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Learning charme models with neural networks
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Under certain Lipschitz-type conditions on the autoregressive and volatility functions of the CHARME model, it is proved that this model is stationary, ergodic and $\tau$-weakly dependent.Abstract:
In this paper, we consider a model called CHARME (Conditional Heteroscedastic Autoregressive Mixture of Experts), a class of generalized mixture of nonlinear nonparametric AR-ARCH time series. Under certain Lipschitz-type conditions on the autoregressive and volatility functions, we prove that this model is stationary, ergodic and $\tau$-weakly dependent. These conditions are much weaker than those presented in the literature that treats this model. Moreover, this result forms the theoretical basis for deriving an asymptotic theory of the underlying (non)parametric estimation, which we present for this model. As an application, from the universal approximation property of neural networks (NN), we develop a learning theory for the NN-based autoregressive functions of the model, where the strong consistency and asymptotic normality of the considered estimator of the NN weights and biases are guaranteed under weak conditions.read more
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Multilayer feedforward networks are universal approximators
TL;DR: It is rigorously established that standard multilayer feedforward networks with as few as one hidden layer using arbitrary squashing functions are capable of approximating any Borel measurable function from one finite dimensional space to another to any desired degree of accuracy, provided sufficiently many hidden units are available.
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Multilayer feedforward networks are universal approximators
HornikK.,StinchcombeM.,WhiteH. +2 more
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Intriguing properties of neural networks
Christian Szegedy,Wojciech Zaremba,Ilya Sutskever,Joan Bruna,Dumitru Erhan,Ian Goodfellow,Rob Fergus,Rob Fergus +7 more
TL;DR: It is found that there is no distinction between individual highlevel units and random linear combinations of high level units, according to various methods of unit analysis, and it is suggested that it is the space, rather than the individual units, that contains of the semantic information in the high layers of neural networks.
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The perceptron: a probabilistic model for information storage and organization in the brain.
TL;DR: This article will be concerned primarily with the second and third questions, which are still subject to a vast amount of speculation, and where the few relevant facts currently supplied by neurophysiology have not yet been integrated into an acceptable theory.
Book
The perception: a probabilistic model for information storage and organization in the brain
TL;DR: The second and third questions are still subject to a vast amount of speculation, and where the few relevant facts currently supplied by neurophysiology have not yet been integrated into an acceptable theory as mentioned in this paper.