Avyukta Manjunatha Vummintala supervised by Dr. Sujit P Gujar received his Master of Science – Dual Degree  in Electronics and Communication Engineering (ECD). Here’s a summary of his research work on The Geometry of Fairness: Post-processing through ROC Spaces:

This thesis addresses the problem of achieving fairness in probabilistic binary classification in the presence of binary protected groups. In many practical scenarios, classifiers assign scores, and decision thresholds are applied post hoc based on the desired trade-off between false positives and false negatives. However, the use of a fixed classifier with arbitrary thresholds may result in disparate treatment across protected groups. To ensure equitable outcomes, we introduce a fairness criterion, denoted $\varepsilon_p$ equalized ROC, which requires that the $\mathcal{L}_p$ norm between the false positive rates (FPRs) and true positive rates (TPRs) of the protected groups remains within a predefined bound $\varepsilon$—regardless of the threshold chosen. To operationalize this notion of fairness, we propose a post-processing approach that transforms the outputs of an existing (potentially unfair) classifier into a randomized and threshold-agnostic classifier that satisfies $\varepsilon_1$ equalized ROC. Central to this approach is a novel threshold query model over ROC curves, which enables controlled manipulation of the classifier’s behavior across groups. We characterize the inherent trade-off between fairness and utility by deriving a theoretical lower bound on AUC loss and proving that some AUC reduction is inevitable under fairness constraints. To realize our fairness objective in practice, we develop a linear-time algorithm, FROC, which guarantees $\varepsilon_1$ equalized ROC compliance. We prove that under reasonable assumptions, FROC achieves optimality with respect to the minimal necessary AUC degradation. Extensive experiments on real-world datasets—using classifiers such as Weighted Ensemble L2, Random Forest (Gini), and FNNC—demonstrate that FROC is both theoretically sound and empirically effective across multiple fairness and performance metrics. The thesis is structured into six chapters, beginning with an introduction to algorithmic bias and culminating in theoretical analysis, algorithmic development, and empirical validation. Through this work, we contribute a principled and practical framework for ensuring fairness in score-based classification systems. 

June 2025