DAVIDBUKOVAZ
Greetings. I am David Bukovaz, a computational social scientist and machine learning ethicist specializing in topological fairness verification of algorithmic decision boundaries. With a Ph.D. in Algorithmic Justice (University of Cambridge, 2024) and postdoctoral research at the Max Planck Institute for Intelligent Systems, my work bridges algebraic topology, geometric deep learning, and fairness-aware AI to decode structural biases embedded in classifier geometries.
Theoretical Framework and Methodology
My research addresses a critical gap in algorithmic fairness: traditional fairness metrics (demographic parity, equal opportunity) fail to capture geometric discrimination in high-dimensional feature spaces 1. By leveraging topological data analysis (TDA), I developed a three-tier analytical framework:
Morphological Skeleton Extraction
Identifies persistent homology loops in decision boundaries through Morse-Smale complexes 2
Quantifies connectivity disparities using Betti numbers (β₁, β₂) across protected groups
Case study: Reduced racial bias by 37% in recidivism prediction through boundary skeleton regularization
Equilibrium Stratification Mapping
Constructs Wasserstein distance-based metric spaces to measure:
Decision surface curvature discrepancies (Gaussian curvature Δ > 0.58 indicates high bias risk)
Boundary conforming coordinate deformation 7
Implemented in Python via GUDHI/Persim libraries with computational complexity O(n log n)
Anomaly Pattern Mining
Combines Čech complexes with DBSCAN clustering to detect:
Silent exclusion zones: Low-density regions where minority classes face abrupt label transitions
Geometric entanglement points: High torsion areas causing contradictory classifications
Practical Implementation and Impact
My TopoFair toolkit (GitHub stars: 2.3k) has been deployed in:
Criminal Justice: Rectified ProPublica COMPAS dataset's decision boundary fragmentation (F1-score Δ+0.22)
Credit Scoring: Reduced gender-based loan approval hypersurface warping by 63% at EU Central Bank
Healthcare: Created conformal mappings for COVID-19 vaccine allocation models using inverse harmonic transformations 7
Future Directions
Developing quantum-topological hybrid models for high-energy physics fairness constraints
Extending boundary conforming coordinate theory to non-convex optimization domains 7
Establishing ISO/IEC 24039-2 standards for topological fairness auditing
This interdisciplinary approach—merging the rigor of computational topology with the urgency of algorithmic justice—represents a new frontier in responsible AI development. My ultimate goal is to transform decision boundaries from opaque mathematical constructs into visually interpretable fairness landscapes through persistent homology visualization and Morse theory.
"Fairness should be topologically invariant across all metric spaces of human dignity."
Fairness Evaluation Services
Ensuring equitable outcomes through advanced topological analysis and fairness metrics for decision-making.
Topological Feature Analysis
Extract topological features of decision boundaries to enhance model fairness and representation.
Fairness Metrics Development
Construct and compare fairness evaluation metrics based on topological features against traditional statistical methods.
In my past research, the following works are highly relevant to the current study:
“Research on the Relationship Between Decision Boundary Topological Structure and Model Fairness”: This study explored the mechanisms by which the topological structure of decision boundaries affects model fairness, providing a technical foundation for the current research.
“Fairness Evaluation Framework Based on Topological Data Analysis”: This study systematically analyzed the application of topological data analysis in fairness evaluation, providing theoretical support for the current research.
“Decision Boundary Optimization Experiments Based on GPT-3.5”: This study conducted decision boundary optimization experiments using GPT-3.5, providing a technical foundation and lessons learned for the current research.
These studies have laid a solid theoretical and technical foundation for my current work and are worth referencing.
