Table 2: Comparisons of F1 scores for benchmark datasets and BIC for real-world datasets (backache, voting). BIC is not applicable to skeletons. The best and runner-up results are marked in bold. Significant differences are marked by  $\dagger$  (paired t-test,  $p < 0.05$ ).
Dataset	n	m	Noise	ζ	Wass	KL	Reg	MMPC	GRASP	Wass+HC	KL+HC	Reg+HC	MMPC+HC	GRASP+HC	HC
asia	8	1000	Noisefree	0	0.7800†	0.7285†	0.7897†	0.9067	0.8167	0.5123	0.6367	0.5743	0.6667	0.6583	0.6550
asia	8	1000	Huber	0.2	0.7333†	0.7124†	0.7297†	0.5468	0.6570	0.3943	0.3724	0.3487	0.2907	0.3664	0.2183
asia	8	1000	Independent	0.2	0.6933	0.6797	0.6868	0.6350	0.3932†	0.2676	0.2632	0.2581	0.2469	0.1204	0.2183
cancer	5	1000	Noisefree	0	1.0000†	1.0000†	1.0000†	0.6133	0.6333	0.2000	0.2629	0.2500	0.2800	0.2800	0.2800
cancer	5	1000	Huber	0.5	0.9156†	0.8933†	0.9092†	0.6133	0.5357	0.4333	0.3833	0.4143	0.2589	0.2714	0.2589
cancer	5	1000	Independent	0.2	0.9048†	0.9029†	0.8992†	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
earthquake	5	1000	Noisefree	0	0.8447†	0.9333†	0.9778	1.0000	0.9778	0.2000	0.2500	0.2500	0.2500	0.2500	0.2278†
earthquake	5	1000	Huber	0.2	0.7509†	0.7509†	0.7509†	0.5978	0.6583†	0.4618	0.4618	0.4618	0.3860	0.4547	0.3860
earthquake	5	1000	Independent	0.2	0.6786†	0.6350†	0.6350†	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
sachs	11	1000	Noisefree	0	0.8357†	0.8402†	0.8374†	0.9697	0.7678†	0.4310†	0.4535†	0.4641†	0.5935	0.4112†	0.5873
sachs	11	1000	Huber	0.2	0.7765	0.8064	0.7893	0.7498	0.5663†	0.5194	0.4815	0.4520	0.4736	0.2380	0.5028
sachs	11	1000	Independent	0.5	0.5268†	0.5208†	0.5172†	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
survey	6	1000	Noisefree	0	0.6596	0.6545	0.6506	0.6533	0.1714†	0.1789	0.1789	0.1789	0.1789	0.0571	0.1789
survey	6	1000	Huber	0.2	0.7303†	0.6778†	0.7095†	0.5396	0.3810	0.1444	0.1444	0.1444	0.1444	0.1516	0.1444
survey	6	1000	Independent	0.2	0.6311†	0.6705†	0.6220†	0.2032	0.0000†	0.1071	0.1071	0.1143	0.1071	0.1080	0.1071
alarm	37	1000	Noisefree	0	0.4750†	0.4533†	0.4533†	0.8525†	0.4533†	0.4533†	0.4533†	0.4533†	0.4533†	0.4533†	0.4533†
alarm	37	1000	Huber	0.2	0.1429†	0.1619†	0.6571†	0.5486	0.1945†	0.2192	0.1680†	0.3148	0.2774	0.2092†	0.2582
alarm	37	1000	Independent	0.2	0.1419†	0.1448†	0.5458†	0.4309	0.2830†	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
barley	48	1000	Noisefree	0	0.1521†	0.2632†	0.4913†	0.5847	0.5636	0.1995	0.1970†	0.2503	0.2510	0.2245	0.2526
barley	48	1000	Huber	0.2	0.1452†	0.1592†	0.4027†	0.4522	0.4000†	0.1396	0.1151	0.1658	0.1463	0.1530	0.1685
barley	48	1000	Independent	0.2	0.1463†	0.1501†	0.2767†	0.4273	0.4923†	0.0598	0.0769	0.0838	0.0727	0.0840	0.0838
voting	17	216	Noisefree	0	N/A	N/A	N/A	N/A	N/A	-2451.8631	-2453.2737	-2453.4091	-2475.5799	-2482.3835	-2456.1489
voting	17	216	Huber	0.2	N/A	N/A	N/A	N/A	N/A	-4418.9731	-4418.9731	-4487.4544	-4450.3941	-4445.0175	-4418.9731
voting	17	216	Independent	0.2	N/A	N/A	N/A	N/A	N/A	-4453.8298	-4453.8298	-4522.5521	-4465.1076	-4473.8612	-4453.8298
backache	32	90	Noisefree	0	N/A	N/A	N/A	N/A	N/A	-1729.8364	-1726.8465	-1710.7248	-1719.5002	-1713.7583	-1729.7991
backache	32	90	Huber	0.2	N/A	N/A	N/A	N/A	N/A	-3186.5001	-3186.5001	-3186.5001	-3186.5001	-3186.5001	-3186.5001
backache	32	90	Independent	0.2	N/A	N/A	N/A	N/A	N/A	-2800.9386	-2800.9386	-2800.9386	-2800.9386	-2800.9386	-2800.9386
connect-4_6000	43	6000	Noisefree	0	N/A	N/A	N/A	N/A	N/A	-38956.4300	-38956.4300	-38954.9501	-39004.8512	-39933.6041†	-38956.4300
connect-4_6000	43	6000	Huber	0.2	N/A	N/A	N/A	N/A	N/A	-99616.2848	-99616.2848	-102878.2766	-99673.5320	-100212.9773	-99616.2848
connect-4_6000	43	6000	Independent	0.2	N/A	N/A	N/A	N/A	N/A	-107403.2543	-107403.2543	-107403.2543	-107403.2543	-107403.2543	-107403.2543