國立東華大學應用數學系

學    生    演    講

主講人：吳俊樟

講  題：Neural Networks for modeling and approximation of conditional densities, set-valued mappings and spatial chaotic differential systems

時  間：103 年 05月 02 日 (星期五)  15: 20-16:50

地  點：理工一館 A324 會議室

大   綱

    This proposal presents organizing and learning neural networks for density support approximation, conditional density function approximation, set-valued mapping reconstruction and spatial chaotic differential system emulation. The proposed learning approaches are data driven and the constructed neural networks are well characterized by algebraic parametric functions, which can be efficiently evaluated with economic storages in parallel and distributed processes and needs no reservations of massive training observations. Density support approximation is an equivalent task of one-class classification, which is translated to two-class classification by adaptive LQ(Loftsgaarden-Quesenberry) thresholding and resolved by advanced supervised learning of multiple Mahalanobis-NRBF(normalized radial basis functions) modules. Conditional density approximation is approached by learning a state-regulated multilayer neural network, of which visible input units simultaneously receive a stimulus a continuous regulating state and the sole network response directly quantifies the conditional probability of the stimulus to the clamped regulating state. The goal of learning a state-regulated neural network is to approximate the conditional density of the stimulus upon the given regulating state. The proposed learning approach combines LQ-information based conditional density estimation with powerful generalization of advanced supervised learning of multiple Mahalanobis-NRBF modules. The derived state-regulated multilayer neural network is employed to identify the membership of a stimulus to the image set in response to a given regulated state and the probability of being the image scope of the underlying set-valued mapping. The regulating state can be considered as internal representations of key attributes for memory recalling and association or images of neural mappings for system inverting. The spatial chaotic differential systems, including the Ikeda map and the Lorenz differential system, are reconstructed by learning interactive multi-layer neural networks. Numerical simulations show encouraging results of emulating the Ikeda map by recursive neural networks and the Lorenz differential system by the proposed Runge-Kutta-gradient embedded neural networks.

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