Robust full Bayesian learning for radial basis networks.
We propose a hierarchical full Bayesian model for radial basis networks. This model treats the model dimension (number of neurons), model parameters, regularization parameters, and noise parameters as unknown random variables. We develop a reversible-jump Markov chain Monte Carlo (MCMC) method to pe...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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2001
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| _version_ | 1826287761252941824 |
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| author | Andrieu, C de Freitas, N Doucet, A |
| author_facet | Andrieu, C de Freitas, N Doucet, A |
| author_sort | Andrieu, C |
| collection | OXFORD |
| description | We propose a hierarchical full Bayesian model for radial basis networks. This model treats the model dimension (number of neurons), model parameters, regularization parameters, and noise parameters as unknown random variables. We develop a reversible-jump Markov chain Monte Carlo (MCMC) method to perform the Bayesian computation. We find that the results obtained using this method are not only better than the ones reported previously, but also appear to be robust with respect to the prior specification. In addition, we propose a novel and computationally efficient reversible-jump MCMC simulated annealing algorithm to optimize neural networks. This algorithm enables us to maximize the joint posterior distribution of the network parameters and the number of basis function. It performs a global search in the joint space of the parameters and number of parameters, thereby surmounting the problem of local minima to a large extent. We show that by calibrating the full hierarchical Bayesian prior, we can obtain the classical Akaike information criterion, Bayesian information criterion, and minimum description length model selection criteria within a penalized likelihood framework. Finally, we present a geometric convergence theorem for the algorithm with homogeneous transition kernel and a convergence theorem for the reversible-jump MCMC simulated annealing method. |
| first_indexed | 2024-03-07T02:03:29Z |
| format | Journal article |
| id | oxford-uuid:9e2ed5f3-9898-449f-bc8b-2b51aa94d632 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T02:03:29Z |
| publishDate | 2001 |
| record_format | dspace |
| spelling | oxford-uuid:9e2ed5f3-9898-449f-bc8b-2b51aa94d6322022-03-27T00:48:18ZRobust full Bayesian learning for radial basis networks.Journal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:9e2ed5f3-9898-449f-bc8b-2b51aa94d632EnglishSymplectic Elements at Oxford2001Andrieu, Cde Freitas, NDoucet, AWe propose a hierarchical full Bayesian model for radial basis networks. This model treats the model dimension (number of neurons), model parameters, regularization parameters, and noise parameters as unknown random variables. We develop a reversible-jump Markov chain Monte Carlo (MCMC) method to perform the Bayesian computation. We find that the results obtained using this method are not only better than the ones reported previously, but also appear to be robust with respect to the prior specification. In addition, we propose a novel and computationally efficient reversible-jump MCMC simulated annealing algorithm to optimize neural networks. This algorithm enables us to maximize the joint posterior distribution of the network parameters and the number of basis function. It performs a global search in the joint space of the parameters and number of parameters, thereby surmounting the problem of local minima to a large extent. We show that by calibrating the full hierarchical Bayesian prior, we can obtain the classical Akaike information criterion, Bayesian information criterion, and minimum description length model selection criteria within a penalized likelihood framework. Finally, we present a geometric convergence theorem for the algorithm with homogeneous transition kernel and a convergence theorem for the reversible-jump MCMC simulated annealing method. |
| spellingShingle | Andrieu, C de Freitas, N Doucet, A Robust full Bayesian learning for radial basis networks. |
| title | Robust full Bayesian learning for radial basis networks. |
| title_full | Robust full Bayesian learning for radial basis networks. |
| title_fullStr | Robust full Bayesian learning for radial basis networks. |
| title_full_unstemmed | Robust full Bayesian learning for radial basis networks. |
| title_short | Robust full Bayesian learning for radial basis networks. |
| title_sort | robust full bayesian learning for radial basis networks |
| work_keys_str_mv | AT andrieuc robustfullbayesianlearningforradialbasisnetworks AT defreitasn robustfullbayesianlearningforradialbasisnetworks AT douceta robustfullbayesianlearningforradialbasisnetworks |