Related papers: On model misspecification and KL separation for Ga…
In this work, we study the maximum matching problem from the perspective of sensitivity. The sensitivity of an algorithm $A$ on a graph $G$ is defined as the maximum Wasserstein distance between the output distributions of $A$ on $G$ and on…
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…
The maximum likelihood threshold of a graph is the smallest number of data points that guarantees that maximum likelihood estimates exist almost surely in the Gaussian graphical model associated to the graph. We show that this graph…
In this paper we introduce a new notion of convergence of sparse graphs which we call Large Deviations or LD-convergence and which is based on the theory of large deviations. The notion is introduced by "decorating" the nodes of the graph…
The crossing number of a graph $G$ is the minimum number of edge crossings over all drawings of $G$ in the plane. A graph $G$ is $k$-crossing-critical if its crossing number is at least $k$, but if we remove any edge of $G$, its crossing…
In this paper, we consider two fundamental cut approximation problems on large graphs. We prove new lower bounds for both problems that are optimal up to logarithmic factors. The first problem is to approximate cuts in balanced directed…
We study the gradient flow for a relaxed approximation to the Kullback-Leibler (KL) divergence between a moving source and a fixed target distribution. This approximation, termed the KALE (KL approximate lower-bound estimator), solves a…
The families of $f$-divergences (e.g. the Kullback-Leibler divergence) and Integral Probability Metrics (e.g. total variation distance or maximum mean discrepancies) are widely used to quantify the similarity between probability…
Structured prediction tasks in machine learning involve the simultaneous prediction of multiple labels. This is typically done by maximizing a score function on the space of labels, which decomposes as a sum of pairwise elements, each…
Let $G$ be a large (simple, unlabeled) dense graph on $n$ vertices. Suppose that we only know, or can estimate, the empirical distribution of the number of subgraphs $F$ that each vertex in $G$ participates in, for some fixed small graph…
The positive discrepancy of a graph $G$ of edge density $p=e(G)/\binom{v(G)}{2}$ is defined as $$\mbox{disc}^{+}(G)=\max_{U\subset V(G)}e(G[U])-p\binom{|U|}{2}.$$ In 1993, Alon proved (using the equivalent terminology of minimum bisections)…
An equivalence graph is a disjoint union of cliques, and the equivalence number $\mathit{eq}(G)$ of a graph $G$ is the minimum number of equivalence subgraphs needed to cover the edges of $G$. We consider the equivalence number of a line…
Denoising diffusions are a powerful method to generate approximate samples from high-dimensional data distributions. Recent results provide polynomial bounds on their convergence rate, assuming $L^2$-accurate scores. Until now, the tightest…
Score-matching generative models have proven successful at sampling from complex high-dimensional data distributions. In many applications, this distribution is believed to concentrate on a much lower $d$-dimensional manifold embedded into…
In this paper, we study the task of detecting the edge dependency between two weighted random graphs. We formulate this task as a simple hypothesis testing problem, where under the null hypothesis, the two observed graphs are statistically…
Motivated by the Beck-Fiala conjecture, we study the discrepancy problem in two related models of random hypergraphs on $n$ vertices and $m$ edges. In the first (edge-independent) model, a random hypergraph $H_1$ is constructed by fixing a…
Estimating Kullback-Leibler divergence from identical and independently distributed samples is an important problem in various domains. One simple and effective estimator is based on the k nearest neighbor distances between these samples.…
Graphical model selection is a seemingly impossible task when many pairs of variables are never jointly observed; this requires inference of conditional dependencies with no observations of corresponding marginal dependencies. This…
Following a general program of studying limits of discrete structures, and motivated by the theory of limit objects of converge sequences of dense simple graphs, we study the limit of graph sequences such that every edge is labeled by an…
If K is an odd-dimensional flag closed manifold, flag generalized homology sphere or a more general flag weak pseudomanifold with sufficiently many vertices, then the maximal number of edges in K is achieved by the balanced join of cycles.…