Table 2. Best known solutions to the benchmark problems
Problem Error of source model −L+λK Best known solutiona Solution of original problem (if available)
Error −L+λK Residual −L Structure FP/FN/LD Stability between runs Average time (s) (1 GHz) Structure FP/FN/LD Time (s) (1 GHz)
simpleLin1 8 8 0 0/0/0 5/5 17
simpleLin2 187.4 140.2 132.2 0/0/– 5/5 86
simpleFb1 7 7 0 0/0/0 5/5 14
simpleFb2 45.46 42.14 34.14 1/1/– 3/5 36
simpleFb3 7 7 0 0/0/0 3/5 41
simpleFb4 18.39 7.071 0.0713 0/0/– 2/5 47 0/0/– –
osc1 6 6.149 0.1491 0/0/0 5/5 18
osc2 122.1 87.34 57.34 0/0/0 4/5 24 – –
metabol1 30 30 0 0/0/0 3/3 5400
metabol2 1214 751.6 601.6 0/0/– 2/3 11 000
metabol3 1442 861.1 696.1 2/1/– 1/5b 13 000
3genes1 39 39 0 0/0/0 3/3 35 000
ss_cascade1 14 14 0 0/0/0 5/5 180 0/0/300 8900
ss_cascade2 14 14 0 0/0/0 4/5 130
ss_cascade3 498.9 476.7 462.7 1/1/– 1/5b 860
ss_branch1 17 17 0 0/0/0 5/5 68 0/0/15 2200
ss_branch2 17 17 0 0/0/0 5/5 110 0/0/5 35 000
ss_branch3 17 17 0 0/0/0 5/5 150 0/0/2 15 000
ss_branch4 17 17 0 0/0/0 5/5 71 0/0/0 25 000
ss_branch5 211.3 142.1 122.1 4/1/– 3/5 300 – –
ss_branch6 18 18 0 0/0/0 5/5 90 0/0/5 1100
ss_5genes1 23 23 0 0/0/0 5/5 600 1/0/– 2.4E+8
ss_5genes2 300.3 211.0 183.0 5/0/– 2/5b 2100
ss_5genes3 23 23 0 0/0/0 5/5 380
ss_5genes4 23 23 0 0/0/0 5/5 640 37/0/– 40 000
ss_5genes5 23 23.00 1.14E−3 0/0/0.02 5/5 400 4/2/– 7200
ss_5genes6 23 23 0 0/0/0 5/5 130 0/0/50 56 000
ss_5genes7 23 23 0 0/0/0 5/5 190 0/0/0.2 15 000
ss_5genes8 28 28 0 0/0/0 5/5 440 0/0/5 26 000
0/0/2.5 7000
ss_15genes1 62 62 0 0/0/0 5/5 1500
ss_15genes2 2010 1783 1478 3/4/– 2/5b 18 000
ss_30genes1 128 128 0 0/0/0 5/5 7900
ss_30genes2 4098 3628 2993 6/7/– 1/3b 94 000 242/10/– 6.2E+6
ss_30genes3 128 128 0 0/0/0 3/3 18 000 0/0/25 8.6E+6
cytokine1 25.92 17.92 1/5c 11 – –
cytokine2 42.17 32.17 1/5c 23
ss_ethanolferm1 127.4 110.4 1/5c 190 err>127.4d –
ss_ethanolferm2 1308 1292 1/5c 360
ss_sosrepair1 2642 2611 1/5c 510 err>2642d 2.7E+5
ss_sosrepair2 2823 2789 1/5c 470
ss_cadBA1 750.6 726.6 1/5c 250 err>750.6d >540
ss_cadBA2 709.1 687.1 1/5c 260
ss_clock1 928.4 803.4 1/5c 360 – 15 000
ss_clock2 814.5 649.5 1/5c 440
aBest known solutions, based on comparsion to the solutions of the original problems. For ss_30genes2, the similarity with the source model strongly indicates that our solution is the best, but since we do not have access to the solution of the original problem this is not confirmed.
b The majority of runs have an error below the error of the source model, but differ slightly in structure.
cReal datasets with relatively few experiments and/or data-points making many similar models reasonable, increasing the variability in found solutions.
dSince no source model is available, we have evaluated the original solution with our error function, and it has an error higher than our solution.
The error of the source model refers to the error of the model from which data was simulated. The best result is taken from several runs with various random seeds. The error, the negative log-likelihood and the number of false positives and negative (FP/FN) reactions are reported. Stability measures the frequency of runs for which the best structure is obtained. Computation time in seconds is given as the average of several runs.