Given:

a function of the argument and set of model parameters
a discrete finite training dataset: representing the available knowledge about the system the model is trying to describe

then matching procedure assumes searching for the specific set of model parameters to minimize the goal function:

G({\bf p}) = \sum_{k=1}^N \, \Psi \left( y^*(x_k) - y_k \right) \rightarrow \textrm{min} \ \Longleftrightarrow \ {\bf p} = {\bf p}_{\rm bestfit}

where is the discrepancy distance function.

The most popular choices are and .

See also