When Composite Likelihood Meets Stochastic Approximation

TL;DR

This paper introduces a stochastic gradient-based approximation method for composite likelihood estimation, enabling efficient inference in complex models with large data and many likelihood components.

Contribution

It proposes a novel stochastic approximation approach for composite likelihood, reducing computational demands while maintaining asymptotic normality of estimators.

Findings

Method is asymptotically normal around true parameters.

Variance accounts for data variability and optimization noise.

Effective in large-scale applications like mental health surveys.

Abstract

A composite likelihood is an inference function derived by multiplying a set of likelihood components. This approach provides a flexible framework for drawing inference when the likelihood function of a statistical model is computationally intractable. While composite likelihood has computational advantages, it can still be demanding when dealing with numerous likelihood components and a large sample size. This paper tackles this challenge by employing an approximation of the conventional composite likelihood estimator, which is derived from an optimization procedure relying on stochastic gradients. This novel estimator is shown to be asymptotically normally distributed around the true parameter. In particular, based on the relative divergent rate of the sample size and the number of iterations of the optimization, the variance of the limiting distribution is shown to compound for two sources of uncertainty: the sampling variability of the data and the optimization noise, with the latter depending on the sampling distribution used to construct the stochastic gradients. The advantages of the proposed framework are illustrated through simulation studies on two working examples: an Ising model for binary data and a gamma frailty model for count data. Finally, a real-data application is presented, showing its effectiveness in a large-scale mental health survey.