Bayesian Fairness Regularization

Description

Bayesian Fairness Regularization incorporates fairness constraints into machine learning models through Bayesian methods, treating fairness as a prior distribution or regularization term. This approach includes techniques like Fair Bayesian Optimization that use constrained optimization to tune model hyperparameters whilst enforcing fairness constraints, and methods that add regularization terms to objective functions to penalize discriminatory predictions. The technique allows for probabilistic interpretation of fairness constraints and can account for uncertainty in both model parameters and fairness requirements.

Example Use Cases

Fairness

Using Fair Bayesian Optimization to tune hyperparameters of credit risk models, automatically balancing predictive accuracy with fairness constraints across different demographic groups whilst accounting for uncertainty in both model performance and fairness requirements.

Implementing Bayesian neural networks with fairness-aware priors for hiring recommendation systems, where uncertainty in fairness constraints is modeled probabilistically to ensure robust fair decision-making across different candidate populations.

Developing insurance premium calculation models using Bayesian fairness regularization to ensure actuarially sound pricing that meets regulatory fairness requirements, with probabilistic modeling of both risk assessment accuracy and demographic equity.

Reliability

Applying Bayesian regularization techniques to medical diagnosis models to ensure reliable performance across patient demographics, using probabilistic constraints to maintain consistent diagnostic accuracy whilst preventing algorithmic bias in healthcare delivery.

Limitations

Prior selection challenges make it difficult to specify appropriate prior distributions for fairness constraints, requiring domain expertise and potentially leading to suboptimal or biased outcomes if priors are poorly chosen.
Computational complexity increases significantly due to Bayesian inference requirements, including sampling methods, variational inference, or optimization over probability distributions, making the approach less scalable for large datasets.
Sensitivity to hyperparameters affects both the Bayesian inference process and fairness regularization terms, requiring careful tuning of multiple parameters that control the trade-off between accuracy, fairness, and computational efficiency.
Convergence and stability issues may arise in Bayesian optimization with fairness constraints, particularly when fairness objectives conflict with performance objectives or when the constraint space becomes highly complex.
Limited theoretical understanding exists for the interaction between Bayesian uncertainty quantification and fairness constraints, making it challenging to provide guarantees about both predictive performance and fairness under uncertainty.

Resources

Bayesian fairness

Research Paper•Dimitrakakis, Christos et al.•May 31, 2017

Foundational paper introducing Bayesian approaches to fairness under parameter uncertainty, demonstrating how Bayesian perspectives lead to fair decision rules

Fair Bayesian Optimization

Research Paper•Perrone, Valerio et al.•Jun 9, 2020

Constrained Bayesian optimization framework for optimizing ML model performance while enforcing fairness constraints through hyperparameter tuning

Fair Gaussian Processes

Software Package

MATLAB implementation of Fair Gaussian Processes with multiple fairness criteria support including statistical parity, equality of opportunity, and equalized odds

Fairness-Aware Classifier with Prejudice Remover Regularizer

Research Paper•Kamishima, Toshihiro et al.•Sep 24, 2012

Seminal paper introducing regularization-based approach to fairness in probabilistic discriminative models with mathematical framework for fairness constraints

Related Techniques

Name	Description	Assurance Goals
Prejudice Remover Regulariser	An in-processing fairness technique that adds a fairness penalty to machine learning models to reduce bias against protected groups. The method works by minimising 'mutual information' - essentially reducing how much the model's predictions reveal about sensitive attributes like race or gender. By adding this penalty term to the learning objective (typically in logistic regression), the technique ensures predictions become less dependent on protected features. This addresses not only direct discrimination but also indirect bias through correlated features. Practitioners can adjust a tuning parameter to balance between maintaining accuracy and removing prejudice from the model.	Fairness Transparency Reliability
Prototype and Criticism Models	Prototype and Criticism Models provide data understanding by identifying two complementary sets of examples: prototypes represent the most typical instances that best summarise common patterns in the data, whilst criticisms are outliers or edge cases that are poorly represented by the prototypes. For example, in a dataset of customer transactions, prototypes might be the most representative buying patterns (frequent small purchases, occasional large purchases), whilst criticisms could be unusual behaviors (bulk buyers, one-time high-value customers). This dual approach reveals both what is normal and what is exceptional, helping understand data coverage and model blind spots.	Explainability Fairness
Concept Activation Vectors	Concept Activation Vectors (CAVs), also known as Testing with Concept Activation Vectors (TCAV), identify mathematical directions in neural network representation space that correspond to human-understandable concepts such as 'stripes', 'young', or 'medical equipment'. The technique works by finding linear directions that separate activations of concept examples from non-concept examples, then measuring how much these concept directions influence the model's predictions. This provides quantitative answers to questions like 'How much does the concept of youth affect this model's hiring decisions?' enabling systematic bias detection and model understanding.	Explainability Fairness Transparency
Preferential Sampling	A preprocessing fairness technique developed by Kamiran and Calders that addresses dataset imbalances by re-sampling training data with preference for underrepresented groups to achieve discrimination-free classification. This method modifies the training distribution by prioritising borderline objects (instances near decision boundaries) from underrepresented groups for duplication whilst potentially removing instances from overrepresented groups. Unlike relabelling approaches, preferential sampling maintains original class labels whilst creating a more balanced dataset that prevents models from learning biased patterns due to skewed group representation.	Fairness Reliability Transparency
Feature Attribution with Integrated Gradients in NLP	Applies Integrated Gradients to natural language processing models to attribute prediction importance to individual input tokens, words, or subword units. This technique computes gradients along a straight-line path from a baseline input (typically all-zeros, padding tokens, or neutral text) to the actual input, integrating these gradients to obtain attribution scores. Unlike vanilla gradient methods, Integrated Gradients satisfies axioms of sensitivity and implementation invariance, making it particularly valuable for understanding transformer-based language models where token interactions are complex.	Explainability Fairness Safety
Equal Opportunity Difference	A fairness metric that quantifies discrimination by measuring the difference in true positive rates (recall) between protected and privileged groups. Based on Hardt et al.'s equality of opportunity framework, this metric computes the maximum difference in TPR across demographic groups, with a value of 0 indicating perfect fairness. The technique provides a mathematical measure of whether qualified individuals from different groups have equal chances of receiving positive predictions.	Fairness Transparency Reliability