Persistence Landscapes Across Privacy Budgets for Explanation Methods Across Differential Privacy Mechanisms

Machine-learning credit scoring must be both auditable and privacy-preserving, yet post-hoc explainers may rely on sensitive records or privileged model access that privacy constraints restrict. We study how local explanations for a feed-forward neural-network credit-risk classifier on the Home Equity Line of Credit (HELOC) dataset change when the data or learning pipeline is sanitized with differential privacy (DP) using additive noise, DP-Stochastic gradient descent (SGD), synthetic data generation, and DP-principal component analysis (PCA). While Local Interpretable Model-agnostic Explanations (LIME), SHapley Additive exPlanations (SHAP), and gradient-based attributions are widely used, their behavior under DP-induced noise remains poorly characterized. Topology-based comparisons using Mapper and persistence summaries can capture explanation structure beyond per-feature averages, but they raise sensitivity and estimation challenges. To close this gap, we treat per-instance attribution vectors as a point cloud, build Mapper graphs using predicted probability as the lens, and convert them to persistence diagrams and persistence landscapes. We introduce a variance-reduced generalized control-variate Monte Carlo (CVMC) estimator for mean landscapes and an adaptive epsilon grid that concentrates computation where stability changes most. Across 49 explainer-mechanism combinations, mean landscapes vary smoothly with privacy budget and exhibit a small set of recurring motifs; in this setting, first-homology landscapes are consistently zero. These results suggest that privatized explanations can remain informative proxies for model behavior, enabling auditing without direct access to raw records and providing a measurable tool for monitoring privacy-interpretability trade-offs and explanation drift in regulated deployments.