wGMDH :: Iteration

Iteration

First the pool of nodes gets extended by putting the i-1-th layer in the pool.

$S_{i}=S_{i-1}\cup L_{i-1}$

The i-th layer gets formed as follows:

$L_{i}\left \{ N_{i}^{j}(N_{k}^{m},N_{l}^{n}):k\neq l,\forall (N_{k}^{m},N_{l}^{n})\in S_{i} \right \}$

i.e. every node from the i-1-th layer gets combined with every node from the pool as inputs, to produce a new node from the i-th layer; coefficients of the new node are obtained by least-squares fitting to the training set.

The next step is to limit $L_{i}$ to a smaller number of nodes to narrow the search space. It is done by introducing an appropriate error criterion, which gets evaluated on the validation set for each node $N_{j}^{i}\in L_{i}$ , and only the best n nodes according to this criterion remain in $L_{i}$ ; others get discarded, thus effectively limiting the search space to a beam of width n.

Algorithms