FIR Volterra kernel neural models and PAC learning

Abstract

The probably approximately correct (PAC) learning theory creates a framework to assess the learning properties of static models for which the data are assumed to be independently and identically distributed (i.i.d.). The present article first extends the idea of PAC learning to cover the learning of modeling tasks with m-dependent sequences of data. The data are assumed to be marginally distributed according to a fixed arbitrary probability.The resulting framework is then applied to evaluate learning of Volterra Kernel FIR models.

Learning of Fir and Arx Neural Networks With Empirical Risk Minimization Algorithm

“…The above results are for the input data that are marginally distributed according to a uniform distribution. The new results in the field ((K. Najarian, 2001a) and (K. Najarian, 2001a)) provide the learning properties of the same families of neural networks assuming an arbitrary distribution. These results are more general and remove the need for the assumption of uniform distribution.…”