Table 3:
Performance of different regularization methods in estimating graphical Granger causality with misspecified groups (30% misspecification); d = 2, T = 10, SNR = 2. 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∣ = 246 Group Size=6 |
p = 120, ∣E∣ = 968 Group Size=6 |
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|---|---|---|---|---|---|---|---|
| n | 160 | 110 | 60 | 160 | 110 | 60 | |
| P | Lasso | 88(2) | 85(3) | 77(5) | 59(1) | 55(1) | 49(2) |
| Grp | 65(2) | 66(2) | 66(3) | 43(3) | 44(4) | 38(4) | |
| Thgrp | 87(3) | 88(3) | 85(3) | 56(6) | 56(6) | 51(7) | |
| Agrp | 65(2) | 66(2) | 66(3) | 45(2) | 45(4) | 39(4) | |
| R | Lasso | 80(3) | 63(3) | 37(2) | 66(1) | 54(1) | 35(1) |
| Grp | 100(0) | 98(2) | 82(6) | 87(2) | 78(3) | 59(4) | |
| Thgrp | 100(0) | 98(2) | 79(6) | 86(2) | 79(3) | 57(4) | |
| Agrp | 100(0) | 98(2) | 82(6) | 86(2) | 78(3) | 58(3) | |
| MCC | Lasso | 84(2) | 73(2) | 53(3) | 62(1) | 54(1) | 41(1) |
| Grp | 81(1) | 80(2) | 74(4) | 61(2) | 58(3) | 47(2) | |
| Thgrp | 93(2) | 93(2) | 82(4) | 69(4) | 66(4) | 53(3) | |
| Agrp | 81(1) | 80(2) | 74(4) | 62(2) | 59(2) | 47(2) | |
| ERR | Lasso | 12.63 | 17.05 | 22.41 | 45.09 | 49.68 | 53.4 |
| LAG | Grp | 9.43 | 8.78 | 15.12 | 18.22 | 18.43 | 29.26 |
| Thgrp | 6.45 | 5.34 | 8.02 | 11.81 | 12.84 | 15.57 | |
| Agrp | 9.11 | 8.78 | 14.96 | 16.32 | 16.9 | 27.69 | |