Related papers: Testing Graphs against an Unknown Distribution
We consider properties of edge-colored vertex-ordered graphs, i.e., graphs with a totally ordered vertex set and a finite set of possible edge colors. We show that any hereditary property of such graphs is strongly testable, i.e., testable…
Network (graph) data analysis is a popular research topic in statistics and machine learning. In application, one is frequently confronted with graph two-sample hypothesis testing where the goal is to test the difference between two graph…
We provide a combinatorial characterization of all testable properties of $k$-uniform hypergraphs ($k$-graphs for short). Here, a $k$-graph property $P$ is testable if there is a randomized algorithm which makes a bounded number of edge…
The locality of a graph problem is the smallest distance $T$ such that each node can choose its own part of the solution based on its radius-$T$ neighborhood. In many settings, a graph problem can be solved efficiently with a distributed or…
Hamiltonian cycles in graphs were first studied in the 1850s. Since then, an impressive amount of research has been dedicated to identifying classes of graphs that allow Hamiltonian cycles, and to related questions. The corresponding…
A random walk on a directed graph gives a Markov chain on the vertices of the graph. An important question that arises often in the context of Markov chain is whether the uniform distribution on the vertices of the graph is a stationary…
A graph property P is strongly testable if for every fixed \epsilon>0 there is a one-sided \epsilon-tester for P whose query complexity is bounded by a function of \epsilon. In classifying the strongly testable graph properties, the first…
We study the sample complexity of nondeterministically testable graph parameters and improve existing bounds on it by several orders of magnitude. The technique used would be also of independent interest. We also discuss the special case of…
Statistical graph models aim at modeling graphs as random realization among a set of possible graphs. One issue is to evaluate whether or not a graph is likely to have been generated by one particular model. In this paper we introduce the…
This extended abstract introduces a class of graph learning applicable to cases where the underlying graph has polytopic uncertainty, i.e., the graph is not exactly known, but its parameters or properties vary within a known range. By…
We study a generalization of the classical hidden clique problem to graphs with real-valued edge weights. Formally, we define a hypothesis testing problem. Under the null hypothesis, edges of a complete graph on $n$ vertices are associated…
The degrees are a classical and relevant way to study the topology of a network. They can be used to assess the goodness-of-fit for a given random graph model. In this paper we introduce goodness-of-fit tests for two classes of models.…
We extend the bounded degree graph model for property testing introduced by Goldreich and Ron (Algorithmica, 2002) to hypergraphs. In this framework, we analyse the query complexity of three fundamental hypergraph properties: colorability,…
Two-sample tests utilizing a similarity graph on observations are useful for high-dimensional and non-Euclidean data due to their flexibility and good performance under a wide range of alternatives. Existing works mainly focused on sparse…
We discuss a graph-based approach for testing spatial point patterns. This approach falls under the category of data-random graphs, which have been introduced and used for statistical pattern recognition in recent years. Our goal is to test…
There has been substantial interest in estimating the value of a graph parameter, i.e., of a real-valued function defined on the set of finite graphs, by querying a randomly sampled substructure whose size is independent of the size of the…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
Graphical models provide a framework for exploration of multivariate dependence patterns. The connection between graph and statistical model is made by identifying the vertices of the graph with the observed variables and translating the…
In reliable decision-making systems based on machine learning, models have to be robust to distributional shifts or provide the uncertainty of their predictions. In node-level problems of graph learning, distributional shifts can be…
Graph-based tests are a class of non-parametric two-sample tests useful for analyzing high-dimensional data. The test statistics are constructed from similarity graphs (such as K-minimum spanning tree), and consequently, their performance…