Automated modeling of stochastic reactions with large measurement time-gaps

  • Authors:
  • Michael Douglas Schmidt;Hod Lipson

  • Affiliations:
  • Cornell University, Ithaca, NY, USA;Cornell University, Ithaca, NY, USA

  • Venue:
  • Proceedings of the 13th annual conference on Genetic and evolutionary computation
  • Year:
  • 2011

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Abstract

Many systems, particularly in biology and chemistry, involve the interaction of discrete quantities, such as individual elements or molecules. When the total number of elements in the system is low, the impact of individual reactions becomes non-negligible and modeling requires the simulation of exact sequences of reactions. In this paper, we introduce an algorithm that can infer an exact stochastic reaction model based on sparse measurements of an evolving system of discrete quantities. The algorithm is based on simulating a candidate model to maximize the likelihood of the data. When the likelihood is too small to provide a search gradient, the algorithm uses the distance of the data to the model's estimated distribution. Results show that this method infers stochastic models reliably with both short time gaps between measurements of the system, and long time gaps where the system state has evolved qualitatively far between each measurement. Furthermore, the proposed metric outperforms optimizing on likelihood or distance components alone. Traits measured on the search novelty, age, and bloat suggest that this algorithm scales well to increasingly complex systems.