Related papers: Testing Graphs against an Unknown Distribution
Uncertainty principles such as Heisenberg's provide limits on the time-frequency concentration of a signal, and constitute an important theoretical tool for designing and evaluating linear signal transforms. Generalizations of such…
The goal of local certification is to locally convince the vertices of a graph $G$ that $G$ satisfies a given property. A prover assigns short certificates to the vertices of the graph, then the vertices are allowed to check their…
High-dimensional feature selection is a central problem in a variety of application domains such as machine learning, image analysis, and genomics. In this paper, we propose graph-based tests as a useful basis for feature selection. We…
We perform a massive evaluation of neural networks with architectures corresponding to random graphs of various types. We investigate various structural and numerical properties of the graphs in relation to neural network test accuracy. We…
Large graphs are sometimes studied through their degree sequences (power law or regular graphs). We study graphs that are uniformly chosen with a given degree sequence. Under mild conditions, it is shown that sequences of such graphs have…
Two-sample tests for multivariate data and non-Euclidean data are widely used in many fields. Parametric tests are mostly restrained to certain types of data that meets the assumptions of the parametric models. In this paper, we study a…
The ability to detect change-points in a dynamic network or a time series of graphs is an increasingly important task in many applications of the emerging discipline of graph signal processing. This paper formulates change-point detection…
Graph generative model evaluation necessitates understanding differences between graphs on the distributional level. This entails being able to harness salient attributes of graphs in an efficient manner. Curvature constitutes one such…
Graph neural networks (GNNs) have achieved remarkable performance on graph-structured data. However, GNNs may inherit prejudice from the training data and make discriminatory predictions based on sensitive attributes, such as gender and…
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…
Property testers are fast, randomized "election polling"-type algorithms that determine if an input (e.g., graph or hypergraph) has a certain property or is $\varepsilon$-far from the property. In the dense graph model of property testing,…
Irregularly sampling a spatially stationary random field does not yield a graph stationary signal in general. Based on this observation, we build a definition of graph stationarity based on intrinsic stationarity, a less restrictive…
Traditionally, graph algorithms get a single graph as input, and then they should decide if this graph satisfies a certain property $\Phi$. What happens if this question is modified in a way that we get a possibly infinite family of graphs…
Graphs may be used to represent many different problem domains -- a concrete example is that of detecting communities in social networks, which are represented as graphs. With big data and more sophisticated applications becoming widespread…
We present the first whiteness test for graphs, i.e., a whiteness test for multivariate time series associated with the nodes of a dynamic graph. The statistical test aims at finding serial dependencies among close-in-time observations, as…
The adjacency matrix is the most fundamental and intuitive object in graph analysis that is useful not only mathematically but also for visualizing the structures of graphs. Because the appearance of an adjacency matrix is critically…
In this paper, matching pairs of random graphs under the community structure model is considered. The problem emerges naturally in various applications such as privacy, image processing and DNA sequencing. A pair of randomly generated…
We consider the detection and localization of change points in the distribution of an offline sequence of observations. Based on a nonparametric framework that uses a similarity graph among observations, we propose new test statistics when…
In order to apply canonical labelling of graphs and isomorphism checking in interactive theorem provers, these checking algorithms must either be mechanically verified or their results must be verifiable by independent checkers. We analyze…
Frei et al. [6] showed that the problem to decide whether a graph is stable with respect to some graph parameter under adding or removing either edges or vertices is $\Theta_2^{\text{P}}$-complete. They studied the common graph parameters…