Table 2.
Mean absolute error (standard error) for each model and each fold (first challenge).
| Individual algorithms | Ensemble learning | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| BLUP-mean | BLUP-quantiles | SVM | 6-layer CNN | Age spe. 6-layer CNN | ResNet | Inception V1 | LM | RF | Mean | Median | |
| Fold 1 | 5.32 (0.19) | 4.90 (0.19) | 5.31 (0.18) | 4.18 (0.16) | 4.01 (0.15) | 4.02 (0.15) | 3.82 (0.14) | 3.46 (0.13)* | 3.62 (0.15) | 3.74 (0.13) | 3.67 (0.14) |
| Fold 2 | 5.05 (0.18) | 4.79 (0.19) | 5.34 (0.18) | 4.47 (0.15) | 4.12 (0.13) | 4.01 (0.14) | 3.97 (0.15) | 3.53 (0.13)* | 3.60 (0.15)* | 3.69 (0.13) | 3.74 (0.13) |
| Fold 3 | 4.90 (0.18) | 4.37 (0.16) | 4.84 (0.17) | 4.41 (0.16) | 4.27 (0.15) | 3.88 (0.14) | 4.00 (0.16) | 3.33 (0.13)* | 3.46 (0.15)* | 3.46 (0.12)* | 3.45 (0.13)* |
| Fold 4 | 5.07 (0.18) | 4.71 (0.18) | 5.06 (0.18) | 4.55 (0.17) | 4.27 (0.16) | 4.11 (0.15) | 3.85 (0.15) | 3.57 (0.13)* | 3.72 (0.14) | 3.68 (0.14) | 3.74 (0.15) |
| Fold 5 | 5.22 (0.19) | 4.69 (0.18) | 5.20 (0.18) | 4.02 (0.16) | 3.89 (0.15) | 3.99 (0.16) | 3.75 (0.15) | 3.34 (0.13)* | 3.51 (0.14) | 3.56 (0.13) | 3.47 (0.13) |
| 5-fold combined MAE | 5.11 | 4.69 | 5.15 | 4.33 | 4.11 | 4.00 | 3.88 | 3.44 | 3.58 | 3.62 | 3.61 |
Fold 1 corresponds to the train-test split used in the Predictive Analytics Competition (PAC) challenge and presented in Table 1. LM (linear model), RF (random forest), mean, and median age scores are the four methods considered for ensemble learning. The standard error [SE = SD/sqrt(N)] reflects the uncertainty around the MAE estimate. A 95% confidence interval may be calculated as MAE ± 1.96 * SE, though it (falsely) assumes normality of the absolute error distribution. For the 5-fold combined MAE, we did not report the SE, as it is notoriously biased downward (54) due to the overlap of the different training/test samples.
Indicates a significant reduction of MAE via ensemble learning compared with Inception alone (p < 0.01, assuming five independent tests).