Related papers: Weakly reflecting graph properties
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…
Let G be a finite graph with the non-k-order property (essentially, a uniform finite bound on the size of an induced sub-half-graph). A major result of the paper applies model-theoretic arguments to obtain a stronger version of…
We propose a novel algorithm for unsupervised graph representation learning with attributed graphs. It combines three advantages addressing some current limitations of the literature: i) The model is inductive: it can embed new graphs…
This paper introduces a novel framework for graph sparsification that preserves the essential learning attributes of original graphs, improving computational efficiency and reducing complexity in learning algorithms. We refer to these…
Coding schemes with extremely low computational complexity are required for particular applications, such as wireless body area networks, in which case both very high data accuracy and very low power-consumption are required features. In…
The theory of representation learning aims to build methods that provably invert the data generating process with minimal domain knowledge or any source of supervision. Most prior approaches require strong distributional assumptions on the…
We say that a graph $H$ dominates another graph $H'$ if the number of homomorphisms from $H'$ to any graph $G$ is dominated, in an appropriate sense, by the number of homomorphisms from $H$ to $G$. We study the family of dominating graphs,…
Symplectic geometry plays an increasingly important role in mathematics, physics and applications, and naturally gives rise to interesting matrix families and properties. One of these is the notion of symplectic eigenvalues, whose existence…
Hypergraphs are structures that can be decomposed or described; in other words they are recursively countable. Here, we get exact and asymptotic enumeration results on hypergraphs by means of exponential generating functions. The number of…
A \emph{mixed graph} is a graph with directed edges, called arcs, and undirected edges. A $k$-coloring of the vertices is proper if colors from ${1,2,...,k}$ are assigned to each vertex such that $u$ and $v$ have different colors if $uv$ is…
We consider a family of problems that are concerned about making predictions for the majority of unlabeled, graph-structured data samples based on a small proportion of labeled samples. Relational information among the data samples, often…
The concepts of faithfulness and strong-faithfulness are important for statistical learning of graphical models. Graphs are not sufficient for describing the association structure of a discrete distribution. Hypergraphs representing…
Two models are introduced to investigate graph matching in the presence of corrupt nodes. The weak model, inspired by biological networks, allows one or both networks to have a positive fraction of molecular entities interact randomly with…
Entropic causal inference is a recent framework for learning the causal graph between two variables from observational data by finding the information-theoretically simplest structural explanation of the data, i.e., the model with smallest…
In this expository article, we give a self-contained introduction to the wonderfully well-behaved class of pseudocompact algebras, focusing on the foundational classes of semisimple and separable algebras. We give characterizations of such…
Counterfactual examples have emerged as an effective approach to produce simple and understandable post-hoc explanations. In the context of graph classification, previous work has focused on generating counterfactual explanations by…
The theory of sparse structures usually uses tree like structures as building blocks. In the context of sparse/dense dichotomy this role is played by graphs with bounded tree depth. In this paper we survey results related to this concept…
Weakly supervised graph anomaly detection aims to unveil unusual graph instances, e.g., nodes, whose behaviors significantly differ from normal ones, given only a limited number of annotated anomalies and abundant unlabeled samples. A major…
Learning the right graph representation from noisy, multi-source data has garnered significant interest in recent years. A central tenet of this problem is relational learning. Here the objective is to incorporate the partial information…
Graphs are a basic tool for the representation of modern data. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dimensional simplicial complex. We show how topological…