相关论文: Outlier-Robust Gromov-Wasserstein for Graph Data

The mechanism for gamma ray bursters and the detection of gravitational waves (GWs) are two outstanding problems facing modern physics. Many models of gamma ray bursters predict copious GW emission, so the assumption of an association…

We aim to solve the problem of data-driven collision-distance estimation given 3-dimensional (3D) geometries. Conventional algorithms suffer from low accuracy due to their reliance on limited representations, such as point clouds. In…

Outlier detection has gained increasing interest in recent years, due to newly emerging technologies and the huge amount of high-dimensional data that are now available. Outlier detection can help practitioners to identify unwanted noise…

We provide a general bound on the Wasserstein distance between two arbitrary distributions of sequences of Bernoulli random variables. The bound is in terms of a mixing quantity for the Glauber dynamics of one of the sequences, and a simple…

We address the problem of efficiently computing Wasserstein distances for multiple pairs of distributions drawn from a meta-distribution. To this end, we propose a fast estimation method based on regressing Wasserstein distance on sliced…

We present a novel framework based on optimal transport for the challenging problem of comparing graphs. Specifically, we exploit the probabilistic distribution of smooth graph signals defined with respect to the graph topology. This allows…

We introduce an RG-inspired coarse-graining for extracting the collective features of data. The key to successful coarse-graining lies in finding appropriate pairs of data sets. We coarse-grain the two closest data in a regular real-space…

Optimal transport (OT) and Gromov-Wasserstein (GW) alignment provide interpretable geometric frameworks for comparing, transforming, and aggregating heterogeneous datasets -- tasks ubiquitous in data science and machine learning. Because…

The Weisfeiler-Lehman (WL) test is a classical procedure for graph isomorphism testing. The WL test has also been widely used both for designing graph kernels and for analyzing graph neural networks. In this paper, we propose the…

The objective of unsupervised graph representation learning (GRL) is to learn a low-dimensional space of node embeddings that reflect the structure of a given unlabeled graph. Existing algorithms for this task rely on negative sampling…

Graph neural networks have demonstrated state-of-the-art performance on knowledge graph tasks such as link prediction. However, interpreting GNN predictions remains a challenging open problem. While many GNN explainability methods have been…

Spatial statistics is a growing discipline providing important analytical techniques in a wide range of disciplines in the natural and social sciences. In the R package GWmodel, we introduce techniques from a particular branch of spatial…

A common way of partitioning graphs is through minimum cuts. One drawback of classical minimum cut methods is that they tend to produce small groups, which is why more balanced variants such as normalized and ratio cuts have seen more…

This paper introduces a novel and generic framework to solve the flagship task of supervised labeled graph prediction by leveraging Optimal Transport tools. We formulate the problem as regression with the Fused Gromov-Wasserstein (FGW) loss…

Overlapping gravitational wave (GW) signals are expected in the third-generation (3G) GW detectors, leading to one of the major challenges in GW data analysis. Inference of overlapping GW sources is complicated - it has been reported that…

This paper deals with bilateral-gamma (BG) approximation to functionals of an isonormal Gaussian process. We use Malliavin-Stein method to obtain the error bounds for the smooth Wasserstein distance. As by-products, the error bounds for…

Optimal Transport has sparked vivid interest in recent years, in particular thanks to the Wasserstein distance, which provides a geometrically sensible and intuitive way of comparing probability measures. For computational reasons, the…

In this paper, we leverage the properties of non-Euclidean Geometry to define the Geodesic distance (GD) on the space of statistical manifolds. The Geodesic distance is a real and intuitive similarity measure that is a good alternative to…

Ferromagnetic exponential random graph models (ERGMs) are random graph models under which the presence of certain small structures (such as triangles) is encouraged; they can be constructed by tilting an Erd\H{o}s--R\'enyi model by the…

Generative adversarial nets (GANs) and variational auto-encoders have significantly improved our distribution modeling capabilities, showing promise for dataset augmentation, image-to-image translation and feature learning. However, to…