Adaptive Learning of Polynomial Networks delivers theoretical and practical knowledge for the development of algorithms that infer linear and non-linear multivariate models, providing a methodology for inductive learning of polynomial neural network models (PNN) from data. The empirical investigations detailed here demonstrate that PNN models evolved by genetic programming and improved by backpropagation are successful when solving real-world tasks. The text emphasizes the model identification process and presents a shift in focus from the standard linear models toward highly nonlinear models that can be inferred by contemporary learning approaches, alternative probabilistic search algorithms that discover the model architecture and neural network training techniques to find accurate polynomial weights, a means of discovering polynomial models for time-series prediction, and an exploration of the areas of artificial intelligence, machine learning, evolutionary computation and neural networks, covering definitions of the basic inductive tasks, presenting basic approaches for addressing these tasks, introducing the fundamentals of genetic programming, reviewing the error derivatives for backpropagation training, and explaining the basics of Bayesian learning. This volume is an essential reference for researchers and practitioners interested in the fields of evolutionary computation, artificial neural networks and Bayesian inference, and will also appeal to postgraduate and advanced undergraduate students of genetic programming. Readers will strengthen their skills in creating both efficient model representations and learning operators that efficiently sample the search space, navigating the search process through the design of objective fitness functions, and examining the search performance of the evolutionary system.