Related papers: Markov Equivalences for Subclasses of Loopless Mix…
We consider the problem of symmetrising a neural network along a group homomorphism: given a homomorphism $\varphi : H \to G$, we would like a procedure that converts $H$-equivariant neural networks to $G$-equivariant ones. We formulate…
The variability of structure in a finite Markov equivalence class of causally sufficient models represented by directed acyclic graphs has been fully characterized. Without causal sufficiency, an infinite semi-Markov equivalence class of…
We propose a Markov chain simulation method to generate simple connected random graphs with a specified degree sequence and level of clustering. The networks generated by our algorithm are random in all other respects and can thus serve as…
We consider the structure learning problem for graphical models that we call loosely connected Markov random fields, in which the number of short paths between any pair of nodes is small, and present a new conditional independence test…
We propose a novel benchmarking methodology for graph neural networks (GNNs) based on the graph alignment problem, a combinatorial optimization task that generalizes graph isomorphism by aligning two unlabeled graphs to maximize overlapping…
One of the major challenges in applications related to social networks, computational biology, collaboration networks etc., is to efficiently search for similar patterns in their underlying graphs. These graphs are typically noisy and…
Based on earlier work by Carlen-Maas and the second- and third-named author, we introduce the notion of intertwining curvature lower bounds for graphs and quantum Markov semigroups. This curvature notion is stronger than both Bakry-\'Emery…
Graphical Markov models determined by acyclic digraphs (ADGs), also called directed acyclic graphs (DAGs), are widely studied in statistics, computer science (as Bayesian networks), operations research (as influence diagrams), and many…
Classical graph matching aims to find a node correspondence between two unlabeled graphs of known topologies. This problem has a wide range of applications, from matching identities in social networks to identifying similar biological…
Semi-supervised learning on graphs is a widely applicable problem in network science and machine learning. Two standard algorithms -- label propagation and graph neural networks -- both operate by repeatedly passing information along edges,…
In this paper, we introduce a novel class of graphical models for representing time lag specific causal relationships and independencies of multivariate time series with unobserved confounders. We completely characterize these graphs and…
We investigate topological, combinatorial, statistical, and enumeration properties of finite graphs with high Kolmogorov complexity (almost all graphs) using the novel incompressibility method. Example results are: (i) the mean and variance…
We consider the graph class Grounded-L corresponding to graphs that admit an intersection representation by L-shaped curves, where additionally the topmost points of each curve are assumed to belong to a common horizontal line. We prove…
The embedding problem of Markov matrices in Markov semigroups is a classic problem that regained a lot of impetus and activities through recent needs in phylogeny and population genetics. Here, we give an account for dimensions $d\leqslant…
Markov models lie at the interface between statistical independence in a probability distribution and graph separation properties. We review model selection and estimation in directed and undirected Markov models with Gaussian…
A labelled Markov decision process is a labelled Markov chain with nondeterminism, i.e., together with a strategy a labelled MDP induces a labelled Markov chain. The model is related to interval Markov chains. Motivated by applications of…
The main result of the paper is motivated by the following two, apparently unrelated graph optimization problems: (A) as an extension of Edmonds' disjoint branchings theorem, characterize digraphs comprising $k$ disjoint branchings $B_i$…
We give a recursion formula to generate all equivalence classes of biconnected graphs with coefficients given by the inverses of the orders of their groups of automorphisms. We give a linear map to produce a connected graph with say, u,…
Many applications in network analysis require algorithms to sample uniformly at random from the set of all graphs with a prescribed degree sequence. We present a Markov chain based approach which converges to the uniform distribution of all…
One main challenge in imbalanced graph classification is to learn expressive representations of the graphs in under-represented (minority) classes. Existing generic imbalanced learning methods, such as oversampling and imbalanced learning…