The nature of statistical learning theory
The nature of statistical learning theory
Sparse bayesian learning and the relevance vector machine
The Journal of Machine Learning Research
Healing the relevance vector machine through augmentation
ICML '05 Proceedings of the 22nd international conference on Machine learning
Local Feature Selection for the Relevance Vector Machine Using Adaptive Kernel Learning
ICANN '09 Proceedings of the 19th International Conference on Artificial Neural Networks: Part I
IEEE Transactions on Fuzzy Systems
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This paper introduces a Bayesian framework to gain sparse solutions in forecasting tasks. In this study, a local identification method based on the Takagi-Sugeno relevance vector machine (TS-RVM) for nonlinear time series forecasting is introduced. The core idea is applying a set of nonlinear models, i.e. local RVM models, as the consequent part of the fuzzy rules. In this method, at first, the fuzzy rules are created based on clustering techniques and the parameters of the rules' premise are tuned. Then, the parameters of each local RVM model are determined in a learning process in a Bayesian framework. It is shown that by utilizing a probabilistic Bayesian learning framework, we can achieve very accurate prediction models. One of the benefits of this model is that it typically uses fewer basis functions in comparison with support and relevance vector machines. Also, it includes automatic estimation of nuisance parameters, and the ability to use arbitrary basis functions (e.g. non mercer kernels). Second, in comparison with global RVM, proposed model have better result in terms of prediction error. Third, it adds in the benefits of probabilistic predictions, providing a probability distribution for predictions, while other function approximators like SVM and ANN are just point estimators.