A Tool for Custom Construction of QMC and RQMC Point Sets

12/18/2020
by   Pierre L'Ecuyer, et al.
0

We present LatNet Builder, a software tool to find good parameters for lattice rules, polynomial lattice rules, and digital nets in base 2, for quasi-Monte Carlo (QMC) and randomized quasi-Monte Carlo (RQMC) sampling over the s-dimensional unit hypercube. The selection criteria are figures of merit that give different weights to different subsets of coordinates. They are upper bounds on the worst-case error (for QMC) or variance (for RQMC) for integrands rescaled to have a norm of at most one in certain Hilbert spaces of functions. Various Hilbert spaces, figures of merit, types of constructions, and search methods are covered by the tool. We provide simple illustrations of what it can do.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

01/16/2020

On Quasi-Monte Carlo Methods in Weighted ANOVA Spaces

In the present paper we study quasi-Monte Carlo rules for approximating ...
07/05/2019

Exploration of a Cosine Expansion Lattice Scheme

In this article, we combine a lattice sequence from Quasi-Monte Carlo ru...
04/06/2020

A quasi-Monte Carlo data compression algorithm for machine learning

We introduce an algorithm to reduce large data sets using so-called digi...
09/15/2020

Weighted integration over a cube based on digital nets and sequences

Quasi-Monte Carlo (QMC) methods are equal weight quadrature rules to app...
10/05/2019

An algorithm to compute the t-value of a digital net and of its projections

Digital nets are among the most successful methods to construct low-disc...
03/31/2022

Consistency of randomized integration methods

For integrable functions we provide a weak law of large numbers for stru...
08/08/2018

Lattice Studies of Gerrymandering Strategies

We propose three novel gerrymandering algorithms which incorporate the s...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.