Real-world optimization scenarios under uncertainty and noise are typically handled with robust optimization techniques, which re-formulate the original optimization problem into a robust... Show moreReal-world optimization scenarios under uncertainty and noise are typically handled with robust optimization techniques, which re-formulate the original optimization problem into a robust counterpart, e.g., by taking an average of the function values over different perturbations to a specific input. Solving the robust counterpart instead of the original problem can significantly increase the associated computational cost, which is often overlooked in the literature to the best of our knowledge. Such an extra cost brought by robust optimization might depend on the problem landscape, the dimensionality, the severity of the uncertainty, and the formulation of the robust counterpart.This paper targets an empirical approach that evaluates and compares the computational cost brought by different robustness formulations in Kriging-based optimization on a wide combination (300 test cases) of problems, uncertainty levels, and dimensions. We mainly focus on the CPU time taken to find robust solutions, and choose five commonly-applied robustness formulations: `"mini-max robustness'', "mini-max regret robustness'', "expectation-based robustness'', ``dispersion-based robustness'', and "composite robustness'' respectively. We assess the empirical performance of these robustness formulations in terms of a fixed budget and a fixed target analysis, from which we find that "mini-max robustness'' is the most practical formulation w.r.t.~the associated computational cost. Show less
Barbour, S.J.; Coppo, R.; Zhang, H.; Liu, Z.H.; Suzuki, Y.; Matsuzaki, K.; ... ; Int IgA Nephropathy Network 2019
ImportanceAlthough IgA nephropathy (IgAN) is the most common glomerulonephritis in the world, there is no validated tool to predict disease progression. This limits patient-specific risk... Show moreImportanceAlthough IgA nephropathy (IgAN) is the most common glomerulonephritis in the world, there is no validated tool to predict disease progression. This limits patient-specific risk stratification and treatment decisions, clinical trial recruitment, and biomarker validation. ObjectiveTo derive and externally validate a prediction model for disease progression in IgAN that can be applied at the time of kidney biopsy in multiple ethnic groups worldwide. Design, Setting, and ParticipantsWe derived and externally validated a prediction model using clinical and histologic risk factors that are readily available in clinical practice. Large, multi-ethnic cohorts of adults with biopsy-proven IgAN were included from Europe, North America, China, and Japan. Main Outcomes and MeasuresCox proportional hazards models were used to analyze the risk of a 50% decline in estimated glomerular filtration rate (eGFR) or end-stage kidney disease, and were evaluated using the R-D(2) measure, Akaike information criterion (AIC), C statistic, continuous net reclassification improvement (NRI), integrated discrimination improvement (IDI), and calibration plots. ResultsThe study included 3927 patients; mean age, 35.4 (interquartile range, 28.0-45.4) years; and 2173 (55.3%) were men. The following prediction models were created in a derivation cohort of 2781 patients: a clinical model that included eGFR, blood pressure, and proteinuria at biopsy; and 2 full models that also contained the MEST histologic score, age, medication use, and either racial/ethnic characteristics (white, Japanese, or Chinese) or no racial/ethnic characteristics, to allow application in other ethnic groups. Compared with the clinical model, the full models with and without race/ethnicity had better R-D(2) (26.3% and 25.3%, respectively, vs 20.3%) and AIC (6338 and 6379, respectively, vs 6485), significant increases in C statistic from 0.78 to 0.82 and 0.81, respectively (Delta C, 0.04; 95% CI, 0.03-0.04 and Delta C, 0.03; 95% CI, 0.02-0.03, respectively), and significant improvement in reclassification as assessed by the NRI (0.18; 95% CI, 0.07-0.29 and 0.51; 95% CI, 0.39-0.62, respectively) and IDI (0.07; 95% CI, 0.06-0.08 and 0.06; 95% CI, 0.05-0.06, respectively). External validation was performed in a cohort of 1146 patients. For both full models, the C statistics (0.82; 95% CI, 0.81-0.83 with race/ethnicity; 0.81; 95% CI, 0.80-0.82 without race/ethnicity) and R-D(2) (both 35.3%) were similar or better than in the validation cohort, with excellent calibration. Conclusions and RelevanceIn this study, the 2 full prediction models were shown to be accurate and validated methods for predicting disease progression and patient risk stratification in IgAN in multi-ethnic cohorts, with additional applications to clinical trial design and biomarker research. Show less
surface. These results unveiled the dynamic interactions between amended biochar and soil oxide minerals which can significantly affect the immobilization pathways of metals in contaminated soils.
Noordam, R.; Bos, M.M.; Wang, H.; Mook-Kanamori, D.; Heemst, D. van; Redline, S. 2018
