Additive Higher-Order Factorization Machines

TL;DR

This paper introduces a scalable tensor product spline model that efficiently captures all higher-order feature interactions, enhancing interpretability and performance in large-scale non-linear regression tasks.

Contribution

It presents a novel factorization-based approach to include all higher-order interactions in semi-parametric models with scalable computational costs.

Findings

Scales better than existing methods in theory and practice

Effective inclusion of all higher-order interactions

Demonstrated improved predictive performance on synthetic and real data

Abstract

In the age of big data and interpretable machine learning, approaches need to work at scale and at the same time allow for a clear mathematical understanding of the method's inner workings. While there exist inherently interpretable semi-parametric regression techniques for large-scale applications to account for non-linearity in the data, their model complexity is still often restricted. One of the main limitations are missing interactions in these models, which are not included for the sake of better interpretability, but also due to untenable computational costs. To address this shortcoming, we derive a scalable high-order tensor product spline model using a factorization approach. Our method allows to include all (higher-order) interactions of non-linear feature effects while having computational costs proportional to a model without interactions. We prove both theoretically and empirically that our methods scales notably better than existing approaches, derive meaningful penalization schemes and also discuss further theoretical aspects. We finally investigate predictive and estimation performance both with synthetic and real data.