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We consider a binary response which is potentially affected by a set of continuous variables. Of special interest is the causal effect on the response due to an intervention on a specific variable. The latter can be meaningfully determined…
We develop a mathematical and interpretative foundation for the enterprise of decision-theoretic statistical causality (DT), which is a straightforward way of representing and addressing causal questions. DT reframes causal inference as…
We define dual-critical graphs as graphs having an acyclic orientation, where the indegrees are odd except for the unique source. We have very limited knowledge about the complexity of dual-criticality testing. By the definition the problem…
P-time event graphs are discrete event systems able to model cyclic production systems where tasks need to be performed within given time windows. Consistency is the property of admitting an infinite execution of such tasks that does not…
Reasoning about the effect of interventions and counterfactuals is a fundamental task found throughout the data sciences. A collection of principles, algorithms, and tools has been developed for performing such tasks in the last decades…
Viral information like rumors or fake news is spread over a communication network like a virus infection in a unidirectional manner: entity $i$ conveys information to a neighbor $j$, resulting in two equally informed (infected) parties.…
Learning the causal structure that underlies data is a crucial step towards robust real-world decision making. The majority of existing work in causal inference focuses on determining a single directed acyclic graph (DAG) or a Markov…
Graph-structured data ubiquitously appears in science and engineering. Graph neural networks (GNNs) are designed to exploit the relational inductive bias exhibited in graphs; they have been shown to outperform other forms of neural networks…
A structural equation model (SEM) is an effective framework to reason over causal relationships represented via a directed acyclic graph (DAG). Recent advances have enabled effective maximum-likelihood point estimation of DAGs from…
Some classical graph problems such as finding minimal spanning tree, shortest path or maximal flow can be done efficiently. We describe slight variations of such problems which are shown to be NP-complete. Our proofs use straightforward…
For a graph (undirected, directed, or mixed), a cycle-factor is a collection of vertex-disjoint cycles covering the entire vertex set. Cycle-factors subject to parity constraints arise naturally in the study of structural graph theory and…
Recursive linear structural equation models and the associated directed acyclic graphs (DAGs) play an important role in causal discovery. The classic identifiability result for this class of models states that when only observational data…
This paper concerns the assessment of direct causal effects from a combination of: (i) non-experimental data, and (ii) qualitative domain knowledge. Domain knowledge is encoded in the form of a directed acyclic graph (DAG), in which all…
We examine ordered graphs, defined as graphs with linearly ordered vertices, from the perspective of homomorphisms (and colorings) and their complexities. We demonstrate the corresponding computational and parameterized complexities, along…
A digraph that represents reasonably a scheduling problem should be a directed acyclic graph. Here down we shall deal with special kind of graded $DAGs$ named $KoDAGs$. For their definition and first primary properties see $ [1]$, where…
We consider the problem of Bayesian causal discovery for the standard model of linear structural equations with equivariant Gaussian noise. A uniform prior is placed on the space of directed acyclic graphs (DAGs) over a fixed set of…
A causal model is an abstract representation of a physical system as a directed acyclic graph (DAG), where the statistical dependencies are encoded using a graphical criterion called `d-separation'. Recent work by Wood & Spekkens shows that…
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 study a graph partition problem where we are given a directed acyclic graph (DAG) whose vertices and arcs can be respectively regarded as tasks and dependencies among tasks. The objective of the problem is to minimize the total energy…
The partition of graphs into "nice" subgraphs is a central algorithmic problem with strong ties to matching theory. We study the partitioning of undirected graphs into same-size stars, a problem known to be NP-complete even for the case of…