Title: Understanding Fairness and Prediction Error through Subspace Decomposition and Influence Analysis
Venue: NeurIPS 2025
Accepted: yes
Keywords: Algorithmic Fairness

Fairness–Utility Trade-off

Sufficient Dimension Reduction

Influence Functions
Abstract: Machine learning models have achieved widespread success but often inherit and amplify historical biases, resulting in unfair outcomes. Traditional fairness methods typically impose constraints at the prediction level, without addressing underlying biases in data representations. In this work, we propose a principled framework that adjusts data representations to balance predictive utility and fairness. Using sufficient dimension reduction, we decompose the feature space into target-relevant, sensitive, and shared components, and control the fairness–utility trade-off by selectively removing sensitive information. We provide a theoretical analysis of how prediction error and fairness gaps evolve as shared subspaces are added, and employ influence functions to quantify their effects on the asymptotic behavior of parameter estimates. Experiments on both synthetic and real-world datasets validate our theoretical insights and show that the proposed method effectively improves fairness while preserving predictive performance.


Peer reviews:
comments: SUMMARY:
This paper proposes sequential fair projection, a fairness-aware learning framework that (i) decomposes feature space via sufficient dimension reduction into three orthogonal sub-spaces (Y-specific, Z-specific, Y-Z correlated) and (ii) controls fairness-utility trade-offs by incrementally adding shared components to the projection. Theoretical guarantees and numerical justifications are provided.

STRENGTHS AND WEAKNESSES:
Strengths: The paper is well-written and easy to follow. The theoretical results are rigorous, with comprehensive numerical results. And the idea is also novel.

Weaknesses:  (i) The sensitive variable is binary in the theoretical and numerical results; (ii) The SDR may be costly for high-dimensional X; (iii) Finite-sample performance is not discussed.

QUESTIONS:
(i) How to extend the current results to the more general $Z$ settings other than the current binary one?

(ii) The SDR procedure may be costly for a high-dimensional covariate $X$. What is the complexity of your algorithm?

(iii) Is it possible to derive a finite sample guarantee (asymptotic results are already provided in the paper)?

(iv) Please discuss potential intersectional fairness. For example, multiple sensitive attributes exist.

LIMITATIONS:
Yes
TITLE: Official Review
CLARITY: 3
IMPACT: 3
ORIGINALITY: 3
DATE: 2025-06-22

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis work proposes a new approach to improve the fairness of algorithmic predictors by addressing the biases in the learned representations of the underlying data. The authors propose a novel approach using *sufficient dimension reduction* that decomposes the data space into sensitive attribute relevant, target variable relevant, and sensitive-target shared components. Using this decomposition, the work shows how the fairness-accuracy tradeoff can be navigated by leveraging these separate representation components. The authors provide a theoretical analysis and also empirically validate their approach on two popular fairness datasets.\n\nSTRENGTHS AND WEAKNESSES:\n## Strengths\n- The work provides a formal framework to study fairness from the perspective of representation subspaces by decomposing it into relevant subspaces. By having separate subspaces for sensitive features, target variable, and also having a subspace focused on the shared relations between the sensitive and target variables, the authors show how we can effectively navigate the accuracy fairness tradeoff.\n- The approach is theoretically well-motivated, and the authors also provide a detailed theoretical analysis of their approach regarding predictive error and fairness tradeoffs. After using SDR to reduce dimensionality and finding the relevant subspaces, finding the most optimal fair predictor reduces to finding the feature subset that can provide high accuracy and low unfairness.\n- Using synthetic data, the authors validate the theoretical results and show how increasing the number of shared components in the predictive process can improve the predictive performance *for all sensitive groups* but also *increase the performance gap* across the different groups, leading to potential unfairness.\n- The authors also show how their method is effective in achieving good accuracy and fairness results in two real-world datasets (Adult and Bank).\n\n## Weaknesses\n- Since this work is highly related to prior works on *fair representation learning*, a more thorough discussion and comparison with more fair representation learning works would have been effective to position the authors' approach. Specifically, it would have been nice to have a discussion and also comparisons to approaches that have looked at fair representation learning, representation disentanglement, e.g., [1] and [2]. Works that have looked at *causal representation learning*, e.g., the work in [3], could also be relevant for a discussion and/or comparison.\n- The author's approach relies on a linear SDR method, and it is unclear how well the method can work if it were necessary to extend it to more nonlinear or complex settings. To this end, the empirical evaluations are limited, focusing on only two tabular datasets without looking into image (e.g., CelebA) or text (e.g., BiasBios) datasets.\n- It would be nice to have an understanding of the efficiency of the proposed method when compared to competing approaches mentioned by the authors, e.g., AdvDebias, and other deep-learning-based representation learning approaches cited here.\n\n[1] Creager, Elliot, et al. \"Flexibly fair representation learning by disentanglement.\" International conference on machine learning. PMLR, 2019.\n\n[2] Louizos, Christos, et al. \"The variational fair autoencoder.\" arXiv preprint arXiv:1511.00830 (2015).\n\n[3] Yang, Mengyue, et al. \"Causalvae: Disentangled representation learning via neural structural causal models.\" Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. 2021.\n\nQUESTIONS:\n* How does the proposed approach's efficiency, specifically using SDR for dimension reduction, compare to other neural representation learning based approaches that look into disentanglement or fairness?\n* Can the proposed approach with linear SDR decomposition also be applied in conjunction with a strong representation learning method for vision and textual settings?\n\nLIMITATIONS:\nLimitations are not discussed in the main paper. However, a brief discussion on technical limitations is provided in the appendix.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-06-23"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nIn the present work, the authors introduce Sequential Fair Projection (SFP), a representation-level debiasing framework based on linear sufficient dimension reduction (SDR): the approach entails (i) decomposing the feature space into label-only, sensitive-only, and shared subspaces; (ii) supplying a family of projection matrices that can re-inject up to m shared directions to trade off fairness and accuracy; (iii) analyzing the prediction error vs distance covariance-based unfairness performance. The practical recipe proposed by the authors is to pick the smallest shared sub-space projection whose validation accuracy is at least 95 % of the original model's performance. The authors validate SFP on synthetic data and two tabular benchmarks (Adult and Bank), where it attains competitive fairness with modest accuracy loss.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths** \n- The manuscript tackles fairness within representations, a worthwhile direction supported by clear notation and an SDR-based derivation. \n- The presented influence-function analysis appears technically sound and may interest theory-minded readers. \n\n**Weaknesses**\n- The contribution feels somewhat incremental because prior work (e.g., Shi et al. 2024) already projects away sensitive subspaces, and iterative “add-back” heuristics are common in fairness fine-tuning. \n- Methodologically, all results hinge on linear SDR projections, both for disentangling and for intersecting subspaces. This assumption is not necessarily realistic in modern representation learning, yet taken for granted in the main (a quick discussion is presented in the limitation section at the end of the appendix). Quantifying the degree of departure from this hypothesis in realistic settings would seem to be a necessary discussion topic in this work.   \n- The empirical evaluations appear limited: experiments cover only two small tabular datasets; no large-scale or pretrained-model study supports the broader narrative, or the competitiveness of the proposed method. \n- The 95 % accuracy threshold and the feature-by-feature loop add a degree of arbitrariness and manual tuning (as many other methods that strike a balance between performance and fairness) and could largely increase computational cost in large-dimensional problems.\n- There are some repetitions and typos, and some observables that would be useful for the reader to interpret the empirical evaluation of the proposed method are left in the appendix.\n\nQUESTIONS:\nOn mixture of label/group information: Can the authors justify and empirically test the assumption that a linear projector might suffice when label and sensitive information are non-linearly entangled? What kind of issues could appear if there is a strong violation of this hypothesis?\n\nOn the chosen fairness-accuracy trade-off: Why choose the ad-hoc “≥ 95 % accuracy” cut-off? How sensitive are results to this hyperparameter? Is there some guarantee that one obtains the \"fairest\" model with that accuracy level? \n\nOn scalability in high-dimensional settings: What is the wall-clock cost of estimating SDR subspaces and looping over m on datasets at the scale of ImageNet, or transformer embeddings?\n\nOn the practical use of Theorems 5.2-5.4: How should a practitioner act on the given asymptotic variance bounds?\n\nEvaluation scope – Why restrict experiments to two small tabular datasets with binary sensitive attributes? Have the authors tried multi-attribute settings or modern vision/NLP benchmarks?\n\nAccuracy–fairness trade-off – On Adult, LR is far more accurate yet only moderately less fair. Could simpler post-hoc methods (e.g., threshold adjustment) close the gap?\n\nReproducibility – Code is promised, but hyper-parameters for SDR (slice count, rank estimation) and optimisation are missing from the main paper.\n\n4. Limitations (as I see them)\n\nLIMITATIONS:\nSome limitations are discussed in a paragraph at the end of the appendix. I believe that, in the spirit of transparency, they should be moved to the main text.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-06-30"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nIn this work the authors argue to look at fairness through representational decomposition, analyzing the separate subspaces\nof a model representation that contain information pertaining to a sensitive attribute, to a target variable, and to both. Their\nanalysis provides a method of interpolating between maximum utility (and worst fairness) and minimum utility (and best\nfairness) by removing more and more of the shared subspace between the two variables. Through extensive theoretical\nanalysis, they demonstrate the utility of their decomposition as a way to debias representations and propose an algorithm to\ncreate fair predictors.\n\nSTRENGTHS AND WEAKNESSES:\n## Strengths\n * The paper provides rigorous theoretical analysis of their approach, demonstrating that their approximation results in non-\nincreasing error for the Bayes predictor as they include more of the shared subspace. Additionally, the authors have\nexperiments (both synthetic and on real-world data) which validate the efficacy of their approach on established fairness\nmetrics.\n\n## Weaknesses\n * In the predictive settings evaluated in the paper, there are many existing (strong) methods for fairness. In fact, part of your\nargument is that moving beyond predictive intervention is important. I think a key piece of evidence missing in this paper is a\nsetting where predictive interventions fail, or where representational fairness is important.\n * Additionally , you may want to look to work on privacy and specifically the privacy funnel [1], where a similar task is at hand:\nhow can we modify X such that it provides no information about a private attribute Z while maintaining maximum utility for Y.\n\n[1] Calmon, F. P., Makhdoumi, A., & Médard, M. (2015, June). Fundamental limits of perfect privacy. ISIT 2015\n\nQUESTIONS:\n* How do these estimators scale with data and representation space size? In your setting you focused on dimensionality\nof 16 in the synthetic setting and of a similar scale for Adult. However, some of your feature embedding baselines scale\nup to LLM feature spaces on the order of hundreds if not thousands of dimensions. Would this method be competitive there?\n\nLIMITATIONS:\nThe authors have not discussed the limitations, but I do not think there are any critical points missing.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-03"}