Related papers: Agreement tests on graphs and hypergraphs
Models based on preferential attachment have had much success in reproducing the power law degree distributions which seem ubiquitous in both natural and engineered systems. Here, rather than assuming preferential attachment, we give an…
We prove local and global inverse theorems for general $3$-wise correlations over pairwise-connected distributions. Let $\mu$ be a distribution over $\Sigma \times \Gamma \times \Phi$ such that the supports of $\mu_{xy}$, $\mu_{xz}$, and…
We consider a generalization of group testing where the potentially contaminated sets are the members of a given hypergraph ${\cal F}=(V,E)$. This generalization finds application in contexts where contaminations can be conditioned by some…
Proximity gaps and correlated agreement have become central tools in the analysis of interactive oracle proofs of proximity (IOPPs) and code-based SNARKs. Informally, a proximity-gap statement says that for a structured set of words -- such…
The hypercontractive inequality on the discrete cube plays a crucial role in many fundamental results in the Analysis of Boolean functions, such as the KKL theorem, Friedgut's junta theorem and the invariance principle. In these results the…
Local certification is a topic originating from distributed computing, where a prover tries to convince the vertices of a graph $G$ that $G$ satisfies some property $\mathcal{P}$. To convince the vertices, the prover gives a small piece of…
We consider random graphs with a given degree sequence and show, under weak technical conditions, asymptotic normality of the number of components isomorphic to a given tree, first for the random multigraph given by the configuration model…
Given a graph $G$, we define ${\bf bcg}(G)$ as the minimum $k$ for which $G$ can be contracted to the uniformly triangulated grid $\Gamma_{k}$. A graph class ${\cal G}$ has the SQG${\bf C}$ property if every graph $G\in{\cal G}$ has…
We uncover a close connection between the second moment of the degree of a typical vertex in a random subgraph and the pairwise negative correlation (p-NC) property. On one hand, we exploit this connection to prove the p-NC property for…
MapReduce (and its open source implementation Hadoop) has become the de facto platform for processing large data sets. MapReduce offers a streamlined computational framework by interleaving sequential and parallel computation while hiding…
The distributed hypothesis testing problem with full side-information is studied. The trade-off (reliability function) between the two types of error exponents under limited rate is studied in the following way. First, the problem is…
We study the power of the bounded-width consistency algorithm in the context of the fixed-template Promise Constraint Satisfaction Problem (PCSP). Our main technical finding is that the template of every PCSP that is solvable in bounded…
For an input graph $G$, an additive spanner is a sparse subgraph $H$ whose shortest paths match those of $G$ up to small additive error. We prove two new lower bounds in the area of additive spanners: 1) We construct $n$-node graphs $G$ for…
Combining test statistics from independent trials or experiments is a popular method of meta-analysis. However, there is very limited theoretical understanding of the power of the combined test, especially in high-dimensional models…
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…
Integration at a point is a new kind of integration derived from integration over an interval in infinitesimal and infinity domains which are spaces larger than the reals. Consider a continuous monotonic divergent function that is…
Multiple raters are often needed to be used interchangeably in practice for measurement or evaluation. Assessing agreement among these multiple raters via agreement indices are necessary before their participation. While the intuitively…
The apparent disconnection between the microscopic and the macroscopic is a major issue in the understanding of complex systems. To this extend, we study the convergence of repeatedly applying local rules on a network, and touch on the…
Tolerance graphs model interval relations in such a way that intervals can tolerate a certain degree of overlap without being in conflict. This subclass of perfect graphs has been extensively studied, due to both its interesting structure…
Aimed at explaining the surprisingly good generalization behavior of overparameterized deep networks, recent works have developed a variety of generalization bounds for deep learning, all based on the fundamental learning-theoretic…