Supervised RBF learning for conditional density estimation and multi-valued function approximation

Supervised RBF learning for conditional density estimation and multi-valued function approximation

碩士 === 國立東華大學 === 應用數學系 === 97 === This work applies supervised learning of RBF (radial basis function) neural networks for data driven density estimation (DE), conditional density estimation (CDE) and multi-valued function approximation. An RBF neural network is organized to approximate the probabi...

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Main Authors: Ya-Wun Tsai, 蔡雅雯
Other Authors: Jiann-Ming Wu
Format: Others
Language:en_US
Published: 2009
Online Access:http://ndltd.ncl.edu.tw/handle/47429415351269813028
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spelling ndltd-TW-097NDHU55070022015-10-13T14:52:53Z http://ndltd.ncl.edu.tw/handle/47429415351269813028 Supervised RBF learning for conditional density estimation and multi-valued function approximation 以ＲＢＦ監督式學習法則為基礎的條件機率密度估計與多值函數近似 Ya-Wun Tsai 蔡雅雯 碩士 國立東華大學 應用數學系 97 This work applies supervised learning of RBF (radial basis function) neural networks for data driven density estimation (DE), conditional density estimation (CDE) and multi-valued function approximation. An RBF neural network is organized to approximate the probability density function underlying given observations. The network function is expected to coincide with the probability density function realized by Parzen windows whose centers are set to all observations. A well trained RBF neural network exactly carries out a mapping that is identical to the pdf of weighted Parzen windows and its built-in parameters in number are irrelevant to the sample size. By numerical simulations, we show the function of a well trained RBF network is robust for density estimation and is more efficient than Parzen windows for density evaluation. We further extend the proposed DE method to resolve conditional density estimation as well as multi-valued function approximation that is essential for solving inverse problems. Numerical simulations show the proposed CDE-based approach is effective for multi-valued function approximation. Jiann-Ming Wu 吳建銘 2009 學位論文 ; thesis 44 en_US
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language en_US
format Others
sources NDLTD
description 碩士 === 國立東華大學 === 應用數學系 === 97 === This work applies supervised learning of RBF (radial basis function) neural networks for data driven density estimation (DE), conditional density estimation (CDE) and multi-valued function approximation. An RBF neural network is organized to approximate the probability density function underlying given observations. The network function is expected to coincide with the probability density function realized by Parzen windows whose centers are set to all observations. A well trained RBF neural network exactly carries out a mapping that is identical to the pdf of weighted Parzen windows and its built-in parameters in number are irrelevant to the sample size. By numerical simulations, we show the function of a well trained RBF network is robust for density estimation and is more efficient than Parzen windows for density evaluation. We further extend the proposed DE method to resolve conditional density estimation as well as multi-valued function approximation that is essential for solving inverse problems. Numerical simulations show the proposed CDE-based approach is effective for multi-valued function approximation.
author2 Jiann-Ming Wu
author_facet Jiann-Ming Wu
Ya-Wun Tsai
蔡雅雯
author Ya-Wun Tsai
蔡雅雯
spellingShingle Ya-Wun Tsai
蔡雅雯
Supervised RBF learning for conditional density estimation and multi-valued function approximation
author_sort Ya-Wun Tsai
title Supervised RBF learning for conditional density estimation and multi-valued function approximation
title_short Supervised RBF learning for conditional density estimation and multi-valued function approximation
title_full Supervised RBF learning for conditional density estimation and multi-valued function approximation
title_fullStr Supervised RBF learning for conditional density estimation and multi-valued function approximation
title_full_unstemmed Supervised RBF learning for conditional density estimation and multi-valued function approximation
title_sort supervised rbf learning for conditional density estimation and multi-valued function approximation
publishDate 2009
url http://ndltd.ncl.edu.tw/handle/47429415351269813028
work_keys_str_mv AT yawuntsai supervisedrbflearningforconditionaldensityestimationandmultivaluedfunctionapproximation
AT càiyǎwén supervisedrbflearningforconditionaldensityestimationandmultivaluedfunctionapproximation
AT yawuntsai yǐrbfjiāndūshìxuéxífǎzéwèijīchǔdetiáojiànjīlǜmìdùgūjìyǔduōzhíhánshùjìnshì
AT càiyǎwén yǐrbfjiāndūshìxuéxífǎzéwèijīchǔdetiáojiànjīlǜmìdùgūjìyǔduōzhíhánshùjìnshì
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