Semidependence

Semidependence is a term used in several disciplines to denote a relationship between entities that lies between independence and dependence. There is no universally accepted formal definition, and the term is often used descriptively rather than as a precisely defined relation.

In probability and statistics, semidependence describes a relationship that is not fully independent, but where the dependence is restricted to certain contexts, components, or regimes. For example, in a two-regime model two variables may be independent within each regime but become dependent when regimes are mixed, so the unconditional joint distribution shows dependence while conditional distributions within regimes are independent. Another framing is that a joint distribution is a mixture of product distributions, implying weak or context-limited dependence.

In information theory and related fields, semidependence can refer to a partial overlap of information: the mutual information between variables is positive but not maximal, indicating partial rather than complete sharing of information.

In systems and computer science, semidependence describes partial coupling between components—changes in one component may affect another, but not under all operating conditions. The degree of coupling can vary with configuration or context.

Properties and limitations: semidependence is not a standard relation with a single axiomatization. It is often sensitive to the modeling framework and can be asymmetric or non-transitive. Because the term is used variably, researchers typically specify the exact meaning within their particular theory or model rather than appealing to a universal definition.

See also: independence, conditional independence, dependence, partial correlation, mixture models, regime-switching models.