Table 1:
Simulation results for linear regression. PMSE: prediction mean squared error. TP: true positives, FP: false positives; number of informative nodes in Type 1 network is 22; number of informative nodes in Type 2 network is 12.
| Method | PMSE | TP | FP | AUC | PMSE | TP | FP | AUC |
|---|---|---|---|---|---|---|---|---|
| Type 1 p = 33 | Type 1 p = 110 | |||||||
| Lasso | 52.3(1.6) | 20.6(0.2) | 7.3(0.3) | 0.778(0.006) | 71.6(1.9) | 17.2(0.3) | 19.6(1.2) | 0.792(0.005) |
| Elastic-net | 50.9(1.4) | 21.8(0.1) | 10.4(0.2) | 0.788(0.004) | 73.7(1.8) | 19.6(0.3) | 46.6(2.9) | 0.811(0.004) |
| Grace | 56.8(1.5) | 21.6(0.1) | 10.1(0.2) | 0.864(0.007) | 87.5(2.0) | 17.9(0.4) | 37.5(2.5) | 0.897(0.004) |
| aGrace | 53.7(1.5) | 22.0(0.0) | 10.7(0.1) | 0.875(0.007) | 76.4(2.1) | 20.6(0.3) | 65.9(3.6) | 0.899(0.005) |
| L∞ | 51.4(1.5) | 21.8(0.1) | 8.9(0.4) | 0.970(0.006) | 66.5(1.7) | 21.5(0.2) | 22.7(1.5) | 0.973(0.005) |
| aL∞ | 54.2(1.3) | 21.8(0.1) | 8.2(0.6) | 0.669(0.034) | 63.5(1.5) | 21.5(0.2) | 19.6(1.4) | 0.946(0.010) |
| TTLP | 54.3(1.6) | 21.9(0.0) | 10.1(0.4) | 0.834(0.019) | 72.6(2.0) | 20.9(0.4) | 44.2(4.6) | 0.920(0.004) |
| LTLP | 51.3(1.2) | 22.0(0.0) | 8.8(0.6) | 0.933(0.005) | 67.1(1.7) | 21.5(0.2) | 57.6(2.7) | 0.897(0.009) |
| BRGL | 51.0(1.3) | 19.5(0.2) | 4.1(0.3) | 0.883(0.008) | 79.7(1.8) | 17.9(0.2) | 22.1(0.9) | 0.867(0.006) |
| Ising(b=7) | 54.9(3.0) | 19.7(0.7) | 2.9(0.7) | 0.925(0.017) | 94.9(5.9) | 15.1(0.9) | 33.9(2.4) | 0.786(0.023) |
| TGLG-I | 50.1(1.3) | 21.9(0.1) | 10.7(0.2) | 0.863(0.010) | 81.4(2.1) | 14.8(0.5) | 22.6(2.6) | 0.779(0.009) |
| TGLG-F | 45.2(1.2) | 22.0(0.0) | 2.2(0.6) | 0.912(0.032) | 63.9(2.8) | 19.7(0.4) | 17.8(2.9) | 0.899(0.016) |
| TGLG-L | 46.0(1.3) | 21.9(0.1) | 1.7(0.5) | 0.968(0.016) | 74.1(2.4) | 17.1(0.5) | 19.3(2.7) | 0.847(0.013) |
| Type 2 p =33 | Type 2 p = 110 | |||||||
| Lasso | 23.1(0.6) | 11.7(0.1) | 11.8(0.6) | 0.830(0.006) | 30.6(0.8) | 9.5(0.2) | 19.1(1.1) | 0.826(0.007) |
| Elastic-net | 23.4(0.6) | 11.8(0.1) | 15.4(0.6) | 0.802(0.006) | 31.4(0.9) | 10.6(0.2) | 34.0(2.1) | 0.818(0.006) |
| Grace | 25.8(0.6) | 11.4(0.1) | 14.7(0.6) | 0.813(0.005) | 35.2(0.8) | 9.1(0.2) | 25.8(1.9) | 0.855(0.005) |
| aGrace | 25.9(0.7) | 12.0(0.0) | 20.3(0.3) | 0.868(0.006) | 32.8(0.8) | 11.6(0.1) | 73.0(3.5) | 0.895(0.007) |
| L∞ | 23.8(0.6) | 11.9(0.1) | 17.2(0.6) | 0.812(0.005) | 30.3(0.7) | 11.3(0.2) | 28.9(1.9) | 0.928(0.005) |
| aL∞ | 26.1(0.7) | 11.9(0.1) | 16.9(0.6) | 0.643(0.018) | 30.6(0.6) | 11.3(0.2) | 27.1(1.7) | 0.893(0.009) |
| TTLP | 25.9(0.8) | 12.0(0.0) | 20.0(0.5) | 0.801(0.008) | 32.2(0.8) | 11.6(0.2) | 64.3(5.2) | 0.923(0.004) |
| LTLP | 24.7(0.7) | 12.0(0.0) | 20.4(0.4) | 0.825(0.008) | 30.6(0.7) | 11.7(0.2) | 75.1(3.6) | 0.864(0.006) |
| BRGL | 23.7(0.6) | 11.4(0.1) | 7.3(0.4) | 0.938(0.007) | 37.7(0.9) | 9.9(0.1) | 23.8(1.1) | 0.876(0.008) |
| Ising(b=7) | 27.8(1.5) | 9.9(0.5) | 11.6(0.8) | 0.855(0.024) | 45.8(2.6) | 7.6(0.6) | 44.5(2.0) | 0.709(0.032) |
| TGLG-I | 23.7(0.6) | 10.8(0.2) | 8.0(0.9) | 0.918(0.006) | 33.9(0.9) | 7.2(0.3) | 7.6(1.5) | 0.829(0.011) |
| TGLG-F | 22.8(0.6) | 11.4(0.1) | 10.2(0.7) | 0.901(0.015) | 28.7(1.1) | 10.5(0.3) | 14.2(2.1) | 0.922(0.012) |
| TGLG-L | 22.3(0.6) | 11.6(0.1) | 8.9(0.6) | 0.930(0.008) | 28.8(0.9) | 8.8(0.3) | 6.4(1.1) | 0.908(0.011) |