
Constructing Low Star Discrepancy Point Sets with Genetic Algorithms
Geometric discrepancies are standard measures to quantify the irregulari...
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Weighted integration over a cube based on digital nets and sequences
QuasiMonte Carlo (QMC) methods are equal weight quadrature rules to app...
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A quasiMonte Carlo data compression algorithm for machine learning
We introduce an algorithm to reduce large data sets using socalled digi...
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Complexity of Computing the Shapley Value in Games with Externalities
We study the complexity of computing the Shapley value in games with ext...
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QuasiMonte Carlo Feature Maps for ShiftInvariant Kernels
We consider the problem of improving the efficiency of randomized Fourie...
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Walsh functions, scrambled (0,m,s)nets, and negative covariance: applying symbolic computation to quasiMonte Carlo integration
We investigate base b Walsh functions for which the variance of the inte...
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Average values of functionals and concentration without measure
Although there doesn't exist the Lebesgue measure in the ball M of C[0,1...
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An algorithm to compute the tvalue of a digital net and of its projections
Digital nets are among the most successful methods to construct lowdiscrepancy point sets for quasiMonte Carlo integration. Their quality is traditionally assessed by a measure called the tvalue. A refinement computes the tvalue of the projections over subsets of coordinates and takes a weighted average (or some other function) of these values. It is also of interest to compute the tvalues of embedded nets obtained by taking subsets of the points. In this paper, we propose an efficient algorithm to compute such measures and we compare our approach with previously proposed methods both empirically and in terms of computational complexity.
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