Formal Determination of Context in Contextual Recursive Cascade Correlation Networks

In this note we consider the Contextual Recursive Cascade Correlation model (CRCC), which is able to learn contextual mappings in structured domains. Specifically, we propose a formal characterization of the `context window`, i.e., given a state variable, the `context window` is the set of state variables directly or indirectly contributing to its determination. On the basis of this definition, a formal expression describing the `context windows` for the CRCC is derived. The resulting expression is very compact and describes the context window as a function of the state variables in the model, and some topological properties of the structures in input to the model. Moreover, the expression elucidates how the shape of the context window is modified by the introduction of new state variables, i.e., hidden units. For comparison, a similar expression is also derived for the non-contextual Recursive Cascade Correlation model