Reasoning for Fairness: A New Approach to Bias in Machine Learning

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Author: Denis Avetisyan

Researchers are exploring the intersection of logic programming and deep learning to build machine learning models that are both accurate and demonstrably fair.

ProbLog4Fairness effectively models label, measurement, and historical biases, achieving performance comparable to systems trained without regard for fairness when evaluated on unbiased data, demonstrating its capacity to mitigate disparate impact without sacrificing overall accuracy.
ProbLog4Fairness effectively models label, measurement, and historical biases, achieving performance comparable to systems trained without regard for fairness when evaluated on unbiased data, demonstrating its capacity to mitigate disparate impact without sacrificing overall accuracy.

This paper introduces ProbLog4Fairness, a neurosymbolic framework leveraging probabilistic logic to model and mitigate bias, improving both fairness and accuracy compared to existing methods.

Defining and addressing algorithmic bias remains a significant challenge, as rigid fairness metrics often fail to capture nuanced, context-specific harms. This paper introduces ProbLog4Fairness: A Neurosymbolic Approach to Modeling and Mitigating Bias, a novel framework that formalizes bias assumptions as probabilistic logic programs, enabling flexible integration with neural networks. By explicitly modeling bias distortions, our approach demonstrably mitigates unfairness in both synthetic and real-world datasets, outperforming existing methods constrained by fixed bias definitions. Could this neurosymbolic approach pave the way for more transparent and adaptable fairness interventions in machine learning?

Unveiling Bias: The Pervasive Challenge in Machine Learning

Despite remarkable advancements, machine learning models are increasingly recognized for their capacity to replicate and even exacerbate existing societal biases. These systems, trained on vast datasets reflecting historical inequalities, can inadvertently learn and perpetuate discriminatory patterns across various domains, from loan applications and hiring processes to criminal justice and healthcare. For instance, facial recognition technology has demonstrated significant disparities in accuracy when identifying individuals from marginalized groups, while algorithms used in predictive policing may disproportionately target specific communities. This isn’t necessarily due to malicious intent in the model’s design, but rather a consequence of the biased data they ingest, leading to unfair or inequitable outcomes that reinforce systemic disadvantages. Consequently, a growing body of research emphasizes the crucial need to move beyond simply achieving high predictive accuracy and prioritize the development of fair and accountable algorithms.

Machine learning models are susceptible to bias not simply through flawed algorithms, but fundamentally through the data upon which they are built and how that data is interpreted. The data generation process itself often reflects existing societal inequalities; if historical data used to train a model contains prejudiced outcomes – for example, underrepresentation of certain demographics in loan approvals – the model will likely perpetuate those same biases. Furthermore, the very act of defining and measuring features can introduce bias; seemingly objective metrics may inadvertently encode subjective judgements or fail to account for systemic disadvantages. A feature intended to assess risk, for instance, could unfairly penalize individuals from historically marginalized groups if it relies on proxies correlated with discriminatory practices. Consequently, a model’s fairness isn’t solely a matter of algorithmic correction, but a critical examination of the entire data lifecycle, from collection to labeling and feature engineering.

The pursuit of high accuracy in machine learning, while historically a primary goal, is increasingly recognized as an incomplete metric for evaluating model success. A model can exhibit exceptional predictive power overall, yet simultaneously deliver systematically unfair or discriminatory outcomes for specific demographic groups. This discrepancy arises because accuracy measures average performance, masking disparities in error rates across different populations. Consequently, a demonstrably fair model isn’t simply one that predicts well, but one that exhibits equitable performance – comparable rates of both correct and incorrect predictions – across all relevant groups. This necessitates a move beyond solely optimizing for overall precision and towards incorporating fairness metrics and bias mitigation techniques as integral components of the model development process, ensuring that the benefits of machine learning are distributed equitably and do not exacerbate existing societal inequalities.

The pursuit of increasingly accurate machine learning models must now extend beyond mere predictive capabilities and actively incorporate the identification and reduction of inherent biases. Current methodologies often prioritize performance metrics without adequately considering the potential for discriminatory outcomes, leading to systems that perpetuate societal inequalities. A fundamental shift necessitates developing techniques that explicitly model the origins of bias – whether in data collection, feature engineering, or algorithmic design – and then implement strategies to mitigate these influences. This includes exploring fairness-aware algorithms, employing diverse and representative datasets, and establishing robust auditing procedures to ensure equitable performance across all demographic groups. Ultimately, the goal is not simply to build models that predict well, but to create systems that are demonstrably fair, accountable, and beneficial for all.

Our method effectively mitigates label bias when the data distribution and labels are not independent, achieving performance comparable to a baseline trained on unbiased data, as demonstrated by consistent accuracy and reduced statistical disparity under increasing bias probabilities.
Our method effectively mitigates label bias when the data distribution and labels are not independent, achieving performance comparable to a baseline trained on unbiased data, as demonstrated by consistent accuracy and reduced statistical disparity under increasing bias probabilities.

ProbLog4Fairness: Integrating Bias Awareness into the System’s Core

ProbLog4Fairness introduces a classification methodology that differs from traditional approaches by embedding bias mitigation directly within the model learning process. Utilizing ProbLog, a probabilistic logic programming language, and its deep learning extension, DeepProbLog, the system moves beyond treating bias as a post-processing step. This integration allows for the explicit representation of biasing factors – originating from data labeling, measurement inaccuracies, or historical trends – as probabilistic dependencies within a Bayesian network. Consequently, classification is performed by reasoning within this network, effectively incorporating bias awareness into each prediction rather than applying corrections after the initial classification outcome is determined.

The ProbLog4Fairness system addresses bias by representing its origins – whether in labeling practices, measurement inaccuracies, or systemic historical data – as explicit factors within a probabilistic logic model. This allows for the quantification of bias propagation through the prediction process. By modeling these sources of bias as probabilistic dependencies, the system can compute the likelihood of biased predictions given specific input data and model parameters. This facilitates analysis of how different bias sources contribute to unfair outcomes and enables the evaluation of mitigation strategies by observing their effect on the probabilistic reasoning process. Specifically, the system leverages Bayesian Networks to represent these dependencies, allowing for the calculation of conditional probabilities that reflect the impact of bias on predicted outcomes, and the identification of sensitive features contributing to unfairness.

Traditional fairness interventions often operate as post-hoc corrections applied to model outputs, potentially introducing distortions or failing to address systemic biases within the model itself. ProbLog4Fairness distinguishes itself by integrating fairness constraints and objectives directly into the learning process. This is achieved by formulating fairness criteria as logical constraints within the ProbLog framework, influencing the probabilistic reasoning and classification decisions from the outset. By embedding fairness considerations into the model’s core logic, the system aims to proactively mitigate bias during training, rather than reactively adjusting predictions after the fact. This approach allows for a more principled and transparent integration of fairness, enabling explicit control over the trade-offs between accuracy and fairness during model development.

ProbLog4Fairness leverages Bayesian Networks to model probabilistic dependencies between variables relevant to bias, including features, labels, and predicted outcomes. These networks, implemented and scaled using DeepProbLog and associated Neural Network architectures, allow for the representation of complex relationships and conditional probabilities. This enables the system to perform probabilistic inference, quantifying the influence of biased data or features on the final prediction. Specifically, the network structure captures how biases propagate through the classification process, allowing for reasoning about the likelihood of unfair outcomes given specific input conditions and learned parameters. The use of DeepProbLog facilitates learning the network parameters from data, while Neural Networks enhance the scalability and expressiveness of the model for complex datasets.

Accuracy and statistical disparity are maximized when the program's parameters are estimated using the correct bias probability, despite training on a fixed bias of 0.3 and evaluating on unbiased data, outperforming the upper baseline.
Accuracy and statistical disparity are maximized when the program’s parameters are estimated using the correct bias probability, despite training on a fixed bias of 0.3 and evaluating on unbiased data, outperforming the upper baseline.

Quantifying Fairness: Beyond Simple Metrics to Understand the Roots of Disparity

ProbLog4Fairness builds upon standard fairness metrics, such as Statistical Parity and Equalized Odds, by incorporating explicit modeling of bias sources. Traditional metrics often treat disparities as outcomes without detailing their origins; ProbLog4Fairness, however, represents these disparities as consequences of underlying probabilistic factors within the model. This approach allows for the identification and quantification of specific bias contributions, enabling a more granular understanding of unfairness. By modeling bias as a probabilistic component, the system moves beyond simply detecting disparity to analyzing why disparities occur, facilitating targeted mitigation strategies. This differs from approaches that treat fairness as a post-hoc constraint, instead integrating it directly into the model’s reasoning process.

Representing fairness as a probabilistic constraint allows for a more granular evaluation of disparities than traditional, deterministic metrics. This approach models fairness not as a binary condition, but as a distribution reflecting the likelihood of equitable outcomes given the input data and model predictions. By defining fairness as a probabilistic constraint – typically expressed as a lower bound on the probability of a favorable outcome for a protected group – the model explicitly accounts for uncertainty and variation in the data. This enables a more nuanced assessment, moving beyond simply identifying whether a disparity exists to quantifying the degree to which fairness is violated, as measured by the probability of constraint satisfaction. This probabilistic framing is crucial for handling real-world datasets with inherent noise and ambiguity, and facilitates a more accurate and reliable evaluation of fairness interventions.

Evaluations conducted on both synthetic and real-world datasets – specifically the Student dataset and the CELEB-A dataset – demonstrate that the ProbLog4Fairness approach achieves accuracy levels comparable to those of established upper baselines, even when subjected to various types of bias. This performance consistency was observed across different bias scenarios, indicating the method’s robustness in maintaining predictive power while addressing fairness concerns. Quantitative results show no statistically significant difference in accuracy between ProbLog4Fairness and the upper baselines under these conditions, validating its effectiveness as a bias mitigation technique without sacrificing overall model performance.

Evaluations on both the synthetic and real-world Student and CELEB-A datasets indicate that the ProbLog4Fairness method effectively reduces statistical disparity with bias mitigation. Specifically, observed disparity levels approached the pre-defined expected levels, demonstrating the model’s ability to align predictions with fairness constraints. This was achieved by explicitly modeling and mitigating sources of bias during the probabilistic inference process, resulting in a measurable reduction in unfair outcomes while maintaining predictive performance. Quantitative results confirm that the method successfully moves the model’s behavior towards the desired fairness target, as defined by the expected statistical disparity.

Evaluation on the Student dataset indicates an improvement in F1 Score when using ProbLog4Fairness with bias mitigation. Specifically, the model achieved a statistically significant increase in F1 Score compared to the baseline. On the CELEB-A dataset, performance with bias mitigation was comparable to the upper baseline, demonstrating no statistically significant difference in accuracy. These results suggest that the approach effectively addresses bias without sacrificing predictive performance on both synthetic and real-world datasets, maintaining comparable or improved accuracy metrics.

Our method effectively reduces label bias in facial feature detection, demonstrably improving F1 scores for unbiased 'Mouth Slightly Open' labels by leveraging combined biasing mechanisms and achieving statistically significant results as shown by the 95% confidence regions.
Our method effectively reduces label bias in facial feature detection, demonstrably improving F1 scores for unbiased ‘Mouth Slightly Open’ labels by leveraging combined biasing mechanisms and achieving statistically significant results as shown by the 95% confidence regions.

Toward Robust and Equitable AI: A Systemic Approach to Bias Mitigation

ProbLog4Fairness presents a novel approach to artificial intelligence development by directly incorporating the modeling of bias into the system’s foundational logic. Rather than treating fairness as a post-hoc correction, this framework proactively accounts for potential biases inherent in data and algorithms, leading to more reliable and equitable outcomes. By explicitly representing biases as probabilistic constraints, the system can evaluate and mitigate unfairness during the learning process itself, increasing the robustness of AI systems against discriminatory results. This proactive stance is particularly valuable in sensitive application areas, where biased algorithms can perpetuate or amplify existing societal inequalities, and offers a pathway towards building AI that consistently delivers fair and just predictions, even in the presence of imperfect or incomplete data.

The potential for biased outcomes in artificial intelligence carries particularly weighty implications within high-stakes domains like healthcare, finance, and criminal justice. In healthcare, algorithmic bias can lead to misdiagnosis or unequal access to treatment, disproportionately affecting vulnerable populations. Within financial systems, biased models may unfairly deny loans or insurance, perpetuating economic disparities. Perhaps most critically, the application of biased AI in criminal justice—such as in risk assessment tools—can exacerbate existing inequalities and lead to unjust sentencing or policing practices. These sectors demand a heightened level of scrutiny and mitigation strategies, as the consequences of algorithmic errors extend far beyond simple inconvenience, impacting fundamental aspects of human life and societal fairness. Addressing bias in these areas isn’t merely a technical challenge; it’s a moral and ethical imperative.

The efficacy of ProbLog4Fairness, and indeed many machine learning systems, is fundamentally linked to the quality of its input features, organized into a Feature Vector. However, this reliance introduces a critical vulnerability: Measurement Bias. Systematic errors during data collection or feature extraction can distort these vectors, leading to skewed model parameters and unfair predictions. Consequently, meticulous attention to feature engineering and data collection protocols is paramount. This includes careful consideration of how features are defined, measured, and preprocessed, alongside robust strategies for identifying and mitigating potential sources of bias in the raw data. Addressing this challenge requires not only statistical rigor but also a deep understanding of the domain from which the data originates, ensuring that the Feature Vector accurately reflects the underlying reality and doesn’t perpetuate existing inequalities.

Achieving genuinely fair and unbiased artificial intelligence necessitates a granular comprehension of how sensitive variables – characteristics like race, gender, or socioeconomic status – influence the very process by which data is created and collected. It’s not enough to simply remove these variables from a model; their impact often permeates the data itself, subtly shaping patterns and outcomes. Understanding this interaction—how historical biases, societal inequalities, or flawed data collection methods introduce systematic errors—allows for the development of mitigation strategies that address the root causes of unfairness. This requires careful consideration of the data generation process, including who is represented in the dataset, how information is recorded, and what assumptions underlie the measurement process, ultimately enabling the creation of models that are not merely free of explicit discrimination, but truly equitable in their predictions and impact.

A central challenge in developing fair and reliable AI lies in determining the necessary amount of data required for accurate parameter estimation, and recent work has formalized this through a derived relationship defining Sample Complexity as $n ≥ 1 / (2ε² ) ln(2 / (1 – γ))$ . This equation reveals a crucial trade-off: achieving higher accuracy ($ε$) or greater confidence ($γ$) necessitates a larger dataset ($n$). Specifically, diminishing returns are observed; as desired precision increases, the data requirements grow exponentially. This highlights that simply collecting more data isn’t always the most efficient solution, but rather a carefully considered balance between data volume, acceptable error, and the level of assurance needed for deployment, especially in sensitive applications where biased outcomes can have significant consequences. The formula provides a quantitative benchmark for researchers and practitioners to assess the feasibility and cost-effectiveness of achieving specific fairness and accuracy goals.

Our approach outperforms mitigation baselines in achieving a higher F1 score on unbiased labels, nearing the expected statistical disparity, and benefits from sensible simplifying assumptions as shown by the 95% confidence region.
Our approach outperforms mitigation baselines in achieving a higher F1 score on unbiased labels, nearing the expected statistical disparity, and benefits from sensible simplifying assumptions as shown by the 95% confidence region.

The pursuit of fairness in machine learning, as detailed in this work, necessitates a holistic understanding of system structure. ProbLog4Fairness embodies this principle by integrating probabilistic logic programming to model and address bias—a complex undertaking demanding attention to interconnected components. As Barbara Liskov aptly stated, “It’s one of the most powerful things about programming: you can take these abstract concepts and turn them into something real.” This rings true for ProbLog4Fairness; it transforms abstract fairness considerations into a concrete, implementable system. The method’s strength lies in its ability to represent causal relationships and dependencies, mirroring the idea that infrastructure should evolve without rebuilding the entire block. By carefully modeling these connections, the system can effectively mitigate bias without sacrificing accuracy, fostering a more robust and equitable outcome.

The Road Ahead

The introduction of ProbLog4Fairness represents, predictably, not a destination but an intersection. The system demonstrates an admirable attempt to bridge the symbolic and sub-symbolic, to impose logical structure upon the often-opaque workings of machine learning. Yet, one cannot simply graft reasoning onto a flawed foundation. The efficacy of this – or any – bias mitigation technique remains inextricably linked to the quality of the data itself. To treat bias as a purely algorithmic problem is akin to attempting to purify a polluted river by cleaning only the outflow.

Future work must address the limitations inherent in translating complex societal biases into probabilistic logical rules. The current framework, while expressive, risks oversimplification, potentially masking subtle forms of discrimination. More crucially, the emphasis should shift from merely detecting and correcting bias to proactively designing systems that are inherently robust to it. This necessitates a deeper understanding of how bias manifests not just in data, but in the very process of model creation and deployment.

Ultimately, the success of neurosymbolic approaches like ProbLog4Fairness will depend on recognizing that fairness is not a technical problem to be ‘solved’, but a continual process of refinement – a constant calibration of structure and behavior. The architecture must reflect the ethics it seeks to uphold, and any deviation from this principle will inevitably reveal the inherent fragility of the system.

Original article: https://arxiv.org/pdf/2511.09768.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

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2025-11-16 21:14