It's necessary to make difference between the original "GMDH
algorithms" and the "algorithms of GMDH type" .
The first ones - work using the minimum of an external criterion
(see figure) and therefore realise objective choice of optimal model.
This original GMDH technique is based on inductive approach: optimal
models are fonded by sorting-out of possible variants and evaluated
by external criterion.
It is calculated on separate part of data sample which is not used
for model creation. That model is better which leads to minimal
value of criterion. To make objective choice, selection is done
without thresholds or coefficients in criterion. We recommend to
calculate criteria two times: first to find the best models at each
layer of selection for structure identification and second time
to find the optimal model. Selection procedure is stopped when minimal
criterion value is reached.
Second is GMDH type algorithms - work on characteristic, expressed
by words: "more complex is the model - more accurate it is".
For it necessary to put definite threshold or to point out coefficients
of weight for the members of the internal criterion formula, to
find optimal model out in a some subjective way. But real problems
usually are presented by short or noised data samples. Unfortunately,
in almost all GMDH type software (ModelQuest, NeuroShell) and research
works in USA and Japan this deductive approach is used, which is
not effective for such kind of data.
Fig.1. External accuracy criterion minima values plotted against
of model structure S for different noise variance .
LCM - locus of criterion minima line;
The inductive approach does not eliminate the experts
or take them away from the computer, but rather assigns them a special
position. Experts indicate the selection criterion of a very general
form and interpret the chosen models. They can influence the result
of modeling by formulating new criteria. Computer becomes an objective
referee for scientific controversies, if criteria ensemble is coordinated
between experts, which take part in discussion.
--- - model choice by criterion minimum;
-··- - model choice by "left corner rule".
The human element often involves errors and undesired decisions.
Objective choice of optimal model by minimum of external criterion
characteristic in actual GMDH algorithms often contradicts with
the opinion of investigator. Objective algorithms gives possibility
to realize real artificial intelligence.