A challenge in understanding the collective behavior of adaptive systems comes from the tension between the desire for parsimonious explanations and the complex contingencies that are necessary to understand biological and social systems. Creating useful, predictive models using limited data from heterogeneous systems becomes a problem in model selection, in which finding the correct degree of abstraction is crucial to avoid both overfitting and oversimplification. I will describe two projects in which we study a system by defining a space of models that varies in the level of abstraction along a single dimension.
First, we developed an automated model selection method that infers dynamical systems describing cellular regulation. Here, we find that coarse-grained, phenomenological models that adapt their level of detail to the available data can perform surprisingly well with little data. Importantly, forgoing the goal of microscopic accuracy allows the method to efficiently make predictions even when important biochemical species are unobserved.
Second, we study conflict in a macaque society, a system in which the components themselves have incentive for making accurate predictions, yet have limited cognitive machinery. In order to predict the makeup of future fights based on the history of past fights, we find that it is important to estimate frequencies of not just individuals but higher-order structures that we find using an adaptive sparse coding technique. We also calculate the amount of information that must be remembered to make accurate predictions using these models.
Bryan Daniels, Postdoctoral Fellow, Center for Complexity and Collective Computation, U of W - Madison