Table 1:
Performance of different regularization methods in estimating graphical Granger causality with balanced group sizes and no misspecification; d = 2, T = 5, SNR = 1.8. Precision (P), Recall (R), MCC are given in percentages (numbers in parentheses give standard deviations). ERR LAG gives the error associated with incorrect estimation of VAR order.
|
p = 60, ∣E∣ =351 Group Size=3 |
p = 120, ∣E∣ =1404 Group Size=3 |
p = 200, ∣E∣ =3900 Group Size=5 |
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|---|---|---|---|---|---|---|---|---|---|---|
| n | 160 | 110 | 60 | 160 | 110 | 60 | 160 | 110 | 60 | |
| P | Lasso | 80(2) | 75(2) | 66(4) | 69(1) | 62(2) | 52(2) | 52(1) | 47(1) | 38(1) |
| Grp | 95(2) | 91(4) | 83(7) | 91(3) | 80(5) | 68(7) | 78(4) | 72(3) | 59(6) | |
| Thgrp | 96(1) | 92(3) | 86(6) | 93(3) | 83(5) | 70(7) | 82(4) | 76(3) | 64(6) | |
| Agrp | 96(2) | 92(4) | 83(7) | 92(3) | 82(5) | 69(7) | 81(3) | 74(3) | 60(6) | |
| R | Lasso | 71(2) | 54(2) | 31(2) | 54(1) | 40(1) | 22(1) | 38(1) | 28(1) | 15(1) |
| Grp | 99(1) | 93(3) | 71(7) | 91(2) | 81(2) | 48(8) | 84(1) | 70(2) | 41(4) | |
| Thgrp | 99(1) | 93(3) | 71(7) | 91(2) | 81(2) | 48(8) | 84(2) | 69(2) | 41(3) | |
| Agrp | 99(1) | 93(3) | 71(7) | 91(2) | 81(2) | 47(8) | 84(1) | 69(2) | 40(4) | |
| MCC | Lasso | 75(2) | 63(2) | 45(3) | 60(1) | 49(1) | 33(1) | 43(1) | 35(1) | 23(1) |
| Grp | 97(1) | 92(3) | 76(5) | 91(1) | 80(2) | 56(2) | 81(2) | 70(2) | 48(2) | |
| Thgrp | 98(1) | 93(2) | 78(5) | 92(1) | 81(2) | 57(3) | 83(2) | 72(2) | 50(3) | |
| Agrp | 97(1) | 92(3) | 76(5) | 91(1) | 81(2) | 56(3) | 82(2) | 71(2) | 48(2) | |
| ERR | Lasso | 10.5 | 11.3 | 13.9 | 16.63 | 17.37 | 16.69 | 19.79 | 20 | 18.52 |
| LAG | Grp | 3.19 | 6.95 | 12.76 | 4.86 | 10.77 | 12.65 | 4.21 | 5.27 | 7.8 |
| Thgrp | 2.83 | 5.87 | 10.01 | 3.98 | 9.03 | 11.19 | 3.06 | 3.91 | 5.68 | |
| Agrp | 3.13 | 6.89 | 12.59 | 4.63 | 10.37 | 12.34 | 3.58 | 4.87 | 7.59 | |