By Gustavo Deco, Dragan Obradovic

ISBN-10: 1461240166

ISBN-13: 9781461240167

ISBN-10: 1461284694

ISBN-13: 9781461284697

Neural networks supply a strong new expertise to version and keep watch over nonlinear and complicated platforms. during this publication, the authors current a close formula of neural networks from the information-theoretic point of view. They express how this attitude presents new insights into the layout conception of neural networks. specifically they convey how those tools will be utilized to the themes of supervised and unsupervised studying together with characteristic extraction, linear and non-linear self sustaining part research, and Boltzmann machines. Readers are assumed to have a easy realizing of neural networks, yet the entire proper suggestions from info idea are rigorously brought and defined. for this reason, readers from a number of assorted clinical disciplines, significantly cognitive scientists, engineers, physicists, statisticians, and machine scientists, will locate this to be a truly helpful creation to this topic.

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45) if the matrix W n has full row rank. 16]). 10] which leads to a learning paradigm for P n which is independent of en in order O(TJ~) . 46) ",,,,T andAn = xx . 49) = W~~ Wn + (~WTn) Wn . 5]). This kind of algorithm is called "stochastic approximation". e. the iterative algorithm converges to the projection PM. 54), d -LSE dt = -trace ((dP)T(dP)) = - ~ ~ (dP)2 ~0 dt dt L L dt ij i j Equality in the above expression is obtained only for dP / dt in P -space is obtained. 61) = 0 0 . 64) also holds at the stationary point, and therefore P and Qx have the same eigenvectors.

The neural architecture is called stochastic if it is composed of stochastic units. 1. (a) Deterministic neuron. (b) Stochastic neuron. A second classification of architectures is defined by the type of connections between the neurons. Principally two types of architecture are defined: feedforward and recurrent. e. there is no backcoupling between neurons. 2 (a). The neurons are arranged in layers. e. all connections are allowed in this case. 2 (b). Recurrent architectures are usually used for the learning of dynamical phenomena since the backcoupling can contain delays.

10]. e. decorrelation, does not necessarily yield "statistical independence". Statistical independence implies that the probability distribution is factorizable. Decorrelation (diagonalization of the covariance matrix) and statistical independency are equivalent only in the Gaussian case (see Chapter 4 for more details about this fact). The next section presents an alternative derivation of PC A as the optimal linear compression method. 2 peA and Optimal Reconstruction This section focuses on reconstruction properties of PCA.

### An Information-Theoretic Approach to Neural Computing by Gustavo Deco, Dragan Obradovic

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