Evolving neural trees for time series prediction using Bayesian evolutionary algorithms

Bayesian evolutionary algorithms (BEAs) are a probabilistic model for evolutionary computation. Instead of simply generating new populations as in conventional evolutionary algorithms, the BEAs attempt to explicitly estimate the posterior distribution of the individuals from their prior probability and likelihood, and then sample offspring from the distribution. We apply the Bayesian evolutionary algorithms to evolving neural trees, i.e. tree-structured neural networks. Explicit formulae for specifying the distributions on the model space are provided in the context of neural trees. The effectiveness and robustness of the method is demonstrated on the time series prediction problem. We also study the effect of the population size and the amount of information exchanged by subtree crossover and subtree mutations. Experimental results show that small-step mutation-oriented variations are most effective when the population size is small, while large-step recombinative variations are more effective for large population sizes.