Learning of nonlinear FIR models under uniform distribution

The PAC learning theory creates a framework to assess the learning properties of a modeling procedure. This paper presents a bound on the size of the training data set required to train a nonlinear FIR model, where the input data are assumed to be generated according to the uniform distribution. The bound is further specified for a family of feedforward neural networks, which utilizes a sigmoid activation function. The learning properties of a neural identification task have been assessed using the aforesaid family of neural networks. Also, using the structural risk minimization algorithm, a learning procedure for the modeling tasks in which the exact number of the hidden neurons is unknown, is introduced.