Since Rendle and Krichene argued that commonly used sampling-based evaluation metrics are "inconsistent" with respect to the global metrics (even in expectation), there have been a few studies on the sampling-based recommender system evaluation. Existing methods try either mapping the sampling-based metrics to their global counterparts or more generally, learning the empirical rank distribution to estimate the top-$K$ metrics. However, despite existing efforts, there is still a lack of rigorous theoretical understanding of the proposed metric estimators, and the basic item sampling also suffers from the "blind spot" issue, i.e., estimation accuracy to recover the top-$K$ metrics when $K$ is small can still be rather substantial. In this paper, we provide an in-depth investigation into these problems and make two innovative contributions. First, we propose a new item-sampling estimator that explicitly optimizes the error with respect to the ground truth, and theoretically highlight its subtle difference against prior work. Second, we propose a new adaptive sampling method which aims to deal with the "blind spot" problem and also demonstrate the expectation-maximization (EM) algorithm can be generalized for such a setting. Our experimental results confirm our statistical analysis and the superiority of the proposed works. This study helps lay the theoretical foundation for adopting item sampling metrics for recommendation evaluation, and provides strong evidence towards making item sampling a powerful and reliable tool for recommendation evaluation.

翻译：自Rendle与Krichene论证常用基于采样的评估指标相对于全局指标（即使在期望意义上）存在“不一致性”以来，关于基于采样的推荐系统评估研究已逐步展开。现有方法或尝试将采样指标映射为全局指标，或更泛化地通过学习经验排序分布来估计top-$K$指标。然而，尽管已有诸多努力，现有指标估计器仍缺乏严格的理论理解，且基础物品采样存在“盲区”问题——即当$K$较小时，恢复top-$K$指标的估计精度仍可能相当不足。本文深入探究上述问题并作出两项创新贡献：首先，提出一种新的物品采样估计器，显式优化与真实值间的误差，并从理论上阐明其与先前工作的细微差异；其次，提出一种旨在解决“盲区”问题的自适应采样方法，并证明期望最大化（EM）算法可被推广至该场景。实验结果验证了统计分析的有效性及所提方法的优越性。本研究为采用物品采样指标进行推荐评估奠定了理论基础，并有力证明了物品采样可成为推荐评估中强大且可靠的工具。