Fitting a deeply-nested hierarchical model to a large book review dataset using a moment-based estimator

TL;DR

This paper introduces a fast, moment-based estimation method for fitting deeply-nested hierarchical models to large datasets, significantly improving computational efficiency over traditional maximum likelihood approaches.

Contribution

The authors extend a moment-based estimator to handle arbitrarily deep hierarchical models, enabling scalable analysis of large, nested datasets in recommender systems and beyond.

Findings

The extended estimator is an order of magnitude faster than maximum likelihood methods.

It effectively fits deep hierarchical models to large-scale book review data.

The method is applicable to various contexts with complex nested structures.

Abstract

We consider a particular instance of a common problem in recommender systems: using a database of book reviews to inform user-targeted recommendations. In our dataset, books are categorized into genres and sub-genres. To exploit this nested taxonomy, we use a hierarchical model that enables information pooling across across similar items at many levels within the genre hierarchy. The main challenge in deploying this model is computational: the data sizes are large, and fitting the model at scale using off-the-shelf maximum likelihood procedures is prohibitive. To get around this computational bottleneck, we extend a moment-based fitting procedure proposed for fitting single-level hierarchical models to the general case of arbitrarily deep hierarchies. This extension is an order of magnetite faster than standard maximum likelihood procedures. The fitting method can be deployed beyond recommender systems to general contexts with deeply-nested hierarchical generalized linear mixed models.