Rethinking Collaborative Metric Learning: Toward an Efficient Alternative without Negative Sampling

TL;DR

This paper analyzes the bias introduced by negative sampling in Collaborative Metric Learning (CML) for recommendation systems and proposes a sampling-free alternative, SFCML, demonstrating improved performance without sampling bias.

Contribution

The paper provides a theoretical analysis of negative sampling bias in CML and introduces a novel sampling-free method, SFCML, to improve generalization in recommendation systems.

Findings

Negative sampling introduces bias in CML's generalization error.

Sampling-free CML (SFCML) eliminates bias caused by negative sampling.

SFCML outperforms traditional CML on seven benchmark datasets.

Abstract

The recently proposed Collaborative Metric Learning (CML) paradigm has aroused wide interest in the area of recommendation systems (RS) owing to its simplicity and effectiveness. Typically, the existing literature of CML depends largely on the \textit{negative sampling} strategy to alleviate the time-consuming burden of pairwise computation. However, in this work, by taking a theoretical analysis, we find that negative sampling would lead to a biased estimation of the generalization error. Specifically, we show that the sampling-based CML would introduce a bias term in the generalization bound, which is quantified by the per-user \textit{Total Variance} (TV) between the distribution induced by negative sampling and the ground truth distribution. This suggests that optimizing the sampling-based CML loss function does not ensure a small generalization error even with sufficiently large training data. Moreover, we show that the bias term will vanish without the negative sampling strategy. Motivated by this, we propose an efficient alternative without negative sampling for CML named \textit{Sampling-Free Collaborative Metric Learning} (SFCML), to get rid of the sampling bias in a practical sense. Finally, comprehensive experiments over seven benchmark datasets speak to the superiority of the proposed algorithm.