# Explaining Latent Factor Models for Recommendation with Influence Functions

arXiv: https://arxiv.org/abs/1811.08120 · HTML: https://mlsanity.com/paper/1811.08120/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Nov 2018.

## Built on by (most cited first, 14 of 14)

- [From Anecdotal Evidence to Quantitative Evaluation Methods: A Systematic Review on Evaluating Explainable AI](https://mlsanity.com/paper/2201.08164/) (2022)
- [Counterfactual Explanations for Neural Recommenders](https://mlsanity.com/paper/2105.05008/) (2021)
- [Measuring "Why" in Recommender Systems: a Comprehensive Survey on the Evaluation of Explainable Recommendation](https://mlsanity.com/paper/2202.06466/) (2022)
- [Reinforced Path Reasoning for Counterfactual Explainable Recommendation](https://mlsanity.com/paper/2207.06674/) (2022)
- [Out-of-Distribution Generalization Analysis via Influence Function](https://mlsanity.com/paper/2101.08521/) (2021)
- [Debiased Explainable Pairwise Ranking from Implicit Feedback](https://mlsanity.com/paper/2107.14768/) (2021)
- [Recommendation Unlearning via Matrix Correction](https://mlsanity.com/paper/2307.15960/) (2023)
- [LANE: Logic Alignment of Non-tuning Large Language Models and Online Recommendation Systems for Explainable Reason Generation](https://mlsanity.com/paper/2407.02833/) (2024)
- [ELIXIR: Learning from User Feedback on Explanations to Improve Recommender Models](https://mlsanity.com/paper/2102.09388/) (2021)
- [Fidelity-Aware Recommendation Explanations via Stochastic Path Integration](https://mlsanity.com/paper/2511.18047/) (2025)
- [Representer Point Selection for Explaining Regularized High-dimensional Models](https://mlsanity.com/paper/2305.20002/) (2023)
- [RecXplainer: Amortized Attribute-based Personalized Explanations for Recommender Systems](https://mlsanity.com/paper/2211.14935/) (2022)
- [From Top-1 to Top-K: A Reproducibility Study and Benchmarking of Counterfactual Explanations for Recommender Systems](https://mlsanity.com/paper/2604.19663/) (2026)
- [Why This, Not That? Mining User Profiles for Pair-wise Counterfactuals](https://mlsanity.com/paper/2608.21662/) (2026)

## Abstract (arXiv)

Latent factor models (LFMs) such as matrix factorization achieve the state-of-the-art performance among various Collaborative Filtering (CF) approaches for recommendation. Despite the high recommendation accuracy of LFMs, a critical issue to be resolved is the lack of explainability. Extensive efforts have been made in the literature to incorporate explainability into LFMs. However, they either rely on auxiliary information which may not be available in practice, or fail to provide easy-to-understand explanations. In this paper, we propose a fast influence analysis method named FIA, which successfully enforces explicit neighbor-style explanations to LFMs with the technique of influence functions stemmed from robust statistics. We first describe how to employ influence functions to LFMs to deliver neighbor-style explanations. Then we develop a novel influence computation algorithm for matrix factorization with high efficiency. We further extend it to the more general neural collaborative filtering and introduce an approximation algorithm to accelerate influence analysis over neural network models. Experimental results on real datasets demonstrate the correctness, efficiency and usefulness of our proposed method.