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R. Jagadeeswaran

Publications and source records attributed to R. Jagadeeswaran.

3 recordsLinked to original sources
arXiv2021

Quasi-Monte Carlo Software

Practitioners wishing to experience the efficiency gains from using low discrepancy sequences need correct, robust, well-written software. This article, based on our MCQMC 2020 tutorial, describes some of the better quasi-Monte Carlo (QMC) software available. We highlight the key software components required by QMC to approximate multivariate integrals or expectations of functions of vector random variables. We have combined these components in QMCPy, a Python open-source library, which we hope will draw the support of the QMC community. Here we introduce QMCPy.

cs.MS↗
arXiv2019

Fast Automatic Bayesian Cubature Using Lattice Sampling

Automatic cubatures approximate multidimensional integrals to user-specified error tolerances. For high dimensional problems, it makes sense to fix the sampling density but determine the sample size, $n$, automatically. Bayesian cubature postulates that the integrand is an instance of a stochastic process. Here we assume a Gaussian process parameterized by a constant mean and a covariance function defined by a scale parameter times a parameterized function specifying how the integrand values at two different points in the domain are related. These parameters are estimated from integrand values or are given non-informative priors. The sample size, $n$, is chosen to make the half-width of the credible interval for the Bayesian posterior mean no greater than the error tolerance. The process just outlined typically requires vector-matrix operations with a computational cost of $O(n^3)$. Our innovation is to pair low discrepancy nodes with matching kernels that lower the computational cost to $O(n \log n)$. This approach is demonstrated using rank-1 lattice sequences and shift-invariant kernels. Our algorithm is implemented in the Guaranteed Automatic Integration Library (GAIL).

math.NA↗