Density-Ratio Based Personalised Ranking from Implicit Feedback

Abstract

Learning from implicit user feedback is challenging as we can only observe positive samples but never access negative ones. Most conventional methods cope with this issue by adopting a pairwise ranking approach with negative sampling. However, the pairwise ranking approach has a severe disadvantage in the convergence time owing to the quadratically increasing computational cost with respect to the sample size; it is problematic, particularly for largescale datasets and complex models such as neural networks. By contrast, a pointwise approach does not directly solve a ranking problem, and is therefore inferior to a pairwise counterpart in top-𝐾 ranking tasks; however, it is generally advantageous in regards to the convergence time. This study aims to establish an approach to learn personalised ranking from implicit feedback, which reconciles the training efficiency of the pointwise approach and ranking effectiveness of the pairwise counterpart. The key idea is to estimate the ranking of items in a pointwise manner; we first reformulate the conventional pointwise approach based on density ratio estimation and then incorporate the essence of ranking-oriented approaches (e.g. the pairwise approach) into our formulation. Through experiments on three real-world datasets, we demonstrate that our approach not only dramatically reduces the convergence time (one to two orders of magnitude faster) but also significantly improving the ranking performance. CCS CONCEPTS• Computing methodologies → Learning from implicit feedback; • Information systems → Recommender systems.

Scalable Personalised Item Ranking through Parametric Density Estimation

“…In contrast to the CPE approach that estimates 𝑝 (𝑦 = +1|𝑢, 𝑖) = 𝑝 (𝑖 |𝑢, 𝑦 = +1)𝑝 (𝑦 = +1|𝑢)/𝑝 (𝑖 |𝑢), the recently-proposed density ratio estimation (DRE) approach [57] directly estimates the density ratio 𝑝 (𝑖 |𝑢, 𝑦 = +1)/𝑝 (𝑖 |𝑢) through the minimisation of the Bregman divergences [55], which can be empirically approximated with positive-unlabelled data. As the main distinction of the DRE approach from its CPE counterpart, the ranker model in the DRE approach does not need to estimate class prior 𝑝 (𝑦 = +1|𝑢) (i.e.…”

“…user's activity), which is a constant value and does not affect the predicted ranking for 𝑢; thus, it avoids the estimation error of 𝑝 (𝑦 = +1|𝑢) in the ranker model. Several studies [45,57] have shown that the advantage of the DRE-based loss functions for top-𝐾 ranking problems by weighing the items in the top of ranked lists in contrast to the CPE approach. Togashi et al [57] empirically demonstrated the advantage of the DRE-based approach in terms of efficiency and effectiveness for top-𝐾 personalised recommendation.…”

“…Several studies [45,57] have shown that the advantage of the DRE-based loss functions for top-𝐾 ranking problems by weighing the items in the top of ranked lists in contrast to the CPE approach. Togashi et al [57] empirically demonstrated the advantage of the DRE-based approach in terms of efficiency and effectiveness for top-𝐾 personalised recommendation. Although their framework can be utilised with an arbitrary weighting strategy, their proposed adaptive and ranking-aware weighting strategies are heuristically designed.…”

“…For mini-batch sampling, we adopted the same user-based sampling strategy as is used in conventional approaches [38,57]. We uniformly sample |U 𝐵 | users and then sample all positive items I + 𝑢 for each user.…”

“…To conduct a fair comparison, we closely follow the settings of the experiments in LightGCN [28] and DREGN-CF [57].…”