On the Regularization Landscape for the Linear Recommendation Models

2026-09-10

AI Summary

本文探讨了线性推荐模型中相似性能背后的原因，发现通过核范数或弗罗贝尼乌斯范数正则化可统一解释，并提出了结合两者优点的新解决方案。

Abstract

Recently, a wide range of recommendation algorithms inspired by deep learning techniques have emerged as the performance leaders on several standard recommendation benchmarks. While these algorithms were built on different DL techniques (e.g., dropouts, autoencoder), they have similar performance and even similar cost functions. This paper studies whether the models' comparable performance are sheer coincidence, or they can be unified under a single framework. We find that all linear performance leaders effectively add only a nuclear-norm based regularizer, or a Frobenius-norm based regularizer. The former ones possess a (surprising) rigid structure that limits the models' predictive power but their solutions are low rank and have closed form. The latter ones are more expressive and more efficient for recommendation but their solutions are either full-rank or require executing hard-to-tune numeric procedures such as ADMM. Along this line of finding, we further propose two low-rank, closed-form solutions, derived from carefully generalizing Frobenius-norm based regularizers. The new solutions get the best of both nuclear-norm and Frobenius-norm world.

Problem

• recommendation algorithms
• regularization
• nuclear-norm
• Frobenius-norm

Innovation

• nuclear-norm
• Frobenius-norm
• low-rank solutions
• closed-form solutions
• unified framework