相关论文: Establishing Markov Equivalence in Cyclic Directed…
In order to define the process of restrosynthesis of a new organic molecule, it is often necessary to be able to draw inspiration from that of a molecule similar to the target one of which we know such a process. To compute such a…
Markov chains are a convenient means of generating realizations of networks, since they require little more than a procedure for rewiring edges. If a rewiring procedure exists for generating new graphs with specified statistical properties,…
Functional causal models (fCMs) specify functional dependencies between random variables associated to the vertices of a graph. In directed acyclic graphs (DAGs), fCMs are well-understood: a unique probability distribution on the random…
Two directed graphs are called covariance equivalent if they induce the same set of covariance matrices, up to a Lebesgue measure zero set, on the random variables of their associated linear structural equation models. For acyclic graphs,…
We study the problem of experimental design for accurately identifying the causal graph structure of a simple structural causal model (SCM), where the underlying graph may include both cycles and bidirected edges induced by latent…
Random directed acyclic graphs (DAGs) based on imposing an order on Erd\H{o}s-R\'enyi and scale free random graphs are widely used for evaluating causal discovery algorithms. We show that in such DAGs, the set of nodes reachable via open…
In probability theory, equalities are much less than inequalities. In this paper, we find a series of equalities which characterize the symmetry of the forming times of a family of similar cycles for discrete-time and continuous-time Markov…
Given a directed graph, we show how to efficiently find a shortest (directed, simple) cycle on an even number of vertices. As far as we know, no polynomial-time algorithm was previously known for this problem. In fact, finding any even…
In this paper, we employ the decomposition of a directed network as an undirected graph plus its associated node metadata to characterise the cyclic structure found in directed networks by finding a Minimal Cycle Basis of the undirected…
Causal discovery from observational data is a challenging task that can only be solved up to a set of equivalent solutions, called an equivalence class. Such classes, which are often large in size, encode uncertainties about the orientation…
The graph alignment problem, which considers the optimal node correspondence across networks, has recently gained significant attention due to its wide applications. There are graph alignment methods suited for various network types, but we…
The approximate uniform sampling of graph realizations with a given degree sequence is an everyday task in several social science, computer science, engineering etc. projects. One approach is using Markov chains. The best available current…
One of the hallmark achievements of the theory of graphical models and Bayesian model selection is the celebrated greedy equivalence search (GES) algorithm due to Chickering and Meek. GES is known to consistently estimate the structure of…
Following the lead of Stanley and Gessel, we consider a morphism which associates to an acyclic directed graph (or a poset) a quasi-symmetric function. The latter is naturally defined as multivariate generating series of non-decreasing…
\Graph similarity computation is an essential task in many real-world graph-related applications such as retrieving the similar drugs given a query chemical compound or finding the user's potential friends from the social network database.…
A directed acyclic graph (DAG) is the most common graphical model for representing causal relationships among a set of variables. When restricted to using only observational data, the structure of the ground truth DAG is identifiable only…
Directed acyclic graphs have been used fruitfully to represent causal strucures (Pearl 1988). However, in the social sciences and elsewhere models are often used which correspond both causally and statistically to directed graphs with…
We further clarify the relation between detailed-balanced and complex-balanced equilibria of reversible chemical reaction networks. Our results hold for arbitrary kinetics and also for boundary equilibria. Detailed balance, complex balance,…
Several types of graphs with different conditional independence interpretations --- also known as Markov properties --- have been proposed and used in graphical models. In this paper we unify these Markov properties by introducing a class…
After a brief review of the key theorems concerning recurrent sequences, we give an explicit computation of the inverse of the Vandermonde matrix. This will then be used to derive sub-exponential decay error terms in the ergodic theorem of…