Strongly Hierarchical Factorization Machines and ANOVA Kernel Regression

TL;DR

This paper introduces Strongly Hierarchical Factorization Machines and ANOVA kernel regression, which efficiently model feature interactions with hierarchical structure, addressing computational, estimation, and structural challenges in high-dimensional sparse data.

Contribution

The paper proposes novel models that incorporate hierarchical structures into factorization machines and kernel regression, solving key issues without complicating optimization.

Findings

Models outperform state-of-the-art methods in user response prediction.

Models achieve significant improvements in stock volatility prediction.

Proposed methods effectively handle high-dimensional sparse data with hierarchical structures.

Abstract

High-order parametric models that include terms for feature interactions are applied to various data mining tasks, where ground truth depends on interactions of features. However, with sparse data, the high- dimensional parameters for feature interactions often face three issues: expensive computation, difficulty in parameter estimation and lack of structure. Previous work has proposed approaches which can partially re- solve the three issues. In particular, models with factorized parameters (e.g. Factorization Machines) and sparse learning algorithms (e.g. FTRL-Proximal) can tackle the first two issues but fail to address the third. Regarding to unstructured parameters, constraints or complicated regularization terms are applied such that hierarchical structures can be imposed. However, these methods make the optimization problem more challenging. In this work, we propose Strongly Hierarchical Factorization Machines and ANOVA kernel regression where all the three issues can be addressed without making the optimization problem more difficult. Experimental results show the proposed models significantly outperform the state-of-the-art in two data mining tasks: cold-start user response time prediction and stock volatility prediction.