Related papers: Derivation-Graph-Based Characterizations of Decida…
In a recent paper published in the Journal of Causal Inference, Philip Dawid has described a graphical causal model based on decision diagrams. This article describes how single-world intervention graphs (SWIGs) relate to these diagrams. In…
Integrated Gradients (IG) is a common explainability technique to address the black-box problem of neural networks. Integrated gradients assumes continuous data. Graphs are discrete structures making IG ill-suited to graphs. In this work,…
Limits of graphs were initiated recently in the two extreme contexts of dense and bounded degree graphs. This led to elegant limiting structures called graphons and graphings. These approach have been unified and generalized by authors in a…
Bayesian networks faithfully represent the symmetric conditional independences existing between the components of a random vector. Staged trees are an extension of Bayesian networks for categorical random vectors whose graph represents…
Modern machine learning has achieved impressive prediction performance, but often sacrifices interpretability, a critical consideration in high-stakes domains such as medicine. In such settings, practitioners often use highly interpretable…
We give a characterization of the sets of graphs that are both definable in Counting Monadic Second Order Logic (CMSO) and context-free, i.e., least solutions of Hyperedge-Replacement (HR) grammars introduced by Courcelle and Engelfriet. We…
The enhanced power graph, $\mathcal{E}(G)$, of a group $G$ has vertex set $G$ and two elements are adjacent if they generate a cyclic subgroup. In the case of finite groups, we identify some striking and unexpected properties of these…
Dependency networks (Heckerman et al., 2000) are potential probabilistic graphical models for systems comprising a large number of variables. Like Bayesian networks, the structure of a dependency network is represented by a directed graph,…
Graph representation learning is a fundamental problem for modeling relational data and benefits a number of downstream applications. Traditional Bayesian-based graph models and recent deep learning based GNN either suffer from…
Conventionally used exponential random graphs cannot directly model weighted networks as the underlying probability space consists of simple graphs only. Since many substantively important networks are weighted, this limitation is…
Given a graph $G$ consider a procedure of building a dominating set $D$ in $G$ by adding vertices to $D$ one at a time in such a way that whenever vertex $x$ is added to $D$ there exists a vertex $y\in N_G[x]$ that becomes dominated only…
Existential rules are a prominent formalism to enrich a database with knowledge from the domain of interest, but make even basic reasoning tasks on the resulting knowledge base undecidable. To circumvent this, several classes of rules…
It is known that families of graphs with a semialgebraic edge relation of bounded complexity satisfy much stronger regularity properties than arbitrary graphs, and that they can be decomposed into very homogeneous semialgebraic pieces up to…
A set $D$ of vertices in a graph $G=(V,E)$ is a degree restricted dominating set for $G$ if each vertex $v_i$ in $D$ is dominating atmost $g(d_i)$ vertices of $V-D$, where $g$ is a function restricting the degree value $d_i$ with respect to…
In this paper, we introduce ergodic sets, subsets of nodes of the networks that are dynamically disjoint from the rest of the network (i.e. that can never be reached or left following to the network dynamics). We connect their definition to…
This paper introduces a set of formally defined and transparent problems for reinforcement learning algorithms with the following characteristics: (1) variable degrees of observability (non-Markov observations), (2) distal and sparse…
A subset $D$ of $V$ is \emph{dominating} in $G$ if every vertex of $V-D$ has at least one neighbour in $D;$ let $\gamma(G)$ be the minimum cardinality among all dominating sets in $G.$ A graph $G$ is $\gamma$-$q$-{\it critical} if the…
Graph-based models form a fundamental aspect of data representation in Data Sciences and play a key role in modeling complex networked systems. In particular, recently there is an ever-increasing interest in modeling dynamic complex…
Classes of graphs with bounded expansion are a generalization of both proper minor closed classes and degree bounded classes. Such classes are based on a new invariant, the greatest reduced average density (grad) of G with rank r,…
The graphoid axioms for conditional independence, originally described by Dawid [1979], are fundamental to probabilistic reasoning [Pearl, 19881. Such axioms provide a mechanism for manipulating conditional independence assertions without…