Everything about Graphoid
Graphoid math statements
A graphoid is a set of statements of the form, "X is irrelevant to Y given that we know Z" where X, Y and Z are sets of variables. The notion of "irrelevance" and "given that we know" may obtain different interpretations, including probabilistic, relational and correlational, depending on the application. These interpretations share common properties that can be captured by paths in graphs. The theory of graphoids characterizes these properties in a finite set of axioms that are common to informational irrelevance and its graphical representations. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: GraphoidA 5-minute orientation
- Pick up a classic book: Introduction aux algèbres de Post et à leurs applicationsThe most-reprinted book on the subject
- Read the landmark paper: GRAPHOID PROPERTIES OF QUALITATIVE POSSIBILISTIC INDEPENDENCE RELATIONSCited 29 times
- Go sideways: Ancestral graphA closely related topic
- Go sideways: Graphical modelA closely related topic
📖 Definitions
Noun A matroid that has two collections of nonempty subsets called circuits and cocircuits such that the intersection of any circuit and cocircuit is not only the identity matroid, no circuit properly contains another circuit, no cocircuit properly contains another cocircuit, and for any painting of M that colors exactly one element green and the rest either red or blue there exists either a circuit containing the green element and no red elements or a cocircuit containing the green element and no blue elements.
Noun A set of statements of the form, "X is irrelevant to Y given that we know Z" where X, Y and Z are sets of variables, which can be manipulated by a set of axioms concerning informational irrelevance and its graphical representation.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
GRAPHOID PROPERTIES OF QUALITATIVE POSSIBILISTIC INDEPENDENCE RELATIONS
Graphoid properties of epistemic irrelevance and independence
Concise representations and construction algorithms for semi-graphoid independency models
Exploiting independencies to compute semigraphoid and graphoid structures
Graphoid properties of concepts of independence for sets of probabilities
Two generalizations of the semi-graphoid rule of probabilistic independence and more
THE GRAPHOID SURFACE
📚 Books worth reading
- 📕Introduction aux algèbres de Post et à leurs applicationsM. Serfati · 1973
- 📕Discrete mathematics and allied topics · 2002
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Ancestral graph In statistics and Markov modeling, an ancestral graph is a type of mixed graph used to provide a graphical representation for the result of marginalizing…
- Graphical model A graphical model or probabilistic graphical model (PGM) or structured probabilistic model is a probabilistic model for which a graph expresses the conditional…
- Polytree In mathematics, and more specifically in graph theory, a polytree (also called directed tree, oriented tree or singly connected network) is a directed…
- Markov blanket In statistics and machine learning, a Markov blanket of a random variable is a set of variables that renders the variable conditionally independent of…
- Do-calculus Do-calculus is a set of mathematical rules devised by Judea Pearl in 1995 to determine whether causal effects can be identified from observational data…
- Bayesian network A Bayesian network (also known as a Bayes network, Bayes net, belief network, or decision network) is a probabilistic graphical model that represents a…
- Causal model In metaphysics and statistics, a causal model (also called a structural causal model) is a conceptual model that represents the causal mechanisms of a…
- Directed acyclic graph In mathematics, particularly graph theory, and computer science, a directed acyclic graph (DAG) is a directed graph with no directed cycles. That is, it…