用用户比较物品对的数据，高效训练推荐系统。
Recommendations with Sparse Comparison Data: Provably Fast Convergence for Nonconvex Matrix Factorization
- 基于物品对比数据学习用户和物品的隐含特征。
- 在稀疏对比数据下，梯度方法仍能指数级快速收敛。
- 适合数据稀疏但需个性化推荐的场景。
本文针对推荐系统中用户通过成对物品比较提供反馈的新学习问题进行理论分析。假设比较行为源于用户与物品的隐含特征，预测偏好可转化为从对比数据中学习这些特征。类似经典矩阵分解，该任务的损失函数为非凸。我们的分析表明，损失函数在真实解附近具有（受限）强凸性，只要初始值合适，梯度方法即可实现指数级收敛。重要的是，这一结果在稀疏数据条件下依然成立——每位用户仅比较少数几对物品。核心技术贡献是将矩阵补全中常用的某些集中不等式推广至本模型。研究证明，从对比数据中学习个性化推荐在计算与统计上均高效。
原文摘要 · Abstract (English)
This paper provides a theoretical analysis of a new learning problem for recommender systems where users provide feedback by comparing pairs of items instead of rating them individually. We assume that comparisons stem from latent user and item features, which reduces the task of predicting preferences to learning these features from comparison data. Similar to the classical matrix factorization problem, the main challenge in this learning task is that the resulting loss function is nonconvex. Our analysis shows that the loss function exhibits (restricted) strong convexity near the true solution, which ensures gradient-based methods converge exponentially, given an appropriate warm start. Importantly, this result holds in a sparse data regime, where each user compares only a few pairs of items. Our main technical contribution is to extend certain concentration inequalities commonly used in matrix completion to our model. Our work demonstrates that learning personalized recommendations from comparison data is computationally and statistically efficient.
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