wGMDH :: Model Selection

Model selection

The total number of possible GMDH models is increasing exponentially by increasing the number of layers. The model selection can be formulated in the following way. Given a validation data set

$D_{v} = \left \{ (\mathbf{x_{vi}},y_{vi}) \right \}_{i=1}^{N}$

of data vectors $\mathbf{x_{vi}}=\left ( x_{vi1}, x_{vi2}, \cdots , x_{viK} \right ), x_{vi}\in \Re^{K}$ and the corresponding output values $y_{vi}\in \Re$ , evaluate the derived model $p(x)$ by using the performance measure $E=E(p(x))$ and align it accordingly. A maximum of $P_{\lambda}$ best qualified models are selected and retained at each layer. In this way the models on the next layer combine only the best models from the previous layers.

Algorithms