Related papers: On the structure of essential graphs for AMP chain…
The correspondence between weighted undirected graphs and reversible Markov chains via vertex random walks is simple and well known. Leveraging this correspondence and ideas from the theory of dynamical systems, we study the structural…
While visual comparison of directed acyclic graphs (DAGs) is commonly encountered in various disciplines (e.g., finance, biology), knowledge about humans' perception of graph similarity is currently quite limited. By graph similarity…
Graphs are quickly emerging as a leading abstraction for the representation of data. One important application domain originates from an emerging discipline called "connectomics". Connectomics studies the brain as a graph; vertices…
In this paper, we tackle structure learning of Directed Acyclic Graphs (DAGs), with the idea of exploiting available prior knowledge of the domain at hand to guide the search of the best structure. In particular, we assume to know the…
We consider the problem of uniformly generating a spanning tree, of a connected undirected graph. This process is useful to compute statistics, namely for phylogenetic trees. We describe a Markov chain for producing these trees. For cycle…
Two directed acyclic graphs (DAGs) are called Markov equivalent if and only if they have the same underlying undirected graph (i.e. skeleton) and the same set of immoralities. Using observational data, a DAG model can only be determined up…
Graph data widely exists in real life, with large amounts of data and complex structures. It is necessary to map graph data to low-dimensional embedding. Graph classification, a critical graph task, mainly relies on identifying the…
We describe a simple algorithm based on a Markov chain process to generate simply connected acyclic directed graphs over a fixed set of vertices. This algorithm is an extension of a previous one, designed to generate acyclic digraphs, non…
Classifying Antimicrobial Peptides (AMPs) from the vast collection of peptides derived from metagenomic sequencing offers a promising avenue for combating antibiotic resistance. However, most existing AMP classification methods rely…
Assume that $G$ is a finite group. For every $a, b \in\mathbb N,$ we define a graph $\Gamma_{a,b}(G)$ whose vertices correspond to the elements of $G^a\cup G^b$ and in which two tuples $(x_1,\dots,x_a)$ and $(y_1,\dots,y_b)$ are adjacent if…
Counting and uniform sampling of directed acyclic graphs (DAGs) from a Markov equivalence class are fundamental tasks in graphical causal analysis. In this paper, we show that these tasks can be performed in polynomial time, solving a…
The invariance properties of interventional distributions relative to the observational distribution, and how these properties allow us to refine Markov equivalence classes (MECs) of DAGs, is central to causal DAG discovery algorithms that…
In many numerical schemes, the computational complexity scales non-linearly with the problem size. Solving a linear system of equations using direct methods or most iterative methods is a typical example. Algebraic multi-grid (AMG) methods…
In this paper we define critical graphs as minimal graphs that support a given set of rates for the index coding problem, and study them for both the one-shot and asymptotic setups. For the case of equal rates, we find the critical graph…
Directed acyclic graph (DAG) models have become widely studied and applied in statistics and machine learning -- indeed, their simplicity facilitates efficient procedures for learning and inference. Unfortunately, these models are not…
Directed graphs naturally model systems with asymmetric, ordered relationships, essential to applications in biology, transportation, social networks, and visual understanding. Generating such graphs enables tasks such as simulation, data…
Continual graph learning (CGL) studies the problem of learning from an infinite stream of graph data, consolidating historical knowledge, and generalizing it to the future task. At once, only current graph data are available. Although some…
We demonstrate that graph-based models are fully capable of representing higher-order interactions, and have a long history of being used for precisely this purpose. This stands in contrast to a common claim in the recent literature on…
Graph neural network (GNN) models are increasingly being used for the classification of electroencephalography (EEG) data. However, GNN-based diagnosis of neurological disorders, such as Alzheimer's disease (AD), remains a relatively…
Deep generative models (DGMs) have recently demonstrated remarkable success in capturing complex probability distributions over graphs. Although their excellent performance is attributed to powerful and scalable deep neural networks, it is,…