Related papers: On the Complexity of Nondeterministically Testable…

We investigate the isomorphism problem in the setting of definable sets (equivalent to sets with atoms): given two definable relational structures, are they related by a definable isomorphism? Under mild assumptions on the underlying…

We consider high-dimensional estimation problems where the number of parameters diverges with the sample size. General conditions are established for consistency, uniqueness, and asymptotic normality in both unpenalized and penalized…

We prove a universality theorem for learning with random features. Our result shows that, in terms of training and generalization errors, a random feature model with a nonlinear activation function is asymptotically equivalent to a…

In this manuscript a unified framework for conducting inference on complex aggregated data in high dimensional settings is proposed. The data are assumed to be a collection of multiple non-Gaussian realizations with underlying undirected…

This article presents a theoretical investigation of generalized encoded forms of networks in a uniform multidimensional space. First, we study encoded networks with (finite) arbitrary node dimensions (or aspects), such as time instants or…

We study the problem nonparametric classification with repeated observations. Let $\bX$ be the $d$ dimensional feature vector and let $Y$ denote the label taking values in $\{1,\dots ,M\}$. In contrast to usual setup with large sample size…

Fox, Gromov, Lafforgue, Naor, and Pach proved a regularity lemma for semi-algebraic $k$-uniform hypergraphs of bounded complexity, showing that for each $\epsilon>0$ the vertex set can be equitably partitioned into a bounded number of parts…

Two-sample feature selection is the problem of finding features that describe a difference between two probability distributions, which is a ubiquitous problem in both scientific and engineering studies. However, existing methods have…

We consider the problem of satisfiability of sets of constraints in a given set of finite uniform hypergraphs. While the problem under consideration is similar in nature to the problem of satisfiability of constraints in graphs, the…

This paper studies hypothesis testing and parameter estimation in the context of the divide and conquer algorithm. In a unified likelihood based framework, we propose new test statistics and point estimators obtained by aggregating various…

In this extended abstract, we present a simple approach to convergence on term graphs that allows us to unify term graph rewriting and infinitary term rewriting. This approach is based on a partial order and a metric on term graphs. These…

We propose novel parameter estimation algorithms for a class of dynamical systems with nonlinear parametrization. The class is initially restricted to smooth monotonic functions with respect to a linear functional of the parameters. We show…

We present a concept of uniform encodability of theories and develop tools related to this concept. As an application we obtain general undecidability results which are uniform for large families of structures. In the way, we define…

Our work builds on known results for k-uniform hypergraphs including the existence of limits, a Regularity Lemma and a Removal Lemma. Our main tool here is a theory of measures on ultraproduct spaces which establishes a correspondence…

The study of networks leads to a wide range of high dimensional inference problems. In many practical applications, one needs to draw inference from one or few large sparse networks. The present paper studies hypothesis testing of graphs in…

We present a simple proof for the universality of invariant and equivariant tensorized graph neural networks. Our approach considers a restricted intermediate hypothetical model named Graph Homomorphism Model to reach the universality…

We use the combination of ideas and results from the theory of graph limits and nonlinear evolution equations to provide a rigorous mathematical justification for taking continuum limit for certain nonlocally coupled networks and to extend…

Spectral analysis of networks states that many structural properties of graphs, such as centrality of their nodes, are given in terms of their adjacency matrices. The natural extension of such spectral analysis to higher order networks is…

We prove that any quasirandom uniform hypergraph $H$ can be approximately decomposed into any collection of bounded degree hypergraphs with almost as many edges. In fact, our results also apply to multipartite hypergraphs and even to the…

We introduce a general class of algorithms and supply a number of general results useful for analysing these algorithms when applied to regular graphs of large girth. As a result, we can transfer a number of results proved for random…