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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| Format: | Others |
| Language: | en_US |
| Published: |
2009
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| Online Access: | http://ndltd.ncl.edu.tw/handle/47429415351269813028 |
| Summary: | 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.
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