Sampling Bias in Estimation of Distribution Algorithms for Genetic Programming Using Prototype Trees

Probabilistic models are widely used in evolutionary and related algorithms. In Genetic Programming (GP), the Probabilistic Prototype Tree (PPT) is often used as a model representation. Drift due to sampling bias is a widely recognised problem, and may be serious, particularly in dependent probability models. While this has been closely studied in independent probability models, and more recently in probabilistic dependency models, it has received little attention in systems with strict dependence between probabilistic variables such as arise in PPT representation. Here, we investigate this issue, and present results suggesting that the drift effect in such models may be particularly severe – so severe as to cast doubt on their scalability. We present a preliminary analysis through a factor representation of the joint probability distribution We suggest future directions for research aiming to overcome this problem.