Group Method of Data Handling (GMDH) - Method description

Like SVMs, GMDH is a wide class of algorithms and GMDH Shell software implements only part of them. Here I give a brief overview of the general case of GMDH:
GMDH is a machine learning method that gradually complicate mathematical models in order to detect the optimal complexity. It uses components of a certain nonlinear multiparametric equation with linear parameters as building blocks. It can employ multilayered structures similar to neural networks or other ways of model complication like genetic algorithms or full combinatorial search. GMDH estimates parameters of every generated model and performs model validation using a separate part of data that was not involved in estimation of parameters. As a result of model validation GMDH algorithm outputs only those models that show better predictive ability. Such details as the type of validation and the class of building blocks are important but depend on user preferences and a particular problem case.
To summarize scientific studies on GMDH I'd say it is a method that produce predictive models or multilayered networks of linear, polynomial, logistic, Gaussian, harmonic and other nonlinear functions selecting only those models that show accurate predictions during validation stage.
It is the state-of-the-art so to say, but if you look into older books you'll find a bit different description. At early stages of GMDH development (started in 1968 by A.G. Ivakhnenko) it was a procedure that selects a number of pairs of polynomial components, fits validation data and brings selected components to the next layer where new input pairs are considered, and so on. This process is finite because validation data doesn't accept complex models. Overcomplicated models are unstable and loose their predictive abilities, so the process stops when a new layer can't show a better validation result.