Related papers: Valid Two-Sample Graph Testing via Optimal Transpo…
We study statistical inference for the optimal transport (OT) map (also known as the Brenier map) from a known absolutely continuous reference distribution onto an unknown finitely discrete target distribution. We derive limit distributions…
Brain connectivity analysis is now at the foreground of neuroscience research. A connectivity network is characterized by a graph, where nodes represent neural elements such as neurons and brain regions, and links represent statistical…
Two-sample hypothesis testing-determining whether two sets of data are drawn from the same distribution-is a fundamental problem in statistics and machine learning with broad scientific applications. In the context of nonparametric testing,…
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…
In this paper, we study the problem of testing the equality of two multivariate distributions. One class of tests used for this purpose utilizes geometric graphs constructed using inter-point distances. So far, the asymptotic theory of…
Two-sample tests for multivariate data and non-Euclidean data are widely used in many fields. Parametric tests are mostly restrained to certain types of data that meets the assumptions of the parametric models. In this paper, we study a…
Network (graph) data analysis is a popular research topic in statistics and machine learning. In application, one is frequently confronted with graph two-sample hypothesis testing where the goal is to test the difference between two graph…
We consider the problem of testing whether a graph's degree distribution belongs to a particular family, such as poisson or scale-free, given that we only observe a sampled subgraph. In particular, we focus on induced subgraph sampling, a…
Graph kernel is a powerful tool measuring the similarity between graphs. Most of the existing graph kernels focused on node labels or attributes and ignored graph hierarchical structure information. In order to effectively utilize graph…
The Erd\"os Renyi graph is a popular choice to model network data as it is parsimoniously parametrized, straightforward to interprete and easy to estimate. However, it has limited suitability in practice, since it often fails to capture…
Random geometric graphs are widely used in modeling geometry and dependence structure in networks. In a random geometric graph, nodes are independently generated from some probability distribution $F$ over a metric space, and edges link…
Hypothesis testing for graphs has been an important tool in applied research fields for more than two decades, and still remains a challenging problem as one often needs to draw inference from few replicates of large graphs. Recent studies…
We study the problem of detecting the edge correlation between two random graphs with $n$ unlabeled nodes. This is formalized as a hypothesis testing problem, where under the null hypothesis, the two graphs are independently generated;…
We consider a two-sample hypothesis testing problem, where the distributions are defined on the space of undirected graphs, and one has access to only one observation from each model. A motivating example for this problem is comparing the…
When deploying a trained machine learning model in the real world, it is inevitable to receive inputs from out-of-distribution (OOD) sources. For instance, in continual learning settings, it is common to encounter OOD samples due to the…
Given a pair of graphs with the same number of vertices, the inexact graph matching problem consists in finding a correspondence between the vertices of these graphs that minimizes the total number of induced edge disagreements. We study…
Testing the equality in distributions of multiple samples is a common task in many fields. However, this problem for high-dimensional or non-Euclidean data has not been well explored. In this paper, we propose new nonparametric tests based…
Current graph neural network (GNN) architectures naively average or sum node embeddings into an aggregated graph representation -- potentially losing structural or semantic information. We here introduce OT-GNN, a model that computes graph…
Optimal transport (OT) distances between probability distributions are parameterized by the ground metric they use between observations. Their relevance for real-life applications strongly hinges on whether that ground metric parameter is…
We introduce the Graph TT (GTT) and Graph OSPA (GOSPA) metrics based on optimal assignment, which allow us to compare not only the edge structures but also general vertex and edge attributes of graphs of possibly different sizes. We argue…