Related papers: Two-Sample Testing with a Graph-Based Total Variat…

Given a random sample of size $n$ from a $p$ dimensional random vector, where both $n$ and $p$ are large, we are interested in testing whether the $p$ components of the random vector are mutually independent. This is the so-called complete…

We study the problem of testing, using only a single sample, between mean field distributions (like Curie-Weiss, Erd\H{o}s-R\'enyi) and structured Gibbs distributions (like Ising model on sparse graphs and Exponential Random Graphs). Our…

We introduce a technique called graph fission which takes in a graph which potentially contains only one observation per node (whose distribution lies in a known class) and produces two (or more) independent graphs with the same node/edge…

Inferring brain connectivity network and quantifying the significance of interactions between brain regions are of paramount importance in neuroscience. Although there have recently emerged some tests for graph inference based on…

A new test statistic based on success runs of weighted deviations is introduced. Its use for observations sampled from independent normal distributions is worked out in detail. It supplements the classic $\chi^{2}$ test which ignores the…

We consider the multiple hypothesis testing (MHT) problem over the joint domain formed by a graph and a measure space. On each sample point of this joint domain, we assign a hypothesis test and a corresponding $p$-value. The goal is to make…

We study a generalization of the classical hidden clique problem to graphs with real-valued edge weights. Formally, we define a hypothesis testing problem. Under the null hypothesis, edges of a complete graph on $n$ vertices are associated…

We study characteristics which might distinguish two-graphs by introducing different numerical measures on the collection of graphs on $n$ vertices. Two conjectures are stated, one using these numerical measures and the other using the deck…

We propose a class of nonparametric two-sample tests with a cost linear in the sample size. Two tests are given, both based on an ensemble of distances between analytic functions representing each of the distributions. The first test uses…

In this paper, we propose a new test for testing the equality of two population covariance matrices in the ultra-high dimensional setting that the dimension is much larger than the sizes of both of the two samples. Our proposed methodology…

Here we propose a new nonparametric framework for two-sample testing, named as the OVL-$q$ ($q = 1, 2, \ldots$). This can be regarded as a natural extension of the Smirnov test, which is equivalent to the OVL-1. We specifically focus on the…

The statistics and machine learning communities have recently seen a growing interest in classification-based approaches to two-sample testing. The outcome of a classification-based two-sample test remains a rejection decision, which is not…

With the proliferation of generative AI and the increasing volume of generative data (also called as synthetic data), assessing the fidelity of generative data has become a critical concern. In this paper, we propose a discriminative…

In this article, we introduce a novel discrepancy called the maximum variance discrepancy for the purpose of measuring the difference between two distributions in Hilbert spaces that cannot be found via the maximum mean discrepancy. We also…

Spectral graph bisections are a popular heuristic aimed at approximating the solution of the NP-complete graph bisection problem. This technique, however, does not always provide a robust tool for graph partitioning. Using a special class…

An isomorphism between two graphs is a bijection between their vertices that preserves the edges. We consider the problem of determining whether two finite undirected weighted graphs are isomorphic, and finding an isomorphism relating them…

The simulation of the physical movement of multi-body systems at an atomistic level, with forces calculated from a quantum mechanical description of the electrons, motivates a graph partitioning problem studied in this article. Several…

The problem of simultaneously testing the marginal distributions of sequentially monitored, independent data streams is considered. The decisions for the various testing problems can be made at different times, using data from all streams,…

Several approaches to testing the hypothesis that two histograms are drawn from the same distribution are investigated. We note that single-sample continuous distribution tests may be adapted to this two-sample grouped data situation. The…

So-called linear rank statistics provide a means for distribution-free (even in finite samples), yet highly flexible, two-sample testing in the setting of univariate random variables. Their flexibility derives from a choice of weights that…