Variable Selection in the Context of AI Fairness

Summary

The paper Variable Selection in the Context of AI Fairness by Ivan Luciano Danesi, Chiara Frigerio, Fabio Maccaferri, Giorgio Alessandro Motta, and Pietro Zecca addresses the challenge of fairness in AI systems, particularly in the context of variable selection and the exclusion of sensitive attributes. The authors argue that traditional approaches to fairness, such as fairness through unawareness (excluding protected attributes from models), are insufficient and can paradoxically introduce or perpetuate bias.

The paper's contributions are threefold: (1) discussing current efforts to understand fairness beyond mathematical and statistical analysis, (2) bridging theory and practice by discussing fairness auditing and compliance with international standards such as the EU AI Act, and (3) presenting a mathematical approach illustrating conditions under which retaining all variables, including sensitive ones, may lead to fairer classification outcomes.

The authors emphasize that fairness is a multifaceted, context-dependent concept that cannot be fully captured by statistical formulas alone. They cite Verma and Rubin (2018), who note that the question Is the classifier fair? depends critically on which definition of fairness one adopts, including measures such as demographic parity, equal opportunity, and individual fairness. They also reference Benthall and Haynes (2019), who argue that even the categories used in machine learning, particularly racial categories, can embed historical biases and oversimplify complex social constructs.

The paper highlights that eliminating sensitive variables does not necessarily prevent discriminatory outcomes, as seemingly neutral features—so-called proxy variables—can encode and perpetuate social biases due to high correlation with protected attributes. Examples include credit scoring, where postal code, employment history, or consumer spending patterns act as proxies for race and socioeconomic background; healthcare, where risk prediction algorithms using spending as a feature undermined fairness; and employment, where gender is indirectly reintroduced through educational institutions or extracurricular activities.

The regulatory landscape is discussed, noting that the GDPR, in force since May 2018, establishes guidelines for data collection and processing, emphasizing data minimization. The European AI Act, a more recent initiative, creates a regulatory framework for AI systems, aiming to safeguard fundamental rights, ensure safety and transparency, and mandate measures against unfair bias in high-risk AI systems. The authors compare these with regulations in the USA and Asia, noting that the EU AI Act is likely to set a global standard for AI regulation.

The methodology involves a pre-literature review conducted using digital libraries such as Elsevier, Google Scholar, and Scopus, following the strategies of Rowley and Slack (2004). The initial research yielded over 50,000 results using keywords such as AI ethics, AI fairness metrics, Explainable AI, AI transparency, Robust AI, Fairness in AI-driven decision making, Sustainable AI in business ecosystem, AI Act EU, Federated learning for privacy, Differential privacy in AI, AI auditing frameworks, Discrimination, Trade-offs in fair AI, social impact of AI, ethics and AI. A further selection of articles was performed using recommendations that articles should be relevant, up to date, have extensive sources referencing, and be written by an authoritative author, resulting in a final set of 33 papers.

The research question is formulated as: "Given a data set D, the fairness assessment of the classifier c can be addressed with a higher level of reliability awareness as the variables of the learning data set D′ (D′ ⊆ D) potentially pertinent to the purpose of the application of the classifier increase without a priori screening and elimination actions." The hypothesis states that the training data set D of a classifier C should be consistent and represent the available operational reality as completely as possible. The authors recommend an initial training phase with the full dataset D to ensure the model incorporates all observed data distributions, mitigating the risk of overlooking minority group patterns.

The paper discusses the distinction between bias and fairness, noting that bias is a systematic error leading to skewed results, while fairness involves normative principles related to justice and equity. Addressing bias often means correcting data imbalances, but fairness requires a broader ethical consideration throughout the AI lifecycle. The authors present various fairness definitions, including fairness through unawareness, demographic parity, equality of opportunity, individual fairness, group fairness, and subgroup fairness.

The core mathematical framework is presented in Section 3. The authors define a classifier C that satisfies fairness through unawareness if the prediction function excludes sensitive attributes from its input. They consider a synthetic dataset of 100,000 entries where all characteristics remain constant except for the sensitive attribute, and argue that if predictions remain identical regardless of variations in the sensitive attribute, the variable could be excluded without compromising predictive performance. However, they note that numerous situations exist where the removal of certain variables affects model behavior.

The mathematical argument proceeds as follows: Let D be an optimized training sample for a generic AI model M, with m, n ∈ N, n ≥ m denoting the number of predictors in D and in a subset D′ ⊂ D obtained by removing n − m variables. Using step forward feature selection, a finite sequence of models Mk is generated. Error optimization (e.g., MSE) allows choosing a subset of cardinality k̄ so that Mk̄,X̄k̄ makes the smallest mistake εk̄. Since D′ is arbitrarily chosen among subsets of assigned cardinality n ≤ m, the authors assume without loss of generality that εn ≥ εk̄.

Let X be the set of variables vectors V representing the population of p subjects on which the classifier C has been trained. Let S be the set of sensitive variables, such that S ⊂ V, then V S = V′. Training the classifier on V′ is not optimal since it results in higher error values. The authors claim that excluding sensitive variables during training is counterproductive because the information loss may affect fairness as well.

Let M and M′ be the outcomes of the classifier C trained on V and V′ respectively. Let Θ be the family of all possible fairness definitions, and ∆ identifies a specific class of subjects potentially discriminated by classification choices. Assessing fairness of a classifier C is equivalent to defining a real valued function fθ,∆ for any θ ∈ Θ and ∆. Since training M is optimal, any other choice including M′ is suboptimal in terms of error, meaning reducing significant information can introduce a higher level of bias.

The bias affects classification in three possible ways: (1) the trained model M′ is less fair than model M (fθ,∆(V, M) ≥ fθ,∆(V′, M′)), (2) the trained model M′ is as fair as model M (fθ,∆(V, M) = fθ,∆(V′, M′)), or (3) the trained model M′ is more fair than model M (fθ,∆(V, M) ≤ fθ,∆(V′, M′)). The authors conclude that the model M trained on V (all variables) is usually preferable or, at worst, equivalent (2 of 3 conditions), justifying the recommendation to train on all variables to optimize predictive performance before evaluating fairness.

Furthermore, if in the third scenario, knowledge of sensitive features allows identification of subjects vi that are fairly classified by M′ but not by M, a new outcome M̃i can be defined that classifies vi fairly while maintaining fθ,∆(V, M̃i) ≥ fθ,∆(V, M) and ε̃i ≥ ε, where ε is the mean square error. By iteration, an outcome M̃ is obtained such that ε ≤ ε̃ ≤ ε + (max∆(M′(vj) − ŷj)2 / p) · card(∆).

The authors advocate for using a model that considers all variables and excludes them based on objective criteria such as error optimization (e.g., MSE). If optimization excludes sensitive variables, they would either have low predictive impact or induce bias, and therefore would not statistically significantly affect the model's decisions or its fairness. Subsequent fairness tests operate on an optimized set of variables with reduced risk of implicit correlation.

In conclusion, the paper demonstrates that excluding critical variables in AI models leads to a potential loss of fairness and explainability. Mathematical measures offer essential tools for assessing algorithmic fairness but do not fully encapsulate the philosophical and sociological essence of fairness. AI models represent only a limited subset of reality, and making fair decisions requires accounting for social implications. The findings align with the objectives of the EU AI Act, which seeks to promote trustworthy and fair AI systems, but the authors advocate for a holistic approach merging mathematical rigor with philosophical ethics and social awareness.

Future research directions include investigating the integration of philosophical theories of fairness and comparative legal frameworks into AI system design, emphasizing empirical studies that provide qualitative analysis of social impacts, unintended consequences, and trade-offs, and conducting long-term studies to evaluate how AI influences social outcomes, trust, and perceptions.

Based on the paper, here are the specific improvements that can be made to AI systems and the resulting capabilities:

1. Replace Fairness through Unawareness with Fairness through Comprehensive Inclusion

• Current flaw: Systems that exclude sensitive attributes (e.g., race, gender) from input features often fail to achieve fairness because proxy variables (e.g., postal code, spending patterns) reintroduce bias indirectly.

• Improvement: Train the model initially on the full dataset including all sensitive and non-sensitive variables. Only after optimizing for predictive error (e.g., MSE) should fairness assessments be performed.

• Resulting capability: The model captures nuanced relationships and avoids implicit bias from proxy correlations, while still allowing for post-hoc fairness evaluation.

2. Implement a Two-Stage Fairness Optimization Protocol

• Stage 1: Optimize classification error using all available predictors (no a priori variable elimination).

• Stage 2: Apply fairness metrics (e.g., demographic parity, equality of opportunity) to the optimized model. If unfairness is detected, use a targeted adjustment—not variable removal—to correct for specific subgroups.

• Resulting capability: The system maintains high predictive accuracy while achieving measurable fairness, avoiding the suboptimal error trap of variable exclusion.

3. Introduce a Fairness-Aware Error Bound for Model Adjustments

• Improvement: When a model trained on all variables is less fair than a reduced model for a specific subgroup, adjust the prediction for that subgroup individually, with a provable error bound:

• ε ≤ ε̃ ≤ ε + (max∆(M′(v j) − ŷ j)2 / p) · card(∆)

• Resulting capability: The system can correct unfair classifications for specific subgroups without degrading overall model performance beyond a mathematically guaranteed limit.

4. Build an Intersectional Fairness Monitoring Module

• Improvement: Instead of evaluating fairness only on single protected attributes, implement subgroup fairness checks that consider intersections (e.g., race × gender × age).

• Resulting capability: The system detects and mitigates bias that would otherwise be invisible when examining each attribute in isolation, aligning with the paper's emphasis on subgroup fairness.

1. Detect hidden proxy bias: It can identify when non-sensitive variables (e.g., ZIP code, education level) act as proxies for protected attributes, and flag these for human review.

2. Provide explainable fairness decisions: By retaining all variables, the system can explain why a decision was made (e.g., which features contributed most), rather than providing a black-box outcome after variable removal.

3. Guarantee bounded fairness corrections: When fairness adjustments are made, the system can mathematically guarantee that the increase in prediction error stays within a specified limit, preventing overcorrection that harms overall accuracy.

4. Comply with EU AI Act and GDPR: The system can demonstrate that it did not arbitrarily exclude variables, but instead used objective statistical criteria (error optimization) to select features, while maintaining transparency and auditability.

5. Support counterfactual fairness testing: The system can generate synthetic datasets where only the sensitive attribute changes, and verify whether predictions remain stable—if they do not, it flags potential discrimination.

6. Enable iterative fairness auditing: After initial training on all variables, the system can run fairness tests and, if needed, apply targeted corrections to specific subgroups, then re-audit—creating a closed-loop fairness improvement process.

Concrete example of improved behavior: In a credit scoring model, instead of removing gender and unknowingly using occupation as a proxy, the improved system would:

• Train on all features (including gender).

• Optimize for loan default prediction accuracy.

• Test for demographic parity across gender groups.

• If unfairness is found, adjust predictions for the disadvantaged group using the bounded error correction formula.

• Report to regulators that fairness was achieved through targeted correction, not through blind variable removal.