On Estimating Recommendation Evaluation Metrics under Sampling

Since the recent study (Krichene and Rendle 2020) done by Krichene and Rendle on the sampling-based top-k evaluation metric for recommendation, there has been a lot of debates on the validity of using sampling to evaluate recommendation algorithms. Though their work and the recent work (Li et al. 2020 ) have proposed some basic approaches for mapping the sampling-based metrics to their global counterparts which rank the entire set of items, there is still a lack of understanding and consensus on how sampling should be used for recommendation evaluation. The proposed approaches either are rather uninformative (linking sampling to metric evaluation) or can only work on simple metrics, such as Recall/Precision (Krichene and Rendle 2020; Li et al. 2020) . In this paper, we introduce a new research problem on learning the empirical rank distribution, and a new approach based on the estimated rank distribution, to estimate the top-k metrics. Since this question is closely related to the underlying mechanism of sampling for recommendation, tackling it can help better understand the power of sampling and can help resolve the questions of if and how should we use sampling for evaluating recommendation. We introduce two approaches based on MLE (Maximal Likelihood Estimation) and its weighted variants, and ME (Maximal Entropy) principals to recover the empirical rank distribution, and then utilize them for metrics estimation. The experimental results show the advantages of using the new approaches for evaluating recommendation algorithms based on top-k metrics.