Related papers: Explicit Bounds for Nondeterministically Testable …
In this paper, we study the maximum number of edges in an $N$-vertex $r$-uniform hypergraph with girth $g$ where $g \in \{5,6 \}$. Writing $\textrm{ex}_r ( N, \mathcal{C}_{<g} )$ for this maximum, it is shown that $\textrm{ex}_r ( N ,…
This paper studies the validity of nonparametric tests used in the regression discontinuity design. The null hypothesis of interest is that the average treatment effect at the threshold in the so-called sharp design equals a pre-specified…
We study the problems of bounding the number weak and strong independent sets in $r$-uniform, $d$-regular, $n$-vertex linear hypergraphs with no cross-edges. In the case of weak independent sets, we provide an upper bound that is tight up…
High dimensional hypothesis test deals with models in which the number of parameters is significantly larger than the sample size. Existing literature develops a variety of individual tests. Some of them are sensitive to the dense and small…
We present a new notion of limits of weighted directed graphs of growing size based on convergence of their random quotients. These limits are specified in terms of random exchangeable measures on the unit square. We call our limits…
This paper develops a threshold regression model where an unknown relationship between two variables nonparametrically determines the threshold. We allow the observations to be cross-sectionally dependent so that the model can be applied to…
In an earlier paper the authors proved that limits of convergent graph sequences can be described by various structures, including certain 2-variable real functions called graphons, random graph models satisfying certain consistency…
We consider the Grenander estimator that is the maximum likelihood estimator for non-increasing densities. We prove uniform central limit theorems for certain subclasses of bounded variation functions and for H\"older balls of smoothness…
We consider graph property testing in $p$-degenerate graphs under the random neighbor oracle model (Czumaj and Sohler, FOCS 2019). In this framework, a tester explores a graph by sampling uniform neighbors of vertices, and a property is…
We establish new upper and lower bounds on the number of queries required to test convexity of functions over various discrete domains. 1. We provide a simplified version of the non-adaptive convexity tester on the line. We re-prove the…
In the {\sc Test Cover} problem we are given a hypergraph $H=(V, \mathcal{E})$ with $|V|=n, |\mathcal{E}|=m$, and we assume that $\mathcal{E}$ is a test cover, i.e. for every pair of vertices $x_i, x_j$, there exists an edge $e \in…
We introduce a new approach to constructing networks with realistic features. Our method, in spite of its conceptual simplicity (it has only two parameters) is capable of generating a wide variety of network types with prescribed…
We present new families of goodness-of-fit tests of uniformity on a full-dimensional set $W\subset\R^d$ based on statistics related to edge lengths of random geometric graphs. Asymptotic normality of these statistics is proven under the…
The \emph{$r$-neighbourhood complexity} of a graph $G$ is the function counting, for a given integer $k$, the largest possible number, over all vertex-subsets $A$ of size $k$, of subsets of $A$ realized as the intersection between the…
Covering arrays are generalizations of orthogonal arrays that have been widely studied and are used in software testing. The probabilistic method has been employed to derive upper bounds on the sizes of minimum covering arrays and give…
This paper considers the problem of testing whether there exists a solution satisfying certain non-negativity constraints to a linear system of equations. Importantly and in contrast to some prior work, we allow all parameters in the system…
Elek and Lippner (2010) showed that the convergence of a sequence of bounded-degree graphs implies the existence of a limit for the proportion of vertices covered by a maximum matching. We provide a characterization of the limiting…
We consider the problem of constructing nonparametric undirected graphical models for high-dimensional functional data. Most existing statistical methods in this context assume either a Gaussian distribution on the vertices or linear…
This paper settles the sample complexity of single-parameter revenue maximization by showing matching upper and lower bounds, up to a poly-logarithmic factor, for all families of value distributions that have been considered in the…
Given a hypergraph $H$, the Planar Support problem asks whether there is a planar graph $G$ on the same vertex set as $H$ such that each hyperedge induces a connected subgraph of $G$. Planar Support is motivated by applications in graph…