Title: Fairness-aware Bayes Optimal Functional Classification
Venue: NeurIPS 2025
Accepted: yes
Keywords: Classification

excess risk

fairness

functional data
Abstract: Algorithmic fairness has become a central topic in machine learning, and mitigating disparities across different subpopulations has emerged as a rapidly growing research area. In this paper, we systematically study the classification of functional data under fairness constraints, ensuring the disparity level of the classifier is controlled below a pre-specified threshold. We propose a unified framework for fairness-aware functional classification, tackling an infinite-dimensional functional space, addressing key challenges from the absence of density ratios and intractability of posterior probabilities, and discussing unique phenomena in functional classification. We further design a post-processing algorithm Fair Functional Linear Discriminant Analysis classifier (Fair-FLDA), which targets at homoscedastic Gaussian processes and achieves fairness via group-wise thresholding. Under weak structural assumptions on eigenspace, theoretical guarantees on fairness and excess risk controls are established. As a byproduct, our results cover the excess risk control of the standard FLDA as a special case, which, to the best of our knowledge, is first time seen. Our theoretical findings are complemented by extensive numerical experiments on synthetic and real datasets, highlighting the practicality of our designed algorithm.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces a novel framework for fairness-aware functional classification, a rapidly growing area within machine learning that addresses disparities across subpopulations. The authors propose a unified approach to classify functional data while controlling the disparity level below a pre-specified threshold, overcoming challenges like the absence of density ratios and intractable posterior probabilities in infinite-dimensional functional spaces. They also develop a post-processing algorithm called Fair Functional Linear Discriminant Analysis (Fair-FLDA), designed for homoscedastic Gaussian processes, which achieves fairness through group-wise thresholding. The paper provides theoretical guarantees for both fairness and excess risk control for Fair-FLDA, including excess risk control for standard FLDA as a byproduct. Some numerical experiments on synthetic and real datasets validate the practicality of their proposed algorithm.\n\nSTRENGTHS AND WEAKNESSES:\n### Strengths\n\nThe theoretical analysis here is incredibly robust, spanning over 50 pages of proofs – I truly appreciate the authors' dedication to that! It's clear they've put a lot of effort into deriving numerous theoretical results, even tackling fairness guarantees. This feels like a significant theoretical step forward, as, to my knowledge, not many papers in this field offer theoretical guarantees for fairness-aware algorithms.\n\n---\n\n### Weaknesses\n\nFirst off, I have to point out that this paper leans heavily on theory (with proofs taking up pages 18 to 70 in the appendix!). Compared to all that intricate theory, the fairness background feels relatively straightforward. This makes me wonder why \"Social and economic aspects of machine learning\" was chosen as the Primary Area instead of \"learning theory,\" which seems like a much better fit for the paper's core.\n\nSetting aside the scope for \"Social and economic aspects of machine learning,\" I also found the paper's motivation a bit unclear and, at times, a little far-fetched.\n\n* For example, the logical connection between the second and third paragraphs in the introduction is weak. Paragraph 2 dives into functional classification, but then paragraph 3 jumps straight to the fairness issues of existing algorithms without explicitly linking them to \"functional classification.\" Why investigate fairness specifically within functional classification? That connection needs to be clearer.\n* Another point: the proposed post-processing algorithm assumes non-sensitive features are Gaussian processes, but there's no explanation for this choice. What's the rationale behind it? Is there existing literature that supports using Gaussian processes in this specific context?\n* Finally, the numerical experiments feel a bit limited, using datasets that aren't widely established in prior literature. I'm not entirely convinced that the setup in this paper will have a broad impact on the fairness community.\n\n**I want to emphasize that, if I've misunderstood anything, please correct me – I'm happy to adjust my rating accordingly! Thanks!**\n\n---\n\nOverall, this strikes me as more of a pure theoretical paper (specifically, a learning theory paper, rather than one focused on \"Social and economic aspects of machine learning\"), analyzing scenarios somewhat related to fairness. It's a bit outside my usual area, and I'm not familiar with some of the theoretical tools, so I can't really judge the novelty of the theoretical contributions. However, given that \"Social and economic aspects of machine learning\" is the chosen primary area, I think these concerns need to be properly addressed for the paper to truly resonate with the fairness community.\n\nQUESTIONS:\nHow does the fairness problem specifically manifest within functional classification, and what motivated this particular area of investigation?\n\nWhat is the justification for assuming Gaussian processes for non-sensitive features in the proposed algorithm, and what literature supports this choice in the functional fairness setting?\n\nWill the numerical experiments using less common datasets have a broad impact on the fairness community, and what are the authors' plans to address this?\n\nLIMITATIONS:\nN/A", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 2, "CLARITY": 1, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-06-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nIn this work the authors consider Bayes-Optimal classification of functional data. While the notions of fairness and Bayes-optimal classifiers does not change in any meaningful way, standard analysis of these results does not readily extend to functional data. For this the authors systematically develop the necessary tools and propose an algorithm Fair Functional Linear Discriminant Analysis classifier (Fair-FLDA) which is a post-processing algorithm to enforce fairness constraints in functional data. This requires a held-out calibration dataset of i.i.d. samples. The authors validate briefly on synthetic and real datasets.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:  \n\nThe problem of fair classification is a substantial one and in the context of medical applications (neuroscience or genetics) and legal decisions (perhaps based on hand-writing recognition) unfairness or discrimination can cause significant harm. The authors do a good job of motivating the project, though I would remove the White House line given the recent 180 shift from the White House along the lines the authors highlight. \n\nThe problem is comprehensively explored and clearly enumerated. The method the authors develop to improve fairness classification also seems to be reasonable (I was unable to check all details of their proofs). \n\nWeaknesses:\n\n  \nWhile the high-level motivation is clear and the transition between each of the derivations is clear, there are several key aspects that I am unclear on. Additionally, I find the experimental validation to be below standard. I enumerate my questions about some areas that lack clarity below:   Are there any works that establish unfairness of classifiers on functional data in particular? The problem of fairness is an important one, but practically the actual problem solved by this paper seems minimal and the experimental validation is lacking.   The authors to not label their axes, provide any legend, or properly outline their experimental set up. Additionally, there are many post- and pre- processing fairness method that would clearly work in this setting and the authors make no attempt (as far as I can see) to discuss or benchmark against them. Without this the evaluation of the paper is incomplete. Why are no pre-processing e.g., reweighing considered as baselines?   In real-world settings how much does the need for calibration data affect the results? As it seems most functional datasets are of limited size, and if you have to split into test, train, validation, and calibration datasets does this not substantially reduce the utility of the proposed approach? This also may need to be explored.   Perhaps this is too harsh of a phrasing, but the communication both in the figure and description of the experimental section is significantly inadequate to understand (1) the scope of fairness issues in the context, (2) the performance of the proposed method versus baselines, (3) the robustness of the proposal to various assumptions. I am happy to hear the counter arguments by the authors on these points and change my mind if they are compelling.\n\nQUESTIONS:\nSee questions in the weaknesses sections.\n\nLIMITATIONS:\nThe empirical validation of this approach is substantially below what we should expect.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-03"}

comments: SUMMARY:
This paper introduces the first framework for fairness-aware classification in the context of functional data analysis (FDA). The authors provide a theoretical characterization of the Bayes-optimal fair classifier under disparity constraints (Theorem 2), propose a practical post-processing algorithm (Fair-FLDA), and establish high-probability guarantees for both fairness satisfaction (Theorem 3) and excess classification risk (Theorem 5). This work bridges the gap between algorithmic fairness and FDA, a domain where fairness considerations have not been previously explored. The mathematical development is rigorous, and the results generalize known finite-dimensional theories to the functional setting.

STRENGTHS AND WEAKNESSES:
Strengths: 
1. The idea of fairness-aware functional classification is new and important for the FDA community, and the paper makes the first steps to address it in a principled way. 
2. The theoretical results are sound – they appear to be derived correctly and with appropriate conditions, and they generalize known results.

Weaknesses:
1. While the paper is carefully crafted and mathematically rigorous, the core methodology—such as group-wise threshold adjustment grounded in the Neyman–Pearson principle and use of Radon–Nikodym derivatives—builds upon existing techniques in fairness-aware classification and functional data analysis. The novelty primarily lies in thoughtfully adapting and unifying these tools in the functional setting, rather than proposing fundamentally new statistical models or algorithmic paradigms.
2. Limited diversity in real-world functional datasets; generalizability to broader FDA applications is not demonstrated.

QUESTIONS:
Please see weaknesses.

LIMITATIONS:
N/A
TITLE: Official Review
CLARITY: 3
IMPACT: 3
ORIGINALITY: 3
DATE: 2025-07-04

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper addresses fairness-aware binary classification for functional data by introducing a post-processing algorithm called Fair Functional Linear Discriminant Analysis (Fair-FLDA). The main contributions include theoretical guarantees on fairness and excess risk control under homoscedastic Gaussian processes, and a novel analysis of eigenspace estimation effects on classification performance. The work provides both theoretical foundations with finite samples and algorithmic implementation, validated through synthetic and real data experiment.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths:**\n1. Novel theoretical contribution combining fairness and functional data analysis, with comprehensive guarantees under weak assumptions\n2. Clear theoretical connections to both FDA and fairness literature and strong motivation of the topic\n\n**Weaknesses:**\n\n1. Limited empirical validation (single synthetic/real dataset) and missing comparisons with adapted existing fairness methods\n2. Lack of justification against simpler alternatives (e.g., dimensionality reduction + standard fair classification)\n3. Practical limitations: In many cases, sensitive attributes may not be avilalbe during both training and testing. Also, missing discussion on multi-class sensitive attribute (e.g., race, age category, etc.)\n4. Concerns around eigenspace estimation reliability and computational efficiency\n\nQUESTIONS:\n1. Why choose this sophisticated approach over simpler alternatives (e.g., dimension reduction + standard fair classification)?\n2. How does the method scale computationally and handle practical challenges (eigenspace estimation, noisy/missing sensitive attributes)?\n3. Can the framework extend to multiple sensitive attributes or multi-class classification?\n4. Can we compare the proposed method with standard fairness methods adapted to functional data?\n\nLIMITATIONS:\n1. Limited empirical evaluation (multiple datasets, baselines, adapted fairness methods) and lack of justification on this\n2. Justification against simpler alternatives\n3. Analysis of practical limitations and computational efficiency\n4. Broader applicability (multiple attributes, missing data scenarios)", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 4, "ORIGINALITY": 2, "DATE": "2025-07-09"}