On the regularization of forgetting recursive least square

In this paper, the regularization of employing the forgetting recursive least square (FRLS) training technique on feedforward neural networks is studied. We derive our result from the corresponding equations for the expected prediction error and the expected training error. By comparing these error equations with other equations obtained previously from the weight decay method, we have found that the FRLS technique has an effect which is identical to that of using the simple weight decay method. This new finding suggests that the FRLS technique is another on-line approach for the realization of the weight decay effect. Besides, we have shown that, under certain conditions, both the model complexity and the expected prediction error of the model being trained by the FRLS technique are better than the one trained by the standard RLS method.