[Paper Review] Explaining Latent Factor Models for Recommendation with Influence Functions

Weiyu Cheng, Yanyan Shen+2 more|arXiv (Cornell University)|Nov 20, 2018

Recommender Systems and Techniques34 references4 citations

TL;DR

This paper proposes FIA, a fast influence analysis method that enables latent factor models (LFMs) like matrix factorization and neural collaborative filtering to generate neighbor-style explanations without requiring auxiliary data. By leveraging influence functions from robust statistics, FIA identifies the most influential training ratings that shape a model's prediction, achieving up to 2,411x speedup over baseline methods while delivering interpretable, user-friendly explanations.

ABSTRACT

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.

Motivation & Objective

• To address the lack of explainability in state-of-the-art latent factor models (LFMs) such as matrix factorization and neural collaborative filtering.
• To develop a general-purpose explanation method that does not rely on auxiliary information like user reviews or item features.
• To enable neighbor-style explanations—e.g., 'this item is similar to ones you liked before'—for LFMs by identifying the most influential training ratings.
• To design an efficient influence computation algorithm suitable for real-world recommendation systems with high scalability.

Proposed method

• FIA uses influence functions from robust statistics to quantify how much each training rating (user, item, rating) affects the model’s prediction for a given test user-item pair.
• For matrix factorization, FIA derives a closed-form approximation of influence scores using the Hessian of the loss function, enabling efficient computation without iterative retraining.
• For neural collaborative filtering (NCF), FIA employs a stochastic approximation method to estimate influence scores efficiently, reducing computational cost while preserving accuracy.
• The method identifies the top-k most influential training ratings from a user’s history or an item’s rating history to generate item-based or user-based explanations.
• Influence scores are computed as the gradient of the model’s prediction with respect to the removal of a training example, enabling precise attribution of prediction impact.
• The approach is orthogonal to model architecture, making it applicable to various LFM variants including MF and NCF without architectural modifications.

Experimental results

Research questions

• RQ1 Can influence functions be effectively used to generate neighbor-style explanations for latent factor models in recommendation systems?
• RQ2 How can influence analysis be made computationally efficient enough for real-world deployment in large-scale recommendation systems?
• RQ3 Can FIA provide accurate and intuitive explanations without relying on auxiliary data such as reviews or item features?
• RQ4 How does the influence distribution of training examples affect model predictions, and what insights can it reveal about model behavior?

Key findings

• FIA achieves up to 2,411x speedup over baseline influence computation (IA) in matrix factorization, with running times under 5 seconds regardless of latent factor dimension.
• In neural collaborative filtering, FIA achieves a speedup of 1,752x over IA, demonstrating strong scalability for deep learning-based recommenders.
• The influence scores are highly concentrated: only a small fraction of training ratings (e.g., top 6) significantly affect the prediction, indicating sparse influence patterns.
• The top influential ratings in item-based explanations are semantically coherent—e.g., for The Lion King (1994), the most influential items are also animated comedies, confirming intuitive relevance.
• The distribution of influence values is centered near zero, with most ratings having negligible impact, suggesting that only a few ratings drive predictions.
• FIA successfully generates human-readable, neighbor-style explanations such as 'we predict your rating for this movie because you previously rated these similar items highly'.