Directed Acyclic Graph (DAG)

A Directed Acyclic Graph (DAG) is a mathematical structure used to represent relationships among a set of variables in a way that is both directional and non-circular. It consists of nodes, which represent variables or events, and directed edges, which represent relationships or influences from one node to another. The direction of an edge indicates an assumed ordering or dependence, meaning that one variable is considered to have a direct effect on another. The defining feature of a DAG is acyclicity: it is not possible to start at one node, follow the direction of the edges, and return to the same node.

DAGs are widely used in statistics, machine learning, and causal inference because they provide a clear and compact way to encode assumptions about dependency and information flow. In probabilistic modeling, DAGs underlie Bayesian networks, where the graph structure specifies conditional independence relationships among variables. In causal analysis, DAGs serve as a visual and formal language for articulating hypotheses about cause and effect, helping to distinguish correlation from causation and to reason about confounding, mediation, and intervention. Their clarity and rigor make DAGs a foundational tool for both theoretical analysis and practical modeling.