Table 1.
Comparison of graph estimation accuracy among the lasso and the adaptive lasso estimators of GGM and CGGM for Example 1, Example 2 (including three scenarios), and Example 3. “ALASSO” means adaptive lasso
Example/scenario | Criteria |
n = 50
|
n = 100
|
||||||
---|---|---|---|---|---|---|---|---|---|
LASSO
|
ALASSO
|
LASSO
|
ALASSO
|
||||||
GGM | CGGM | GGM | CGGM | GGM | CGGM | GGM | CGGM | ||
EX1 | FP | 1 | 0.51 | 1 | 0.15 | 1 | 0.40 | 1 | 0.05 |
FN | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
PATH | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | |
EX2-SC1 | FP | 0.84 | 0.02 | 0.54 | 0.06 | 0.93 | 0.01 | 0.67 | 0.02 |
FN | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
PATH | 0 | 1 | 0.01 | 0.63 | 0 | 1 | 0.98 | 1 | |
EX2-SC2 | FP | 0.98 | 0.55 | 0.96 | 0.31 | 1 | 0.51 | 1 | 0.22 |
FN | 0.06 | 0.01 | 0.15 | 0.02 | 0.02 | 0 | 0.08 | 0 | |
PATH | 0 | 0.57 | 0 | 0.71 | 0 | 0.79 | 0 | 0.98 | |
EX2-SC3 | FP | 0.71 | 0.68 | 0.18 | 0.19 | 0.75 | 0.77 | 0.10 | 0.11 |
FN | 0 | 0 | 0.01 | 0.02 | 0 | 0 | 0 | 0 | |
PATH | 0 | 0.43 | 0.80 | 0.52 | 0 | 0.56 | 1 | 0.87 | |
EX3 | FP | 0.79 | 0.23 | 0.41 | 0.09 | 0.83 | 0.16 | 0.59 | 0.03 |
FN | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
PATH | 0 | 0.94 | 0.95 | 0.99 | 0 | 1 | 1 | 1 |