@article{winkel_stallrich_storlie_reich_2021, title={Sequential Optimization in Locally Important Dimensions}, volume={63}, ISSN={["1537-2723"]}, DOI={10.1080/00401706.2020.1714738}, abstractNote={Abstract Optimizing an expensive, black-box function is challenging when its input space is high-dimensional. Sequential design frameworks first model with a surrogate function and then optimize an acquisition function to determine input settings to evaluate next. Optimization of both and the acquisition function benefit from effective dimension reduction. Global variable selection detects and removes input variables that do not affect across the input space. Further dimension reduction may be possible if we consider local variable selection around the current optimum estimate. We develop a sequential design algorithm called sequential optimization in locally important dimensions (SOLID) that incorporates global and local variable selection to optimize a continuous, differentiable function. SOLID performs local variable selection by comparing the surrogate’s predictions in a localized region around the estimated optimum with the p alternative predictions made by removing each input variable. The search space of the acquisition function is further restricted to focus only on the variables that are deemed locally active, leading to greater emphasis on refining the surrogate model in locally active dimensions. A simulation study across multiple test functions and an application to the Sarcos robot dataset show that SOLID outperforms conventional approaches. Supplementary materials for this article are available online.}, number={2}, journal={TECHNOMETRICS}, author={Winkel, Munir A. and Stallrich, Jonathan W. and Storlie, Curtis B. and Reich, Brian J.}, year={2021}, month={Apr}, pages={236–248} }
 @article{reich_kalendra_storlie_bondell_fuentes_2012, title={Variable selection for high dimensional Bayesian density estimation: application to human exposure simulation}, volume={61}, journal={Journal of the Royal Statistical Society. Series C, Applied Statistics}, author={Reich, B. J. and Kalendra, E. and Storlie, C. B. and Bondell, H. D. and Fuentes, M.}, year={2012}, pages={47–66} }
 @article{storlie_bondell_reich_zhang_2011, title={Surface estimation, variable selection, and the nonparametric oracle property}, volume={21}, number={2}, journal={Statistica Sinica}, author={Storlie, C. B. and Bondell, H. D. and Reich, B. J. and Zhang, H. H.}, year={2011}, pages={679–705} }
 @article{storlie_bondell_reich_2010, title={A Locally Adaptive Penalty for Estimation of Functions With Varying Roughness}, volume={19}, ISSN={["1537-2715"]}, DOI={10.1198/jcgs.2010.09020}, abstractNote={We propose a new regularization method called Loco-Spline for nonparametric function estimation. Loco-Spline uses a penalty which is data driven and locally adaptive. This allows for more flexible estimation of the function in regions of the domain where it has more curvature, without over fitting in regions that have little curvature. This methodology is also transferred into higher dimensions via the Smoothing Spline ANOVA framework. General conditions for optimal MSE rate of convergence are given and the Loco-Spline is shown to achieve this rate. In our simulation study, the Loco-Spline substantially outperforms the traditional smoothing spline and the locally adaptive kernel smoother. Code to fit Loco-Spline models is included with the Supplemental Materials for this article which are available online.}, number={3}, journal={JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS}, author={Storlie, Curtis B. and Bondell, Howard D. and Reich, Brian J.}, year={2010}, month={Sep}, pages={569–589} }
 @misc{storlie_helton_2008, title={Multiple predictor smoothing methods for sensitivity analysis: Description of techniques}, volume={93}, number={1}, journal={Reliability Engineering & System Safety}, author={Storlie, C. B. and Helton, J. C.}, year={2008}, pages={28–54} }
 @article{storlie_helton_2008, title={Multiple predictor smoothing methods for sensitivity analysis: Example results}, volume={93}, ISSN={["1879-0836"]}, DOI={10.1016/j.ress.2006.10.013}, abstractNote={The use of multiple predictor smoothing methods in sampling-based sensitivity analyses of complex models is investigated. Specifically, sensitivity analysis procedures based on smoothing methods employing the stepwise application of the following nonparametric regression techniques are described in the first part of this presentation: (i) locally weighted regression (LOESS), (ii) additive models, (iii) projection pursuit regression, and (iv) recursive partitioning regression. In this, the second and concluding part of the presentation, the indicated procedures are illustrated with both simple test problems and results from a performance assessment for a radioactive waste disposal facility (i.e., the Waste Isolation Pilot Plant). As shown by the example illustrations, the use of smoothing procedures based on nonparametric regression techniques can yield more informative sensitivity analysis results than can be obtained with more traditional sensitivity analysis procedures based on linear regression, rank regression or quadratic regression when nonlinear relationships between model inputs and model predictions are present.}, number={1}, journal={RELIABILITY ENGINEERING & SYSTEM SAFETY}, author={Storlie, Curtis B. and Helton, Jon C.}, year={2008}, month={Jan}, pages={55–77} }
 @article{helton_johnson_oberkampf_storlie_2007, title={A sampling-based computational strategy for the representation of epistemic uncertainty in model predictions with evidence theory}, volume={196}, ISSN={["1879-2138"]}, DOI={10.1016/j.cma.2006.10.049}, abstractNote={Evidence theory provides an alternative to probability theory for the representation of epistemic uncertainty in model predictions that derives from epistemic uncertainty in model inputs, where the descriptor epistemic is used to indicate uncertainty that derives from a lack of knowledge with respect to the appropriate values to use for various inputs to the model. The potential benefit, and hence appeal, of evidence theory is that it allows a less restrictive specification of uncertainty than is possible within the axiomatic structure on which probability theory is based. Unfortunately, the propagation of an evidence theory representation for uncertainty through a model is more computationally demanding than the propagation of a probabilistic representation for uncertainty, with this difficulty constituting a serious obstacle to the use of evidence theory in the representation of uncertainty in predictions obtained from computationally intensive models. This presentation describes and illustrates a sampling-based computational strategy for the representation of epistemic uncertainty in model predictions with evidence theory. Preliminary trials indicate that the presented strategy can be used to propagate uncertainty representations based on evidence theory in analysis situations where naïve sampling-based (i.e., unsophisticated Monte Carlo) procedures are impracticable due to computational cost.}, number={37-40}, journal={COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING}, author={Helton, J. C. and Johnson, J. D. and Oberkampf, W. L. and Storlie, C. B.}, year={2007}, pages={3980–3998} }