between Reeb graphs.

Extends Teichmüller distance concept to non-distance maps.

The Wasserstein distance and its variations, e.g., the sliced-Wasserstein (SW) distance, have recently drawn attention from the machine learning community. The SW distance, specifically, was shown to have similar properties to the Wasserstein distance, while being much simpler to compute, and is therefore used in vario…

We define a novel class of distances between statistical multivariate distributions by modeling an optimal transport problem on their marginals with respect to a ground distance defined on their conditionals. These new distances are metrics whenever the ground distance between the marginals is a metric, generalize both…

In the present paper we calculate the Gromov-Hausdorff distance between an arbitrary simplex (a metric space all whose non-zero distances are the same) and a finite metric space whose non-zero distances take two distinct values (so-called $2$-distance spaces). As a corollary, a complete solution to generalized Borsuk p…

New toolkit for directed distances improves flexibility of OT problems.

There have lately been several suggestions for parametrized distances on a graph that generalize the shortest path distance and the commute time or resistance distance. The need for developing such distances has risen from the observation that the above-mentioned common distances in many situations fail to take into ac…

A new robust metric compares distributions more accurately than existing methods.

A new metric HCP distance for comparing distributions.

Formula for interleaving distance of rectangle persistence modules.

Graph distance metric learning serves as the foundation for many graph learning problems, e.g., graph clustering, graph classification and graph matching. Existing research works on graph distance metric (or graph kernels) learning fail to maintain the basic properties of such metrics, e.g., non-negative, identity of i…

New distances measure mixtures of Gaussians, useful in machine learning.

New distances for comparing multivariate normal distributions.

The paper introduces a new Wasserstein distance for approximating posteriors in inverse problems.

Finite mapping class groups for Heegaard splittings with distance ≥ 3, but not for distance 2.

Distance plays a fundamental role in measuring similarity between objects. Various visualization techniques and learning tasks in statistics and machine learning such as shape matching, classification, dimension reduction and clustering often rely on some distance or similarity measure. It is of tremendous importance t…

The paper studies horofunction compactifications of symmetric cones under Finsler distances.

A new supervised tree-Wasserstein distance improves document classification.

Identifying statistical dependence between the features and the label is a fundamental problem in supervised learning. This paper presents a framework for estimating dependence between numerical features and a categorical label using generalized Gini distance, an energy distance in reproducing kernel Hilbert spaces (RK…

CADM proposes a cluster-specific distance metric for categorical data clustering.

Estimates manifold distances using graph Laplacian, proving consistency.

Transforms distance-based outlier scores into interpretable probabilistic estimates.

New distances defined on Legendrian spaces without positive loops.

A distance-squared function is one of the most significant functions in the application of singularity theory to differential geometry. Moreover, distance-squared mappings are naturally extended mappings of distance-squared functions, wherein each component is a distance-squared function. In this paper, compositions of…

A method for fast estimation of Wasserstein distances using sliced Wasserstein distances.

The study bounds distances in simplicial complexes and defines new invariants for 3-manifolds and handlebody-knots.

The literature postulates that the dynamic time warping (dtw) distance can cope with temporal variations but stores and processes time series in a form as if the dtw-distance cannot cope with such variations. To address this inconsistency, we first show that the dtw-distance is not warping-invariant. The lack of warpin…

The distance function $\varrho(p,q)$ (or $d(p,q)$) of a distance space (general metric space) is not differentiable in general. We investigate such distance spaces over $\mathbb R^n$, whose distance functions are differentiable like in case of Finsler spaces. These spaces have several good properties, yet they are no F…

Using Blanchfield pairings, we show that two Alexander polynomials cannot be realized by a pair of matrices with Gordian distance one if a corresponding quadratic equation does not have an integer solution. We also give an example of how our results help in calculating the Gordian distances, algebraic Gordian distances…

We investigate the use of Minimax distances to extract in a nonparametric way the features that capture the unknown underlying patterns and structures in the data. We develop a general-purpose and computationally efficient framework to employ Minimax distances with many machine learning methods that perform on numerica…

The paper explores selecting the parameter α for Fermat distance to balance geometry and noise.

The paper introduces a statistical distance matrix for better feature representation and clustering.

Learning a distance function or metric on a given data manifold is of great importance in machine learning and pattern recognition. Many of the previous works first embed the manifold to Euclidean space and then learn the distance function. However, such a scheme might not faithfully preserve the distance function if t…

Differentially private data structures for estimating distances between strings.

An alternating distance is a link invariant that measures how far away a link is from alternating. We study several alternating distances and demonstrate that there exist families of links for which the difference between certain alternating distances is arbitrarily large. We also show that two alternating distances, t…