Neural Computation
Due to bugs in the MCMC sampler for the IHM, IDM, IRM, and IRMCB models, the inference and predictions for these models were not correct. We have therefore revised the sampler in the toolbox accompanying the article and rerun the experiments of Tables
The new results show that the BCD outperforms the existing methods for about half of the considered networks, but not for the majority, as we originally stated (see the updated Table
Table 1: Network Properties and Results of Analysis.
Network Properties | Clusters | AUC [%] | |||||||
N | N+ | WGH. | DIR. | IRM | BCD | γ | IRM | BCD | |
USAir97 | 332 | 2126 | 14.4(2) | 19.0(3) | 1.00(0) | 95.2(14) | 94.5(15) | ||
USPowerGrid | 4941 | 6594 | 16.6(5) | 37.8(32) | 0.04(0) | 81.4(10) | 77.0(16) | ||
Football | 115 | 613 | 11.0(0) | 13.6(4) | 0.10(0) | 88.0(43) | 87.9(35) | ||
Celegans | 306 | 2345 | ✓ | ✓ | 36.8(10) | 29.8(9) | 1.00(0) | 88.7(8) | 89.1(2) |
yeast | 2361 | 6646 | 25.0(0) | 32.6(12) | 1.00(0) | 88.7(5) | 87.5(7) | ||
lesmis | 77 | 254 | ✓ | 12.6(4) | 12.4(4) | 0.99(1) | 93.0(39) | 94.2(27) | |
Geom | 7343 | 11898 | ✓ | 71.2(14) | 76.8(9) | 0.98(1) | 89.4(8) | 89.4(10) | |
netscience | 1589 | 2742 | ✓ | 8.2(2) | 8.4(2) | 0.89(4) | 59.5(21) | 65.7(24) | |
cond-mat | 16726 | 47594 | ✓ | 53.0(7) | 53.8(41) | 0.31(11) | 71.5(4) | 75.9(8) | |
SciMet | 3084 | 10413 | ✓ | 19.0(3) | 23.0(7) | 1.00(0) | 90.7(9) | 89.1(8) | |
smaGri | 1059 | 4919 | ✓ | 13.8(5) | 19.0(4) | 1.00(0) | 92.4(7) | 89.2(8) | |
smallW | 396 | 994 | ✓ | 8.8(2) | 11.4(5) | 1.00(0) | 99.1(3) | 98.3(5) | |
NIPS | 234 | 598 | 8.0(0) | 30.6(15) | 0.03(0) | 89.1(26) | 89.4(25) | ||
NIPSCW | 2865 | 4733 | ✓ | 32.0(4) | 85.6(23) | 0.01(0) | 90.4(12) | 89.7(5) |
Table 2: Area Under Curve (AUC) [%] Link Prediction Score.
BCD | BCD | |||||
IHW | IDM | IRM | IRMCB | Shared γ | Separate γ | |
USAir97 | 80.3(25) | 85.2(16) | 95.2(14) | 94.4(13) | 94.5(15) | 95.3(12) |
USPowerGrid | 75.8(11) | 74.4(19) | 81.4(10) | 82.9(13) | 77.0(16) | 80.7(17) |
Football | 84.4(41) | 84.7(38) | 88.0(43) | 88.2(36) | 87.9(35) | 88.6(41) |
Celegans | 57.9(21) | 57.6(27) | 88.7(8) | 89.2(6) | 89.1(2) | 88.9(5) |
yeast | 71.7(27) | 83.8(4) | 88.7(5) | 88.6(7) | 87.5(7) | 87.4(7) |
lesmis | 60.0(25) | 79.7(62) | 93.0(39) | 97.1(29) | 94.2(27) | 96.1(23) |
Geom | 70.8(20) | 73.4(5) | 89.4(8) | 88.8(4) | 89.4(10) | 90.1(7) |
netscience | 67.0(21) | 53.8(19) | 59.5(21) | 58.4(23) | 65.7(24) | 68.2(17) |
cond-mat | 65.4(8) | 64.1(5) | 71.5(4) | 68.5(3) | 75.9(8) | 74.5(16) |
SciMet | 74.0(6) | 80.9(5) | 90.7(9) | 90.5(6) | 89.1(8) | 89.6(6) |
smaGri | 71.4(9) | 82.8(10) | 92.4(7) | 92.4(5) | 89.2(8) | 89.3(5) |
smallW | 84.0(16) | 90.8(10) | 99.1(3) | 99.0(3) | 98.3(5) | 97.7(6) |
NIPS | 89.7(25) | 92.5(28) | 89.1(26) | 87.4(45) | 89.4(25) | 94.5(17) |
NIPSCW | 68.5(37) | 83.7(14) | 90.4(12) | 89.9(5) | 89.7(5) | 91.5(6) |
Table 3: Average per Iteration CPU Time.
BCD | BCD | |||||
IHW | IDM | IRM | IRMCB | Shared γ | Separate γ | |
USAir97 | 0.23(4) | 0.29(0) | 0.29(2) | 0.40(6) | 2.68(21) | 3.09(25) |
USPowerGrid | 1.83(3) | 2.42(3) | 3.96(38) | 5.34(38) | 64.13(376) | 69.01(479) |
Football | 0.04(0) | 0.06(0) | 0.07(0) | 0.08(0) | 0.74(4) | 1.11(6) |
Celegans | 0.23(4) | 0.18(1) | 0.37(4) | 0.55(7) | 4.63(44) | 5.32(43) |
yeast | 1.92(29) | 2.60(18) | 2.92(21) | 5.48(22) | 30.81(180) | 40.74(269) |
lesmis | 0.06(1) | 0.04(0) | 0.06(0) | 0.08(1) | 0.50(3) | 0.64(3) |
Geom | 9.73(120) | 9.44(141) | 16.92(383) | 31.09(742) | 188.23(1146) | 320.29(705) |
netscience | 0.62(5) | 1.25(5) | 2.09(9) | 2.54(15) | 15.92(93) | 17.72(99) |
cond-mat | 45.89(1566) | 46.60(1797) | 50.21(2068) | 72.85(187) | 245.70(2914) | 739.99(7486) |
SciMet | 2.30(32) | 2.58(4) | 3.82(5) | 6.87(42) | 57.39(399) | 63.27(367) |
smaGri | 0.86(16) | 1.07(3) | 1.15(2) | 2.01(23) | 14.83(76) | 14.47(37) |
smallW | 0.35(5) | 0.37(0) | 0.51(3) | 0.83(15) | 3.93(10) | 4.40(20) |
NIPS | 0.10(1) | 0.11(1) | 0.21(1) | 0.30(5) | 1.74(12) | 2.29(13) |
NIPSCW | 2.33(31) | 1.43(4) | 2.28(19) | 3.69(35) | 32.13(350) | 39.62(371) |