Semi-Unsupervised Weighted Maximum-Likelihood Estimation of Joint Densities for the Co-Training of Adaptive Activation Functions

The paper presents an explicit maximum-likelihood algorithm for the estimation of the probabilistic-weighting density functions that are associated with individual adaptive activation functions in neural networks. A partially unsupervised technique is devised which takes into account the joint distribution of input features and target outputs. Combined with the training algorithm introduced in the companion paper [2], the solution proposed herein realizes a well-defined, specific instance of the novel learning machine. The extension of the overall training method to more-than-one hidden layer architectures is pointed out, as well. A preliminary experimental demonstration is given, outlining how the algorithm works. © 2012 Springer-Verlag.