Generation of discrete random variables in scalable frameworks

TL;DR

This paper introduces a scalable, parallelizable framework for simulating discrete random variables with diverse distributions, inspired by discrete choice models, emphasizing fully parallel operations and associative finalization.

Contribution

It proposes a novel paradigm for discrete variable simulation that enhances scalability and parallelism, expanding classical algorithms with new noise handling and associative operations.

Findings

Characterization of algorithms suitable for parallel discrete simulation

Introduction of a new paradigm inspired by discrete choice models

Framework accommodates additive and multiplicative noise

Abstract

In this paper, we face the problem of simulating discrete random variables with general and varying distributions in a scalable framework, where fully parallelizable operations should be preferred. The new paradigm is inspired by the context of discrete choice models. Compared to classical algorithms, we add parallelized randomness, and we leave the final simulation of the random variable to a single associative operation. We characterize the set of algorithms that work in this way, and those algorithms that may have an additive or multiplicative local noise. As a consequence, we could define a natural way to solve some popular simulation problems.