Fast Moment-Based Estimation for Hierarchical Models

TL;DR

This paper introduces a fast, moment-based estimation method for hierarchical models that significantly reduces computation time while maintaining competitive prediction accuracy, making it suitable for large-scale applications.

Contribution

It presents a novel, computationally efficient moment-based approach for hierarchical model estimation, inspired by Cochran's 1937 method, with proven effectiveness in large-scale settings.

Findings

Reduces computation time from hours to minutes in large-scale applications

Provides consistent parameter estimates with competitive prediction error

Offers a practical alternative to likelihood-based methods for hierarchical models

Abstract

Hierarchical models allow for heterogeneous behaviours in a population while simultaneously borrowing estimation strength across all subpopulations. Unfortunately, existing likelihood-based methods for fitting hierarchical models have high computational demands, and these demands have limited their adoption in large-scale prediction and inference problems. This paper proposes a moment-based procedure for estimating the parameters of a hierarchical model which has its roots in a method originally introduced by Cochran in 1937. The method trades statistical efficiency for computational efficiency. It gives consistent parameter estimates, competitive prediction error performance, and substantial computational improvements. When applied to a large-scale recommender system application and compared to a standard maximum likelihood procedure, the method delivers competitive prediction performance while reducing the sequential computation time from hours to minutes.