# Density-Ratio Based Personalised Ranking from Implicit Feedback

arXiv: https://arxiv.org/abs/2101.07481 · HTML: https://mlsanity.com/paper/2101.07481/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jan 2021.

## Built on by (most cited first, 4 of 4)

- [The Minority Matters: A Diversity-Promoting Collaborative Metric Learning Algorithm](https://mlsanity.com/paper/2209.15292/) (2022)
- [Improved Diversity-Promoting Collaborative Metric Learning for Recommendation](https://mlsanity.com/paper/2409.01012/) (2024)
- [Direct Debiased Machine Learning via Bregman Divergence Minimization](https://mlsanity.com/paper/2510.23534/) (2025)
- [Scalable Personalised Item Ranking through Parametric Density Estimation](https://mlsanity.com/paper/2105.04769/) (2021)

## Abstract (arXiv)

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 large-scale 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.