Improving model accuracy using optimal linear combinations of trained neural networks

Neural network (NN) based modeling often requires trying multiple networks with different architectures and training parameters in order to achieve an acceptable model accuracy. Typically, only one of the trained networks is selected as "best" and the rest are discarded. The authors propose using optimal linear combinations (OLC's) of the corresponding outputs on a set of NN's as an alternative to using a single network. Modeling accuracy is measured by mean squared error (MSE) with respect to the distribution of random inputs. Optimality is defined by minimizing the MSE, with the resultant combination referred to as MSE-OLC. The authors formulate the MSE-OLC problem for trained NN's and derive two closed-form expressions for the optimal combination-weights. An example that illustrates significant improvement in model accuracy as a result of using MSE-OLC's of the trained networks is included.