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Explore advanced statistical frameworks for developing trustworthy machine learning systems through this comprehensive conference lecture that addresses critical challenges in privacy protection and uncertainty quantification. Delve into two major theoretical contributions: first, learn how Gaussian Differential Privacy (GDP) extends to general Riemannian manifolds using the Bishop-Gromov comparison theorem, with practical calibration methods including efficient procedures for one-dimensional manifolds and MCMC-based algorithms for constant-curvature spaces. Discover how this Riemannian Gaussian mechanism based on geodesic distance achieves improved utility compared to traditional Riemannian Laplace mechanisms, particularly demonstrated on spherical spaces. Second, examine innovative approaches to online inference for smoothed quantile regression, including incremental updating estimators for low-dimensional models and online debiased lasso techniques for high-dimensional sparse settings. Understand how these streaming-ready procedures use only current data and compact history summaries while correcting online approximation errors to deliver asymptotically valid confidence intervals and statistical tests. See practical applications through simulations and real-world data analyses including bike-sharing demand prediction and index-fund analysis that demonstrate the reliability and scalability of these methods. Gain insights into how these complementary advances provide essential components for trustworthy machine learning: privacy-preserving data access and statistically sound inference capabilities suitable for modern streaming environments.
