Table 5.2.
Quantitive comparison among different estimators on the Erdös-Rényi model. Since A-PISTA and F-APISTA can output valid results for large α’s, their estimators attains better performance than other competitors. The SCIO(P) and CLIME estimators use the ℓ1 norm regularization with no bias reduction. Thus their performance is worse than the other competitors in both parameter estimation and graph estimation.
| Method | d | ‖Θ̂−Θ‖F | ‖Θ̂−Θ‖1 | T. P. R. | F. P. R. | α̂ |
|---|---|---|---|---|---|---|
| PISTA | 200 | 3.2647(0.1235) | 1.6807(0.2675) | 1.0000(0.0000) | 0.0587(0.0013) | 0.20 |
| 400 | 4.5609(0.7666) | 2.2113(0.3358) | 1.0000(0.0000) | 0.0295(0.0091) | 0.20 | |
| 800 | 5.0751(0.3832) | 2.5718(0.2826) | 1.0000(0.0000) | 0.0099(0.0020) | 0.20 | |
| APISTA | 200 | 2.2888(0.1141) | 1.1644(0.2343) | 1.0000(0.0000) | 0.0193(0.0005) | 0.33 |
| 400 | 3.2206(0.2733) | 1.4974(0.2778) | 1.0000(0.0000) | 0.0067(0.0100) | 0.33 | |
| 800 | 4.0929(0.1862) | 1.6347(0.2023) | 1.0000(0.0000) | 0.0036(0.0008) | 0.50 | |
| F-APISTA | 200 | 2.2890(0.1161) | 1.1647(0.2390) | 1.0000(0.0000) | 0.0197(0.0007) | 0.33 |
| 400 | 3.2251(0.2702) | 1.4928(0.2731) | 1.0000(0.0000) | 0.0060(0.0102) | 0.33 | |
| 800 | 4.0984(0.1891) | 1.6397(0.2096) | 1.0000(0.0000) | 0.0034(0.0009) | 0.50 | |
| SCIO(P) | 200 | 3.4277(0.5405) | 1.5213(0.3223) | 1.0000(0.0000) | 0.0618(0.0170) | 0.00 |
| 400 | 5.7144(0.8158) | 1.9057(0.2933) | 0.9994(0.0017) | 0.0341(0.0145) | 0.00 | |
| CLIME | 200 | 3.6297(0.6103) | 1.4876(0.2855) | 1.0000(0.0000) | 0.0581(0.0159) | 0.00 |
| 400 | 5.9206(0.8385) | 1.8246(0.2817) | 1.0000(0.0000) | 0.0320(0.0112) | 0.00 | |