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arxiv: 2507.19067 · v2 · submitted 2025-07-25 · 💻 cs.IR · cs.AI· cs.NE

PBiLoss: Popularity-Aware Regularization to Improve Fairness in Graph-Based Recommender Systems

Mohammad Naeimi , Mostafa Haghir Chehreghani This is my paper

Pith reviewed 2026-05-19 02:53 UTC · model grok-4.3

classification 💻 cs.IR cs.AIcs.NE
keywords popularity biasgraph neural networksrecommender systemsfairnessregularizationsampling strategiesGNN recommenders
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The pith

PBiLoss reduces popularity bias in graph recommender systems by penalizing popular items in the training loss.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces PBiLoss to address the tendency of graph neural network recommenders to over-favor popular items, which limits personalization and creates unfair exposure for less popular content. It adds a regularization term to the standard training objective that discourages this bias through targeted sampling of popular positives and negatives. Two ways to mark items as popular are tested: a fixed threshold or a threshold-free adaptive approach. The resulting method plugs directly into existing models such as LightGCN. Experiments on three datasets show gains in fairness measures while accuracy stays unchanged.

Core claim

PBiLoss augments traditional training objectives by penalizing the model's inclination toward popular items, thereby encouraging the recommendation of less popular but potentially more personalized content. It introduces Popular Positive (PopPos) and Popular Negative (PopNeg) sampling strategies together with either a fixed popularity threshold or an adaptive distinction without threshold, and integrates as a model-agnostic regularization into graph-based frameworks.

What carries the argument

PBiLoss regularization term that penalizes popular-item preference via PopPos and PopNeg sampling and flexible popularity distinction.

If this is right

  • PRU and PRI fairness metrics drop by up to 10 percent relative to prior baselines.
  • Standard accuracy and ranking metrics remain intact across Epinions, iFashion, and MovieLens.
  • The same loss augments LightGCN and similar graph models without changes to their architecture.
  • Both fixed-threshold and threshold-free popularity marking give users of the method implementation choices.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same penalty idea could be applied to other recommendation biases such as position or demographic skew.
  • Greater exposure for tail items may raise long-term user satisfaction with niche content.
  • Online A/B tests measuring click-through rates on less-popular items would test whether offline fairness gains translate to real behavior.

Load-bearing premise

Penalizing popular items through PopPos and PopNeg sampling plus threshold or adaptive distinction improves fairness without introducing new biases or lowering representation quality.

What would settle it

A replication on a new dataset where PRU and PRI show no reduction or where accuracy falls below baseline levels would indicate the approach does not deliver the claimed benefits.

Figures

Figures reproduced from arXiv: 2507.19067 by Mohammad Naeimi, Mostafa Haghir Chehreghani.

Figure 1
Figure 1. Figure 1: The effect of w on PBiLoss [PITH_FULL_IMAGE:figures/full_fig_p024_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The effect of α on PBiLoss with fixed popularity threshold. the fixed popularity threshold method. For the regularization weight w, we explore a range of values from 0.05 to 0.0005 and examine their impact on both recommendation performance (e.g., NDCG, F1-Score) and fairness metrics (PRI and PRU). The results indicate that moderate values of w achieve an optimal balance between accuracy and fairness. Lowe… view at source ↗
read the original abstract

Recommender systems based on graph neural networks (GNNs) have been proved to perform well on user-item interactions. However, they commonly suffer from popularity bias -- the tendency to over-recommend popular items -- resulting in less personalization, unfair exposure and lower recommendation diversity. Current solutions address popularity bias through different stages of the recommendation pipeline, including pre-processing methods that may distort data distributions, in-processing approaches which can complicate optimization, and post-processing techniques that are limited in correcting bias already embedded in the learned representations. To address these limitations, we propose PBiLoss, a novel regularization-based loss function designed to explicitly counteract popularity bias in graph-based recommenders. PBiLoss augments traditional training objectives by penalizing the model's inclination toward popular items, thereby encouraging the recommendation of less popular but potentially more personalized content. We introduce two sampling strategies -- Popular Positive (PopPos) and Popular Negative (PopNeg) -- and explore two methods to distinguish popular items -- one based on a fixed popularity threshold and another without any threshold -- making the approach flexible and adaptive. Our proposed method is model-agnostic and can be seamlessly integrated into state-of-the-art graph-based frameworks such as LightGCN and its variants. Extensive experiments carried out on datasets including Epinions, iFashion, and MovieLens highlight the advantages of the PBiLoss for enhancing fairness in recommendations, decreasing PRU and PRI by up to 10\%, compared to other baseline models, while maintaining accuracy and other standard metrics intact in the process.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript proposes PBiLoss, a regularization-based loss function to mitigate popularity bias in graph neural network recommender systems. It augments objectives such as BPR with penalties derived from Popular Positive (PopPos) and Popular Negative (PopNeg) sampling, using either a fixed popularity threshold or an adaptive (threshold-free) distinction between popular and less popular items. The approach is presented as model-agnostic and integrable with frameworks like LightGCN; experiments on Epinions, iFashion, and MovieLens report up to 10% reductions in PRU and PRI fairness metrics while accuracy and other standard metrics remain comparable to baselines.

Significance. If the fairness gains prove robust, PBiLoss would provide a lightweight in-processing regularization that avoids distorting input distributions (pre-processing) or requiring separate post-hoc correction, while remaining compatible with existing GNN training pipelines. The dual sampling strategies and flexible popularity distinction add practical adaptability. The work is strengthened by its explicit integration into LightGCN-style models and evaluation across three distinct datasets, but its broader impact is limited by the absence of theoretical analysis of the modified optimization landscape.

major comments (3)
  1. [§5] §5 (Experiments): The reported reductions in PRU and PRI (up to 10%) are presented without statistical significance tests, error bars from multiple random seeds, or explicit details on baseline re-implementations and hyperparameter search procedures; this weakens the claim that accuracy is maintained while fairness improves, as post-hoc choices in popularity definition or sampling could influence the observed deltas.
  2. [§4] §4 (Method): The PBiLoss formulation introduces a regularization weight and a popularity threshold (or adaptive variant) as free parameters whose values directly control the strength of the penalty on popular items; no sensitivity analysis or ablation on how these parameters interact with graph degree distributions is provided, leaving open whether the fairness-accuracy trade-off generalizes beyond the three evaluated datasets.
  3. [§3–4] §3–4 (Sampling and Loss Construction): The central assumption that PopPos/PopNeg sampling selectively down-weights gradients for popular items without under-sampling high-degree nodes (which dominate LightGCN message passing) or altering long-tail item rankings is not supported by any closed-form analysis of the resulting stationary point or graph Laplacian; both the fairness improvement and accuracy preservation therefore rest entirely on the empirical outcomes for the specific degree distributions in Epinions, iFashion, and MovieLens.
minor comments (2)
  1. [Abstract] Abstract and §2: The definitions of the fairness metrics PRU and PRI should be stated explicitly at first use rather than assumed known, to improve accessibility for readers outside the immediate subfield.
  2. [§4.1] §4.1: Notation for the popularity distinction (threshold vs. adaptive) could be unified with a single equation or pseudocode block to clarify the two variants side-by-side.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback. We address each major comment below and outline planned revisions to strengthen the manuscript.

read point-by-point responses

  1. Referee: [§5] §5 (Experiments): The reported reductions in PRU and PRI (up to 10%) are presented without statistical significance tests, error bars from multiple random seeds, or explicit details on baseline re-implementations and hyperparameter search procedures; this weakens the claim that accuracy is maintained while fairness improves, as post-hoc choices in popularity definition or sampling could influence the observed deltas.

    Authors: We agree that statistical rigor would strengthen the claims. In the revised manuscript we will report all metrics averaged over five random seeds with standard deviations and error bars, include paired statistical significance tests (e.g., t-tests) for the observed fairness improvements, and expand the experimental section with explicit hyperparameter search ranges, grid-search details, and re-implementation notes for all baselines to improve reproducibility. revision: yes

  2. Referee: [§4] §4 (Method): The PBiLoss formulation introduces a regularization weight and a popularity threshold (or adaptive variant) as free parameters whose values directly control the strength of the penalty on popular items; no sensitivity analysis or ablation on how these parameters interact with graph degree distributions is provided, leaving open whether the fairness-accuracy trade-off generalizes beyond the three evaluated datasets.

    Authors: We acknowledge the value of sensitivity analysis for assessing generalization. We will add a new subsection with ablation studies varying the regularization weight λ and the popularity threshold (both fixed and adaptive variants) across the three datasets. These experiments will explicitly examine interactions with item degree distributions (e.g., by stratifying results on high- vs. low-degree items) to demonstrate robustness of the fairness-accuracy trade-off. revision: yes

  3. Referee: [§3–4] §3–4 (Sampling and Loss Construction): The central assumption that PopPos/PopNeg sampling selectively down-weights gradients for popular items without under-sampling high-degree nodes (which dominate LightGCN message passing) or altering long-tail item rankings is not supported by any closed-form analysis of the resulting stationary point or graph Laplacian; both the fairness improvement and accuracy preservation therefore rest entirely on the empirical outcomes for the specific degree distributions in Epinions, iFashion, and MovieLens.

    Authors: We recognize that a closed-form analysis of the modified stationary points or Laplacian would offer additional theoretical grounding. Our work is primarily empirical and model-agnostic; we will expand the discussion in §§3–4 to provide a more detailed qualitative justification of how PopPos/PopNeg sampling affects gradients and rankings, supported by degree-distribution statistics from the evaluated datasets. A full mathematical derivation of the optimization landscape, however, lies outside the current scope of the paper. revision: partial

Circularity Check

0 steps flagged

No significant circularity in PBiLoss proposal

full rationale

The paper introduces PBiLoss as a novel regularization loss that augments existing objectives (e.g., BPR) via new PopPos/PopNeg sampling and threshold-based or adaptive popularity distinction mechanisms. These components are explicitly defined as additions to the training pipeline and integrated into models such as LightGCN. Reported fairness gains (PRU/PRI reductions up to 10%) and preserved accuracy are presented solely as outcomes of experiments on Epinions, iFashion, and MovieLens. No equations, derivations, or claims in the text reduce any central result to a self-definition, a fitted parameter renamed as prediction, or a self-citation chain; the method is model-agnostic and rests on empirical validation rather than tautological construction.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard recommender system assumptions plus two tunable elements for defining and penalizing popularity; no new entities are postulated.

free parameters (2)
  • regularization weight for PBiLoss
    Strength of the added penalty term must be chosen or tuned to balance bias reduction against accuracy.
  • popularity threshold
    One variant uses a fixed threshold to label popular items; its value is data-dependent and affects sampling.
axioms (1)
  • domain assumption Popularity bias is primarily caused by over-representation of popular items in learned embeddings and can be mitigated by explicit penalization during optimization.
    Invoked to justify the regularization approach over data or post-processing alternatives.

pith-pipeline@v0.9.0 · 5816 in / 1224 out tokens · 49649 ms · 2026-05-19T02:53:15.061822+00:00 · methodology

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