Quasi-Monte Carlo methods

By L. Einkemmer. 2010

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Citations in the corpus

Determinantal Point Processes for Machine Learning (2012, methodology): “This deterministic uniformity property makes quasirandom sets useful for Monte Carlo estimation via (among other results) the Koksma-Hlawka inequality [Hlawka, 1961, Niederreiter , 1992].”
Orthogonal Random Features (2016, background): “It is well known that the convergence of MonteCarlo can be largely improved by carefully choosing a deterministic sequence instead of random samples [17].”
Variance-based sensitivity analysis of model outputs using surrogate models (2011, methodology): “To enhance the convergence of the estimators of the sensitivity indices, we used samples of quasirandom numbers, also known as low-discrepancy sequences (Sobol, 1990; Homma and Saltelli, 1995).”
Convergence rates for a class of estimators based on Stein’s method (2016, background): “Accelerated rates of convergence can be achieved by other means, including quasi-Monte Carlo (QMC; [33]).”
TT-cross approximation for multidimensional arrays (2010, methodology): “For large values of the dimensionality d such integrals are usually computed by Monte Carlo or Quasi Monte Carlo methods [37], or by sparse grid approaches [18], or sometimes by using analytical decompositions [8].”
Black-box Importance Sampling (2016, background): “In the light of this, bound (7) is a form of the worse case bounds of the kernel-based quadrature rules (e.g., Chen et al., 2010; Bach, 2015; Huszár and Duve-naud, 2012; Niederreiter, 2010).”