Sequential design of computer experiments to minimize integrated response functions

By William I. Notz, Thomas J. Santner, Brett Williams. 2000

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Citations in the corpus

Fast Bayesian Optimization of Machine Learning Hyperparameters on Large Datasets (2016, background): “ction evaluations against the beneﬁt of learning about the scaling behavior of fand, ultimately, about which conﬁgurations work best on the full dataset. Following the nomenclature of Williams et al. [26], we call s2[0;1] an environmental variable that can be changed freely during optimization, but ”
Taking the Human Out of the Loop: A Review of Bayesian Optimization (2016, neutral): “, [33] and [159]).”
A Tutorial on Bayesian Optimization (2018, methodology): “dom environmental conditions (Chang et al., 2001) in statistics, multi-task Bayesian optimization (Swersky et al., 2013) in machine learning, along with optimization of integrated response functions (Williams et al., 2000) and optimization with expensive integrands (Toscano-Palmerin and Frazier, 201”
Towards efﬁcient Bayesian Optimization for Big Data (2015, background): “Following Williams et al. [7], we contrast the typical inputs of Bayesian optimization (here: hyperparameters) to environmental inputs, which can be set freely during optimization, but which are ﬁxed at evaluation time (here: dataset size).”
Surrogate-based Analysis and Optimization (2005, methodology): “Adaptive DOE in which model appraisal information is used to place additional samples have also been proposed [40–42].”
Adaptive Designs of Experiments for Accurate Approximation of a Target Region (2010, unknown): “A popular heuristic to minimize sequentially the IMSE is to find the point where the prediction variance is maximum [ [18, 21]], which can be used here with the weighted prediction variance.”
Sequential Model-Based Optimization for General Algorithm Configuration (2011, unknown): “performance across problem instances [21].”
Fast Bayesian hyperparameter optimization on large datasets (2017, methodology): “Following the nomenclature of Williams et al. (2000), we call s ∈ [0 , 1] an environmental variable that can be changed freely during optimization, but that is set to s = 1 (i.e., the entire dataset size), at evaluation time.”
Dynamic Trees for Learning and Design (2009, methodology): “freedom (this is similar to the marginal improvement derived in Williams et al., 2000 ).”
Fixed-domain asymptotics for a subclass of Matern-type Gaussian random fields (2005, methodology): “iplicative Mat´ern-type covariance function and not an isotropic one. GAUSSIAN RANDOM FIELDS 3 The class of multiplicative Mat´ern-type covariance functions has nonetheless been used in, for example, [14]. A referee noted that the multiplicative Mat´ern-type covariance function and an isotropic oneh”
Kriging metamodeling in simulation: A review (2009, methodology): “• Reference [54] uses a Bayesian approach to derive sequential IMSE (Integrated MSE) designs.”
Inconsistent Estimation and Asymptotically Equal Interpolations in Model-Based Geostatistics (2004, methodology): “The Matérn class has also been used by Handcock and Stein (1993), Handcock and Wallis (1994), Williams, Santner, and Notz (2000), and Diggle, Ribeiro, and Christensen (2002).”
The Knowledge-Gradient Policy for Correlated Normal Beliefs (2009, background): “extended to the noisy case by Williams et al. (2000) , and then later by Huang et al. (2006),”
A new acquisition function for Bayesian optimization based on the moment-generating function (2017, background): “, Studentt processes [14], [15] and random forest [13].”