nips nips2005 nips2005-167 nips2005-167-reference knowledge-graph by maker-knowledge-mining
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Author: Patrick Flaherty, Adam Arkin, Michael I. Jordan
Abstract: We address the problem of robust, computationally-efficient design of biological experiments. Classical optimal experiment design methods have not been widely adopted in biological practice, in part because the resulting designs can be very brittle if the nominal parameter estimates for the model are poor, and in part because of computational constraints. We present a method for robust experiment design based on a semidefinite programming relaxation. We present an application of this method to the design of experiments for a complex calcium signal transduction pathway, where we have found that the parameter estimates obtained from the robust design are better than those obtained from an “optimal” design. 1
[1] I. Ford, D.M. Titterington, and C.P. Kitsos. Recent advances in nonlinear experiment design. Technometrics, 31(1):49–60, 1989.
[2] L. Vandenberghe, S. Boyd, and W. S.-P. Determinant maximization with linear matrix inequality constraints. SIAM Journal on Matrix Analysis and Applications, 19(2):499–533, 1998.
[3] G.A.F. Seber and C.J. Wild. Nonlinear Regression. Wiley-Interscience, Hoboken, NJ, 2003.
[4] A.C. Atkinson and A.N. Donev. Optimum Experimental Designs. Oxford University Press, 1992.
[5] S. Boyd and L. Vandenberghe. Convex Optimization. Cambridge University Press, 2003.
[6] G.E.P Box, W.G. Hunter, and J.S. Hunter. Statistics for Experimenters: An Introduction to Design, Data Analysis, and Model Building. John Wiley and Sons, New York, 1978.
[7] S.D. Silvey. Optimal Design. Chapman and Hall, London, 1980.
[8] D.V. Lindley. On the measure of information provided by an experiment. The Annals of Mathematical Statistics, 27(4):986–1005, 1956.
[9] L. Pronzato and E. Walter. Robust experiment design via maximin optimization. Mathematical Biosciences, 89:161–176, 1988.
[10] L. Vandenberghe and S. Boyd. Semidefinite programming. SIAM Review, 38(1):49–95, 1996.
[11] L. El Ghaoui, L. Oustry, and H. Lebret. Robust solutions to uncertain semidefinite programs. SIAM J. Optimization, 9(1):33–52, 1998.
[12] L. El Ghaoui and H. Lebret. Robust solutions to least squares problems with uncertain data. SIAM J. Matrix Anal. Appl., 18(4):1035–1064, 1997.
[13] L.A. Segel and M. Slemrod. The quasi-steady state assumption: A case study in perturbation. SIAM Review, 31(3):446–477, 1989.
[14] G. Lemon, W.G. Gibson, and M.R. Bennett. Metabotropic receptor activation, desensitization and sequestrationi: modelling calcium and inositol 1,4,5-trisphosphate dynamics following receptor activation. Journal of Theoretical Biology, 223(1):93–111, 2003.
[15] A.C. Atkinson. The usefulness of optimum experiment designs. JRSS B, 58(1):59–76, 1996.
[16] J.F. Sturm. Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optimization Methods and Software, 11:625–653, 1999.