Table 4:
Average CPU time (s)
| Sample size | |||
|---|---|---|---|
| 50 | 100 | 200 | |
| Number of latent confounders Q = 0 | |||
| Our approach (t-distributed individual-specific effects) | 27.20 | 56.93 | 141.84 |
| Our approach (Gaussian individual-specific effects) | 35.48 | 69.59 | 117.10 |
| LvLiNGAM (1 latent confounder) | 2.41 | 2.55 | 9.91 |
| LvLiNGAM (4 latent confounders) | 22.25 | 30.12 | 87.96 |
| SLIM (1 latent confounder) | 5.89 | 6.25 | 6.81 |
| SLIM (4 latent confounders) | 7.60 | 8.14 | 9.13 |
| SLIM (10 latent confounders) | 10.88 | 12.02 | 13.96 |
| LiNGAM-GC-UK | 0.00 | 0.00 | 0.00 |
| ICA-LiNGAM | 0.04 | 0.03 | 0.02 |
| DirectLiNGAM | 0.00 | 0.01 | 0.01 |
| Pairwise LiNGAM | 0.00 | 0.00 | 0.00 |
| Post-nonlinear causal model | 19.59 | 27.68 | 57.37 |
| Number of latent confounders Q = 1: | |||
| Our approach (t-distributed individual-specific effects) | 35.87 | 65.55 | 131.25 |
| Our approach (Gaussian individual-specific effects) | 37.12 | 75.11 | 114.37 |
| LvLiNGAM (1 latent confounder) | 2.40 | 2.53 | 13.93 |
| LvLiNGAM (4 latent confounders) | 21.50 | 29.50 | 92.19 |
| SLIM (1 latent confounder) | 5.88 | 6.01 | 6.69 |
| SLIM (4 latent confounders) | 7.59 | 8.19 | 8.96 |
| SLIM (10 latent confounders) | 10.96 | 11.79 | 13.68 |
| LiNGAM-GC-UK | 0.00 | 0.00 | 0.00 |
| ICA-LiNGAM | 0.05 | 0.03 | 0.03 |
| DirectLiNGAM | 0.01 | 0.01 | 0.01 |
| Pairwise LiNGAM | 0.00 | 0.00 | 0.00 |
| Post-nonlinear causal model | 18.17 | 28.83 | 51.63 |
| Number of latent confounders Q = 6: | |||
| Our approach (t-distributed individual-specific effects) | 42.66 | 76.29 | 132.43 |
| Our approach (Gaussian individual-specific effects) | 33.13 | 69.07 | 104.83 |
| LvLiNGAM (1 latent confounder) | 2.40 | 2.56 | 9.38 |
| LvLiNGAM (4 latent confounders) | 22.17 | 30.12 | 83.01 |
| SLIM (1 latent confounder) | 5.89 | 6.22 | 6.77 |
| SLIM (4 latent confounders) | 7.58 | 8.18 | 9.11 |
| SLIM (10 latent confounders) | 11.03 | 12.02 | 13.91 |
| LiNGAM-GC-UK | 0.00 | 0.00 | 0.00 |
| ICA-LiNGAM | 0.06 | 0.05 | 0.05 |
| DirectLiNGAM | 0.01 | 0.01 | 0.01 |
| Pairwise LiNGAM | 0.00 | 0.00 | 0.00 |
| Post-nonlinear causal model | 18.71 | 29.62 | 52.21 |
| Number of latent confounders Q = 12: | |||
| Our approach (t-distributed individual-specific effects) | 29.16 | 59.30 | 134.89 |
| Our approach (Gaussian individual-specific effects) | 32.18 | 68.14 | 104.76 |
| LvLiNGAM (1 latent confounder) | 2.35 | 2.50 | 13.58 |
| LvLiNGAM (4 latent confounders) | 21.51 | 30.10 | 94.08 |
| SLIM (1 latent confounder) | 5.90 | 6.03 | 6.62 |
| SLIM (4 latent confounders) | 7.58 | 7.99 | 8.97 |
| SLIM (10 latent confounders) | 10.92 | 11.68 | 13.74 |
| LiNGAM-GC-UK | 0.00 | 0.00 | 0.00 |
| ICA-LiNGAM | 0.07 | 0.08 | 0.07 |
| DirectLiNGAM | 0.01 | 0.02 | 0.02 |
| Pairwise LiNGAM | 0.00 | 0.00 | 0.00 |
| Post-nonlinear causal model | 18.21 | 29.21 | 51.89 |