Structure Identification by Optimized Interventions

We consider the problem of optimal experimental design in structure identification. Whereas standard approaches simply minimize Shannon’s entropy of the estimated parameter posterior, we show how to select between alternative model configurations, too. Our method specifies the intervention that makes an experiment capable of determining whether or not a particular configuration hypothesis is correct. This is performed by a novel clustering technique in approximated Bayesian parameter estimation for non-linear dynamical systems. The computation of the perturbation that minimizes the effective number of clusters in the belief state is constrained by the increase of the expected Kullback-Leibler divergence between the parameter prior and the posterior. This enables the disambiguation of persisting alternative explanations in cases where standard design systematically fails. Its applicability is illustrated with a biochemical Goodwin model, showing correct identification between multiple kinetic structures. We expect that our approach will prove useful especially for complex structures with reduced observability and multimodal posteriors.