title: Prediction uncertainty and optimal experimental design for learning dynamical systems.
abstract: Dynamical systems are frequently used to model biological systems. When these models are fit to data, it is necessary to ascertain the uncertainty in the model fit. Here, we present prediction deviation, a metric of uncertainty that determines the extent to which observed data have constrained the model's predictions. This is accomplished by solving an optimization problem that searches for a pair of models that each provides a good fit for the observed data, yet has maximally different predictions. We develop a method for estimating a priori the impact that additional experiments would have on the prediction deviation, allowing the experimenter to design a set of experiments that would most reduce uncertainty. We use prediction deviation to assess uncertainty in a model of interferon-alpha inhibition of viral infection, and to select a sequence of experiments that reduces this uncertainty. Finally, we prove a theoretical result which shows that prediction deviation provides bounds on the trajectories of the underlying true model. These results show that prediction deviation is a meaningful metric of uncertainty that can be used for optimal experimental design.
authors.affiliation: Operations Research Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
authors.forename: Benjamin
authors.initials: B
authors.lastname: Letham
authors.affiliation: Department of Chemical Engineering, Arizona State University, Tempe, Arizona 85281, USA.
authors.forename: Portia A
authors.initials: PA
authors.lastname: Letham
authors.affiliation: Department of Computer Science and Department of Electrical and Computer Engineering, Duke University, Durham, North Carolina 27708, USA.
authors.forename: Cynthia
authors.initials: C
authors.lastname: Rudin
authors.affiliation: Koch Institute for Integrative Cancer Research, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
authors.forename: Edward P
authors.initials: EP
authors.lastname: Browne
mesh_terms: D015658:HIV Infections; D006801:Humans; D007858:Learning; D008962:Models, Theoretical; D035501:Uncertainty