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Learning Fair Representations for Recommendation: A Graph-based Perspective

Le Wu, Lei Chen, Pengyang Shao, Richang Hong, Xiting Wang, Meng Wang

arXiv:2102.09140v3cs.IR

TL;DR

Recommender systems’ user-item graphs create collaborative correlations that standard instance-independent fairness methods may miss, allowing sensitive attributes to leak through behavior and graph structure. FairGo filters embeddings from arbitrary recommendation models and adversarially learns against sensitive-attribute prediction from both user embeddings and ego-centric graphs. Experiments report effective fair recommendation, while higher-order graph modeling is bounded because larger neighborhoods overlap substantially.

  • Problem

    Standard fairness methods assume independent instances, but recommender systems contain collaborative user-item graph correlations through which sensitive information can remain exposed.

  • Method

    FairGo applies sensitive-attribute filters to user and item embeddings and uses graph-based adversarial learning to obfuscate sensitive information in embeddings and user-centric graph structures.

  • Results

    The results clearly show FairGo’s effectiveness for fair recommendation on real-world datasets with varying sensitive information.

  • Takeaways & Limitations

    FairGo provides a model-agnostic framework that can be applied to multiple sensitive attributes and current recommendation models.

  • Takeaways & Limitations

    The model does not report results beyond three layers because larger ego-centric subgraphs substantially overlap with those of other users.

Abstract

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As a key application of artificial intelligence, recommender systems are among the most pervasive computer aided systems to help users find potential items of interests. Recently, researchers paid considerable attention to fairness issues for artificial intelligence applications. Most of these approaches assumed independence of instances, and designed sophisticated models to eliminate the sensitive information to facilitate fairness. However, recommender systems differ greatly from these approaches as users and items naturally form a user-item bipartite graph, and are collaboratively correlated in the graph structure. In this paper, we propose a novel graph based technique for ensuring fairness of any recommendation models. Here, the fairness requirements refer to not exposing sensitive feature set in the user modeling process. Specifically, given the original embeddings from any recommendation models, we learn a composition of filters that transform each user's and each item's original embeddings into a filtered embedding space based on the sensitive feature set. For each user, this transformation is achieved under the adversarial learning of a user-centric graph, in order to obfuscate each sensitive feature between both the filtered user embedding and the sub graph structures of this user. Finally, extensive experimental results clearly show the effectiveness of our proposed model for fair recommendation. We publish the source code at https://github.com/newlei/FairGo.

1 INTRODUCTION

Recommender systems can reproduce demographic and other biases, while standard fairness methods often overlook the collaborative graph structure linking users and items. FairGo addresses this by filtering sensitive information from embeddings and user-centric graph representations while preserving recommendation accuracy.

  • Recommendation results can favor particular demographic groups, including gender-based discrimination in career recommendations and racial disparities in advertising.
  • Fair representation learning filters sensitive information from data representations while maintaining the main task.
  • User and item embeddings are central to modern recommendation models, but sensitive attributes can leak through correlations between user behavior and attributes.
  • Independent fairness models are insufficient because collaborative correlations can expose sensitive attributes through each user’s graph structure.
  • FairGo is model-agnostic: it transforms user and item embeddings into a filtered space using sensitive-attribute filters and graph-based adversarial training.
  • Experiments on two real-world datasets with varying sensitive information show the proposed model’s effectiveness for fair recommendation.

2 RELATED WORK

Recommendation systems learn from user-item interactions represented as a bipartite graph, using latent-factor or graph-based embedding models. Fairness research spans several paradigms, while recommendation-specific work studies demographic disparity and fairness metrics.

  • Recommendation Algorithms: A recommender system contains user and item sets whose interactions form a rating matrix and a user-item bipartite graph.
  • Recommendation Algorithms: High-quality user and item embeddings support preference prediction, with ratings estimated from the inner product of corresponding embeddings.
  • Recommendation Algorithms: Latent-factor models learn free entity embeddings, whereas neural graph models iteratively aggregate neighborhood information through graph convolution layers.
  • Algorithmic Fairness and Applications: Algorithmic fairness research includes causal, ranking-based, and fair representation learning approaches, with group fairness widely used to assess treatment of underrepresented groups.
  • Recommendation Fairness: Recommendation-fairness studies report popularity and demographic disparities, including unequal utility across demographic groups and fairness effects from post-processing.

3 THE PROPOSED FAIRGO MODEL

FairGo filters embeddings from arbitrary recommendation models to preserve preference prediction while preventing sensitive information from being exposed by user embeddings or ego-centric graph structures. Its adversarial framework combines node-level and graph-level fairness objectives, with learned higher-order aggregation improving the representation of local structure.

  • 3.1 Overall Architecture: FairGo takes pretrained user and item embeddings plus sensitive attributes as input, targeting model-agnostic fair representation learning in a filtered space.
  • 3.1 Overall Architecture: The filter network contains one sub-filter per sensitive attribute and transforms each user and item into filtered embeddings used for recommendation.
  • 3.1 Overall Architecture: FairGo balances recommendation accuracy with fairness by retaining preference information while preventing filtered representations from leaking sensitive attributes.
  • 3.2 Graph based Adversarial Learning for Fairness Modeling: Each discriminator predicts a sensitive attribute from filtered embeddings, while adversarial training makes the filters obfuscate that information.
  • 3.2 Graph based Adversarial Learning for Fairness Modeling: An ego-centric network centers on a user and summarizes the local user-item neighborhood whose structure should not expose that user’s sensitive attribute.
  • 3.2 Graph based Adversarial Learning for Fairness Modeling: Graph-level fairness complements node-level fairness by combining sensitive-attribute objectives over filtered embeddings and ego-centric graph summaries.
  • 3.2.1 Summary Network for Ego-centric Graph.: The model aggregates representations across up to L neighborhood orders, while learned MLP aggregation avoids manually tuning balance parameters across layers.
  • 3.2.1 Summary Network for Ego-centric Graph.: Simple averaging fails to account for differing higher-order graph structures because more distant neighbors may expose less sensitive information than closer neighbors.

4 THEORETICAL ANALYSIS

The theoretical analysis characterizes the model’s objective as preserving rating information while suppressing sensitive-attribute information in filtered embeddings. It also establishes conditional independence in the infinite-adversarial-weight limit, while noting that this limit discards rating prediction.

  • The overall objective decomposes into independent contributions from sub-discriminators, one for each sensitive attribute.
  • The analysis defines the filtered-embedding distribution by integrating over original user and item embeddings under the filter mapping.This alternative distribution supports analysis of the model’s objective in the filtered space.
  • When the adversarial weight tends to infinity, and both networks have sufficient capacity and reach optimal values, filtered embeddings become conditionally independent of sensitive attributes.
  • The infinite-weight result is too strict because it removes the rating-prediction objective from the model.
  • Given sufficient discriminator capacity, the objective minimizes conditional entropy between ratings and filtered embeddings while maximizing it between each sensitive attribute and those embeddings.

5 EXPERIMENTS

Experiments evaluate FairGo across two recommendation datasets, model families, sensitive-attribute settings, and graph-summary designs. Results show improved fairness with competitive recommendation performance, while higher-order graph modeling adds runtime and training difficulty.

  • Experimental Setup: Experiments use MovieLens-1M and Lastfm-360K, evaluating recommendation and fairness across single and compositional sensitive-attribute settings.MovieLens includes gender, age, and occupation; the evaluation uses RMSE for recommendation and AUC or micro-F1 for sensitive-information exposure.
  • Experimental Setup: FairGo is compared with PMF, GCN, ICML_2019, and Non-parity under latent-factor and graph-based recommendation settings.The study includes both base recommendation models and fairness-aware baselines designed for sensitive attributes or fairness regularization.
  • Overall Performance: GCN improves recommendation performance but exposes more sensitive information than PMF, while direct sensitive-information filters reduce recommendation performance by 5% to 10%.The paper attributes GCN’s pattern to graph-structure modeling and hidden features correlated with sensitive attributes.
  • Overall Performance: FairGo_GCN reaches the best recommendation and fairness performance among the compared fairness-aware models.The authors select FairGo_GCN for detailed analysis because it outperforms FairGo_PMF on both recommendation and fairness.
  • Detailed Model Analysis: Learning-based aggregation performs best across settings, while higher-order graph modeling improves fairness and recommendation accuracy but increases runtime and training difficulty.The comparison covers local value-function aggregation, first-order neighborhood modeling, and learning-based aggregation.

6 CONCLUSIONS AND FUTURE WORK

The paper concludes that FairGo addresses recommendation fairness from a graph perspective while remaining model-agnostic and supporting multiple sensitive attributes. Experiments on real-world datasets showed its effectiveness, with future work targeting job and education recommendation.

  • FairGo considers fairness from a graph perspective for current recommendation models.
  • The proposed framework is model-agnostic and can be applied to multiple sensitive attributes.
  • Experimental results on real-world datasets clearly showed the effectiveness of the proposed model.
  • Future work will explore applications in job or education recommendation.

A PROOFS

This appendix section provides details of proofs concerning the correlation between the overall and sub value functions and the proof of Lemma 1.

  • The appendix gives proof details for the correlation between the overall value function in Eq.(4) and the sub value function in Eq.(16).
  • It also provides proofs of Lemma 1.

A.1 Correlation between the overall value function (Eq.(4)) with multiple attributes and the sub value function (Eq.(16)) that deals with a single attribute.

The appendix shows that the overall value function can be decomposed into independent single-attribute combinations, with each sub-discriminator contributing an attribute-specific term while using filtered embeddings for prediction and discrimination.

  • The overall value function combines the rating-prediction term with discriminator terms over filtered embeddings.The mapping F transforms original embeddings into filtered embeddings, and p_u is summarized from that filtered space.
  • The overall value function can be analyzed through the contribution of each sub-discriminator D_k for attribute k.
  • For the k-th attribute, the sub-value function retains rating prediction and subtracts a weighted discriminator log-likelihood for x_uk.
  • Because both rating prediction and discrimination rely on F = F(G_u, E, X), the analysis defines a distribution over the filtered embedding space.
  • Multiple attributes can be split into independent combinations of single attributes, extending single-attribute analysis to multiple attributes.

A.2 Proofs of Lemma 1

The proof derives the optimal discriminator by formulating the value function for one attribute in the filtered embedding space and solving the constrained optimization over predicted probabilities.

  • The proof begins with the value function for the k-th attribute in the filtered embedding space.
  • With fixed filtered embeddings, only the discriminator term is relevant to the discriminator’s optimization.The proof notes that p_u aggregates f_u and f_v, while f_v is irrelevant to the discriminator’s best solution.
  • The discriminator optimization imposes the equality constraint that predicted probabilities sum to 1.
  • The proof uses a Lagrangian dual problem, sets the partial derivative with respect to q_Dk to zero, and applies the equality constraint.
  • Substituting the resulting condition back into the optimization yields the optimal discriminator.

B DETAILS OF GROUP FAIRNESS RESULTS

The paper evaluates fairness using sensitive-attribute classification accuracy and group fairness metrics. Statistical parity compares predicted ratings across user groups, including multi-valued attributes.

  • Fairness is first measured through classification accuracy for each sensitive attribute.
  • Statistical parity measures predicted-rating discrepancy between male and female users for binary attributes.
  • For multi-valued attributes, users are grouped by attribute value and their predicted-rating standard deviation measures parity.

B.2 Equal Opportunity

Equal opportunity extends group fairness beyond predicted-rating parity by comparing prediction accuracy across groups. The evaluation uses group-level standard deviations for multi-valued attributes and reports stronger performance in some datasets than others.

  • B.2 Equal Opportunity: Equal opportunity evaluates parity in prediction accuracy across sensitive-attribute groups.
  • B.2 Equal Opportunity: For multi-valued attributes, equal opportunity is computed across binary attribute values and summarized by standard deviation.
  • B.2 Equal Opportunity: FairGo achieves the best results for binary gender and both group fairness metrics on Lastfm-360K.
  • B.2 Equal Opportunity: On MovieLens, FairGo is not best for multi-valued attributes under equal opportunity, possibly because adversarial training needs sufficient user data.
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