Monte Carlo with QMCPy for Vector Functions of Integrals

Monte Carlo methods present an efficient approach for approximating the expected value of a random variable. Algorithms exist to adaptively sample the random variable until a user defined error tolerance is satisfied with high probability. This work describes an extension of such methods which supports adaptive sampling to satisfy error criteria for vector functions of multiple expectations. Although several functions involving multiple expectations are being evaluated, only one random sequence is required, albeit sometimes of larger dimension than the underlying randomness. These enhanced Monte Carlo and Quasi-Monte Carlo algorithms are implemented in the QMCPy Python package with support for vectorized, economical, and parallel function evaluation. We exemplify these capabilities on problems from machine learning and global sensitivity analysis. This is joint work with Jagadeeswaran Rathinavel, Principal AI/Data Scientist at Wi-Tronix LLC.

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