Crossparameter

Crossparameter is a term used in statistical modeling, machine learning, and related engineering disciplines to describe a parameter or parameterization that ties together multiple components of a model. The exact meaning of crossparameter varies by context, and the term is not universally standardized.

In statistics and econometrics, crossparameterization often refers to reparameterizing a model to impose cross-equation constraints or to link parameter vectors across related models. This can improve identifiability, interpretability, or shrinkage by introducing shared structure between components rather than estimating them independently.

In machine learning, the concept may describe approaches that share or tie parameters across different branches of a network or across tasks in multi-task learning. A crossparameter can be a single parameter that governs behavior in multiple sub-models, enforcing consistency and potentially reducing overfitting. It is also used to describe parameterizations that capture interactions between factors, introducing cross terms to model joint effects rather than treating effects in isolation.

In system identification and physics, crossparameterization appears as coupling terms that connect parameters governing different physical quantities. Such cross terms are used to model cross-effects or dynamic relationships that emerge only when multiple components interact.

Etymology and usage: The term reflects a general idea of coupling or sharing parameters across parts of a model, but its precise meaning depends on the discipline and the specific modeling approach. See also: parameter sharing, reparameterization, coupling constraints, interaction terms, cross-term parameterization.