Clayton Scott
EECS and StatisticsUniversity of Michigan
Robust Kernel Density Estimation
Kernel Density Estimate
KDE = mean in RKHS
Robust Kernel Density Estimate
Robust Multivariate Mean
Majorization / Minimization
Iterative Re-Weighted Least Squares
IRWLS Computation
Kernel IRWLS Convergence
Representer Theorem
Robustness Interpretation # 1
Connection to Data Depth
Influence Function
Influence Function
Influence Function
Robustness Interpretation # 2
Asymptotics: σ fixed
Asymptotics: σ fixed
Robustness Interpretation # 3
Asymptotics: σ → 0
Example: Hampel Loss
Anomaly Detection
Anomaly Detection
Anomaly Detection: AUC versus ε
Anomaly Detection: AUC versus ε
Anomaly Detection: AUC versus ε
Anomaly Detection: AUC versus ε
Anomaly Detection: AUC versus ε
Anomaly Detection: AUC versus ε
Robustness Interpretation # 4:
Extensions / Open Questions
Anomaly Detection: Average Ranks