Related papers: Characteristic Imsets for Cyclic Linear Causal Mod…
The regularity of an edge ideal of a finite simple graph $G$ is at least the induced matching number of $G$ and is at most the minimum matching number of $G$. If $G$ possesses a dominating inuduced matching, i.e., an induced matching which…
Describing families of ideals that are minimally generated by at least one, or by all, of their reduced Gr\"obner bases is a central topic in commutative algebra. In this paper, we address this problem in the context of toric ideals of…
In this paper we study linear non-Gaussian graphical models from the perspective of algebraic statistics. These are acyclic causal models in which each variable is a linear combination of its direct causes and independent noise. The…
Causal identification is at the core of the causal inference literature, where complete algorithms have been proposed to identify causal queries of interest. The validity of these algorithms hinges on the restrictive assumption of having…
The incidence matrix of a graph is totally unimodular if and only if the graph is bipartite, i.e., it contains no odd cycles. We extend the characterization of total unimodularity to hypergraphs whose hyperedges of size at least four are…
Graphs are expressive abstractions representing more effectively relationships in data and enabling data science tasks. They are also a widely adopted paradigm in causal inference focusing on causal directed acyclic graphs. Causal DAGs…
Causal modelling frameworks link observable correlations to causal explanations, which is a crucial aspect of science. These models represent causal relationships through directed graphs, with vertices and edges denoting systems and…
The correlations that can be observed between a set of variables depend on the causal structure underpinning them. Causal structures can be modeled using directed acyclic graphs, where nodes represent variables and edges denote functional…
Let $D$ be a weighted oriented graph with the underlying graph $G$ and $I(D), I(G) $ be the edge ideals corresponding to $D$ and $G$ respectively. We show that the regularity of edge ideal of a certain class of weighted oriented graph…
A fundamental challenge of scientific research is inferring causal relations based on observed data. One commonly used approach involves utilizing structural causal models that postulate noisy functional relations among interacting…
The feed-forward relationship naturally observed in time-dependent processes and in a diverse number of real systems -such as some food-webs and electronic and neural wiring- can be described in terms of so-called directed acyclic graphs…
We present the first comprehensive analysis of temporal settings for directed temporal graphs, fully resolving their hierarchy with respect to support, reachability, and induced-reachability equivalence. These notions, introduced by…
The topological classification of the inner mappings on the fully invariant regular components of the wandering set with a special attracting boundary up to the topological conjugacy is defined in terms of distinguishing graph. Two inner…
Causal inference with observational data critically relies on untestable and extra-statistical assumptions that have (sometimes) testable implications. Well-known sets of assumptions that are sufficient to justify the causal interpretation…
In many application areas---lending, education, and online recommenders, for example---fairness and equity concerns emerge when a machine learning system interacts with a dynamically changing environment to produce both immediate and…
The directions of an infinite graph $G$ are a tangle-like description of its ends: they are choice functions that choose compatibly for all finite vertex sets $X\subseteq V(G)$ a component of $G-X$. Although every direction is induced by a…
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…
A concentration graph associated with a random vector is an undirected graph where each vertex corresponds to one random variable in the vector. The absence of an edge between any pair of vertices (or variables) is equivalent to full…
Deciding whether a collection of unrooted trees is compatible is a fundamental problem in phylogenetics. Two different graph-theoretic characterizations of tree compatibility have recently been proposed. In one of these, tree compatibility…
In this work, we study the equivalence of various robustness properties of toric ideals of weighted oriented graphs. For any weighted oriented graph $D$, if its toric ideal $I_D$ is generalized robust (or weakly robust), then we show that…