On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals

By J. Halton. 1960

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Citations in the corpus

Determinantal Point Processes for Machine Learning (2012, background): “In fact, it is possible to construct quasirandom sequences where the discrepancy of the first k elements is O((logk)D/k); the first such sequence was proposed by [64].”
Apollo: A flexible, powerful and customisable freeware package for choice model estimation and application (2019, methodology): “We first set the type of draws in interDrawsType, where different pre-defined types of draws are available in Apollo, including (but not limited to) pmc for pseudo-Monte Carlo draws, halton for Halton draws Halton (1960) and mlhs for MLHS draws (Hess et al., 2006).”
Best practices for differentiated products demand estimation with PyBLP (2020, methodology): “By default, PyBLP scales by N so that after two-step GMM the objective equals the Hansen (1982) J statistic, the scale of which is invariant to problem size.”
Good permutations for deterministic scrambled Halton sequences in terms of L2-discrepancy (2006, background): “Halton [5] extends this definition to the s-dimensional sequence {xi}, defining xn = ( b1(n), .”
A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks (2022, methodology): “This study also considers other low-discrepancy sequences, including the Halton sequence [32] and the Hammersley sequence [33].”
Domain-specific Genetic Algorithm for Multi-tenant DNNAccelerator Scheduling (2021, methodology): “We include multiple population-based optimizations [21, 32, 33, 34, 37, 38, 51, 69, 80, 85] and two RL methods: A2C [72] which is used in [67, 104] for scheduling and PPO2 [93], which is one of the advanced policy-gradient methods that succeed in many fields and is used in [9,87] for resource schedu”
Applications of randomized low discrepancy sequences to the valuation of complex securities (2000, background): “The monograph by Niederreiter (1992) provides an excellent discussion of these sequences.”