Hard contamination scenarios

Question

Where do robust covariance estimators work, and where should users be cautious?

Design

This benchmark creates several contamination mechanisms:

• mean-shift outliers;

• clustered contamination;

• variance contamination;

• leverage contamination;

• heavy-tailed inliers.

These scenarios are intentionally not all favorable to MCD. The goal is to teach users when robust covariance assumptions match the data and when the geometry is ambiguous.

Results table

Hard contamination scenarios

scenario	contamination	method	rel_fro_error	seconds	support_purity	outlier_leakage	support_size	radial_kurtosis
mean_shift	0.2	robustcov FastMCD	0.1352	0.046352	1.0000	0.0000	786	142.4016
mean_shift	0.2	sklearn MinCovDet	0.1107	0.123946	1.0000	0.0000	786
variance	0.2	robustcov RegTyler	0.1087	0.000875				225.0001
variance	0.2	robustcov FastMCD	0.1341	0.044778	1.0000	0.0000	790	341.7775
heavy_tail_inliers	0.2	robustcov FastMCD	0.0886	0.046087				7.7035
heavy_tail_inliers	0.2	sklearn MinCovDet	0.1205	0.114427

Interpretation

Mean-shift and variance contamination are favorable settings for robust covariance. Clustered and leverage scenarios can be genuinely ambiguous: the algorithm may not be able to distinguish a bad cluster from a legitimate subpopulation without domain knowledge. This is why robust-distance plots and diagnostic reports are part of the package rather than optional decoration.

Run it yourself

python benchmarks/hard_contamination_scenarios.py --csv results/hard_scenarios.csv