On parametric families for sampling binary data with specified mean and correlation

TL;DR

This paper introduces a class of binary parametric families using generalized linear models to effectively model high-dimensional binary data with specified mean and correlation, outperforming existing methods.

Contribution

It proposes a novel approach based on logistic conditionals to approximate Ising-type distributions, enabling better modeling of binary data with desired statistical properties.

Findings

Outperforms competing approaches in feasible correlation modeling

Provides a practical approximation to Ising distributions

Demonstrates effectiveness through empirical evidence

Abstract

We discuss a class of binary parametric families with conditional probabilities taking the form of generalized linear models and show that this approach allows to model high-dimensional random binary vectors with arbitrary mean and correlation. We derive the special case of logistic conditionals as an approximation to the Ising-type exponential distribution and provide empirical evidence that this parametric family indeed outperforms competing approaches in terms of feasible correlations.