The Rosenblatt Bayesian Algorithm Learning in a Nonstationary Environment

• Published in: IEEE transaction on neural networks and learning systems 2007-03, Vol.18 (2), p.584-588
• Main Author: de Oliveira, E.A.
• Format: Article
• Language: English
• Subjects: Algorithms; Artificial Intelligence; Artificial neural networks; Bayes Theorem; Bayesian analysis; Bayesian methods; Biological neural networks; Computer Simulation; Covariance matrix; Distance learning; Drift; Entropy; Feedback; Gaussian distribution; Gradient methods; Information Storage and Retrieval - methods; Learning; Models, Theoretical; Neural networks; Neural Networks (Computer); Neurons; Nonstationary environments; Online gradient methods; Pattern classification; Pattern Recognition, Automated - methods; Stochastic Processes; Studies; time- varying environment
• ISSN: 1045-9227; 2162-237X; 1941-0093; 2162-2388
• DOI: 10.1109/TNN.2006.889943

In this letter, we study online learning in neural networks (NNs) obtained by approximating Bayesian learning. The approach is applied to Gibbs learning with the Rosenblatt potential in a nonstationary environment. The online scheme is obtained by the minimization (maximization) of the Kullback-Leibler divergence (cross entropy) between the true posterior distribution and the parameterized one. The complexity of the learning algorithm is further decreased by projecting the posterior onto a Gaussian distribution and imposing a spherical covariance matrix. We study in detail the particular case of learning linearly separable rules. In the case of a fixed rule, we observe an asymptotic generalization error e g propalpha -1 for both the spherical and the full covariance matrix approximations. However, in the case of drifting rule, only the full covariance matrix algorithm shows a good performance. This good performance is indeed a surprise since the algorithm is obtained by projecting without the benefit of the extra information on drifting