Related papers: On the Complexity of Nondeterministically Testable…
We point out necessary and sufficient conditions of uniform consistency of nonparametric sets of alternatives for widespread nonparametric tests. Nonparametric sets of alternatives can be defined both in terms of distribution function and…
This paper illustrates the richness of the concept of regular sets of time bounds and demonstrates its application to problems of computational complexity. There is a universe of bounds whose regular subsets allow to represent several time…
Parallelism is often required for performance. In these situations an excess of non-determinism is harmful as it means the program can have several different behaviours or even different results. Even in domains such as high-performance…
Almost forty years ago, Connes, Feldman and Weiss proved that for measurable equivalence relations the notions of amenability and hyperfiniteness coincide. In this paper we define the uniform version of amenability and hyperfiniteness for…
We propose a new adequacy test and a graphical evaluation tool for nonlinear dynamic models. The proposed techniques can be applied in any setup where parametric conditional distribution of the data is specified, in particular to models…
Accurate and automated detection of anomalous samples in a natural image dataset can be accomplished with a probabilistic model for end-to-end modeling of images. Such images have heterogeneous complexity, however, and a probabilistic model…
Two-sample hypothesis testing for network comparison presents many significant challenges, including: leveraging repeated network observations and known node registration, but without requiring them to operate; relaxing strong structural…
This paper develops analityc methods for investigating uniform hypergraphs. Its starting point is the spectral theory of 2-graphs, in particular, the largest and the smallest eigenvalues of 2-graphs. On the one hand, this simple setup is…
A massive dataset often consists of a growing number of (potentially) heterogeneous sub-populations. This paper is concerned about testing various forms of heterogeneity arising from massive data. In a general nonparametric framework, a set…
We consider the problem of recovering a subhypergraph based on an observed adjacency tensor corresponding to a uniform hypergraph. The uniform hypergraph is assumed to contain a subset of vertices called as subhypergraph. The edges…
The notion of nowhere denseness is one of the central concepts of the recently developed theory of sparse graphs. We study the properties of nowhere dense graph classes by investigating appropriate limit objects defined using the…
The considered problem is uniform convergence of sequences of hypergeometric series. We give necessary and sufficient conditions for uniformly dominated convergence of infinite sums of proper bivariate hypergeometric terms. These conditions…
The purpose of this article is to show that even the most elementary problems in asymptotic extremal graph theory can be highly non-trivial. We study linear inequalities between graph homomorphism densities. In the language of quantum…
The parametrization theorem is derived in a flat nD pseudo-complex affine space. The pseudo-complex hyperbolic space accomodates n-number of uncompactified time-like extra dimensions with sugnature (s,r), where s and r are the numbers of…
A sensitivity analysis in an observational study tests whether the qualitative conclusions of an analysis would change if we were to allow for the possibility of limited bias due to confounding. The design sensitivity of a hypothesis test…
The task of finding an extension to a given partial drawing of a graph while adhering to constraints on the representation has been extensively studied in the literature, with well-known results providing efficient algorithms for…
In a series of recent works, we have generalised the consistency results in the stochastic block model literature to the case of uniform and non-uniform hypergraphs. The present paper continues the same line of study, where we focus on…
In a recent work (ECCC, TR18-171, 2018), we introduced models of testing graph properties in which, in addition to answers to the usual graph-queries, the tester obtains {\em random vertices drawn according to an arbitrary distribution…
Determining whether two graphs are structurally identical is a fundamental problem with applications spanning mathematics, computer science, chemistry, and network science. Despite decades of study, graph isomorphism remains a challenging…
Current approaches to neural network verification focus on specifications that target small regions around known input data points, such as local robustness. Thus, using these approaches, we can not obtain guarantees for inputs that are not…