Introducing graphical models to analyze genetic programming dynamics

  • Authors:
  • Erik Hemberg;Constantin Berzan;Kalyan Veeramachaneni;Una-May O'Reilly

  • Affiliations:
  • MIT CSAIL, Cambridge, MA, USA;Tufts University, Medford, MA, USA;MIT CSAIL, Cambridge, MA, USA;MIT CSAIL, Cambridge, MA, USA

  • Venue:
  • Proceedings of the twelfth workshop on Foundations of genetic algorithms XII
  • Year:
  • 2013

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Abstract

We propose graphical models as a new means of understanding genetic programming dynamics. Herein, we describe how to build an unbiased graphical model from a population of genetic programming trees. Graphical models both express information about the conditional dependency relations among a set of random variables and they support probabilistic inference regarding the likelihood of a random variable's outcome. We focus on the former information: by their structure, graphical models reveal structural dependencies between the nodes of genetic programming trees. We identify graphical model properties of potential interest in this regard - edge quantity and dependency among nodes expressed in terms of family relations. Using a simple symbolic regression problem we generate a graphical model of the population each generation. Then we interpret the graphical models with respect to conventional knowledge about the influence of subtree crossover and mutation upon tree structure.