Algorithm 659

By P. Bratley, B. Fox. 1988

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Citations in the corpus

Determinantal Point Processes for Machine Learning (2012, background): “The Sobol sequence [134], introduced later, offers improved uniformity properties and can be generated efficiently [18].”
Digital Nets and Sequences: Discrepancy Theory and Quasi-Monte Carlo Integration (2010, methodology): “For an efficient implementation of Sobol′ sequences see [3, 18] and for questions concerning the choice of polynomials gi,0, .”
Ancient numerical daemons of conceptual hydrological modeling: 2. Impact of time stepping schemes on model analysis and prediction (2010, methodology): “[27] The total global sensitivity indices Sj TOT, based on the RMSE model performance measure, were calculated using 10,000 parameter sets sampled using quasi‐random Sobol’ sequences [Bratley and Fox, 1988].”
Critical Hyper-Parameters: No Random, No Cry (2017, methodology): “The Sobol sequence [19] is also a popular choice and can be constructed using Gray codes [3].”
Construction and Comparison of High-Dimensional Sobol' Generators (2011, methodology): “Direction numbers are selected by the following rules (see, e.g., Bratley and Fox, 1988).”
Multi-Objective Parameter Selection for Classifiers (2012, unknown): “For an exemplary implementation, see Bratley and Fox (1988).”
Quasi Importance Sampling (2005, methodology): “We used a base-2 Niederreiter sequence [22], and a Sobol sequence [23] and repeated the experiments for fixed values of N with 1000 different randomly shifted point sets.”
A study on algorithms for optimization of Latin hypercubes (2006, methodology): “For the generation of Sobol sequences, which are based on completely different ideas, we refer to [4] and the references therein.”
Bayesian Optimization and Semiparametric Models with Applications to Assistive Technology (2014, methodology): “Algorithm 1 Selecting the next point to evaluate Input: Observations {xn, yn}n=1 {Generate a set of M candidate points from the Sobol sequence [Bratley and Fox, 1988]} Xcand = Sobol(M) {Generate H Gaussian process hyperparameter samples [Murray and Adams, 2010]} for h = 1 to H do Sample θh {See Sect”
Sourcebook of parallel computing (2003, methodology): “There are existing implementations of the Halton, Faure, Niederreiter and Soboĺ sequences [139, 140, 351] that are computationally efficient.”
Solving Probabilistic Optimal Power Flow Problem Using Quasi Monte Carlo Method and Ninth-Order Polynomial Normal Transformation (2014, methodology): “A thorough introduction of the Sobol sequence is presented in [17] and [18].”
Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index (2010, background): “[3] P. Bratley, B.L. Fox, Algorithm 659 implementing Sobol’s quasirandom sequence generator, ACM Transactions on Mathematical Software 14 (1) (1988) 88–100.”