RT Journal Article
ID 4a0c548e5b08f8c3
A1 Dinh, Vu
A1 Rundell, Ann E.
A1 Buzzard, Gregery T.
T1 EFFECTIVE SAMPLING SCHEMES FOR BEHAVIOR DISCRIMINATION IN NONLINEAR SYSTEMS
JF International Journal for Uncertainty Quantification
JO IJUQ
YR 2014
FD 2014-10-17
VO 4
IS 6
SP 535
OP 554
K1 representation of uncertainty
K1 variance reduction methods
K1 high-dimensional methods
K1 classification
K1 sequential data
K1 probabilistic inference
K1 biological modeling
AB Behavior discrimination is the problem of identifying sets of parameters for which the system does (or does not) reach
a given set of states. While there are a variety of methods to address this problem for linear systems, few successful techniques have been developed for nonlinear models. Existing methods often rely on numerical simulations without rigorous bounds on the numerical errors and usually require a large number of model evaluations, rendering those methods impractical for studies of high-dimensional and expensive systems. In this work, we describe a probabilistic framework to estimate the boundary that separates contrasting behaviors and to quantify the uncertainty in this estimation. In our approach, we directly parameterize the, yet unknown, boundary by the zero level-set of a polynomial function, then use statistical inference on available data to identify the coefficients of the polynomial. Building upon this framework, we consider the problem of choosing effective data sampling schemes for behavior discrimination of nonlinear systems in two different settings: the low-discrepancy sampling scheme, and the uncertainty-based sequential sampling scheme. In both cases, we successfully derive theoretical results about the convergence of the expected boundary to the true boundary of interest. We then demonstrate the efficacy of the method in several application contexts with a focus on biological models. Our method outperforms previous approaches to this problem in several ways and proves to be effective to study high-dimensional and expensive systems.
PB Begell House
LK http://dl.begellhouse.com/journals/52034eb04b657aea,21fe10c229b8ad74,4a0c548e5b08f8c3.html