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Download e-book for kindle: Adaptive Learning of Polynomial Networks: Genetic by Hitoshi Iba, Nikolay Y. Nikolaev

By Hitoshi Iba, Nikolay Y. Nikolaev

This ebook offers theoretical and useful wisdom for develop­ ment of algorithms that infer linear and nonlinear versions. It bargains a technique for inductive studying of polynomial neural community mod­els from information. The layout of such instruments contributes to raised statistical info modelling while addressing projects from a variety of parts like method id, chaotic time-series prediction, monetary forecasting and information mining. the most declare is that the version identity approach comprises numerous both vital steps: discovering the version constitution, estimating the version weight parameters, and tuning those weights with recognize to the followed assumptions concerning the underlying facts distrib­ ution. while the training approach is equipped in keeping with those steps, played jointly one by one or individually, one may possibly anticipate to find types that generalize good (that is, are expecting well). The publication off'ers statisticians a shift in concentration from the traditional worry types towards hugely nonlinear types that may be came upon via modern studying techniques. experts in statistical studying will examine substitute probabilistic seek algorithms that observe the version structure, and neural community education concepts that establish exact polynomial weights. they are going to be happy to determine that the found types should be simply interpreted, and those types imagine statistical prognosis via common statistical potential. masking the 3 fields of: evolutionary computation, neural net­works and Bayesian inference, orients the ebook to a wide viewers of researchers and practitioners.

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Extra info for Adaptive Learning of Polynomial Networks: Genetic Programming, Backpropagation and Bayesian Methods (Genetic and Evolutionary Computation)

Example text

The adaptive PNN algorithms are able to learn the weights of highly nonlinear models. A PNN consists of nodes, or neurons, linked by connections associated with numeric weights. Each node has a set of incoming connections from other nodes and one (or more) outgoing connections to other nodes. All nonterminal nodes, including the fringe nodes connected to the inputs, are called hidden nodes. The input vector is propagated forward through the network. During the forward pass it is weighted by the connection strengths and filtered by the activation functions in the nodes, producing an output signal at the root.

Several backpropagation training techniques for polynomial networks are developed in Chapters 6 and 7 in the spirit of the feed-forward neural networks theory. Gradient descent training rules for higher-order networks with polynomial activation functions are derived. This makes it possible to elaborate first-order and second-order backpropagation training algorithms. In addition to this, advanced techniques proposed for neural networks, like second-order pruning, are apphed to polynomial networks.

The MaxOrder can be found by increasing the order of a randomly generated PNN, and measuring its error on the concrete sample: a^ = Yln=i iVn ~~ ^(^n))^/(A^ — M^ — 1), where W is the number of the model weights. The denominator makes the error increase if the model becomes larger than the most probable degree. Linear Implementation of P N N Trees. The design of tree- structured polynomial networks involves three issues: 1) how to represent the tree nodes; 2) how to represent the topological connections between the nodes; and 3) how to perform tree traversal.

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