Table 1 Summary of the metrics obtained during the cross-validation and testing phases of the regression models used to predict chronological age based on mandibular size and sex, along with their optimal hyperparameters.
From: Age estimation of children and adolescents from mandibles using machine learning
Model | Optimal hyperparameters | Test data results [CI95%] | Cross-validation results [CI95%] |
|---|---|---|---|
Gradient boosting | learning_rate: 0.1 | MSE = 3.74 [2.73–4.81] | MSE = 2.37 [1.96–2.84] |
max_depth: 4 | RMSE = 1.93 [1.65–2.19] | RMSE = 1.54 [1.40–1.69] | |
min_samples_split: 2 | R2 = 0.38 [0.21–0.53] | R2 = 0.56 [0.46–0.64] | |
n_estimators: 100 | MAE = 1.54 [1.33–1.76] | MAE = 1.21 [1.09–1.32] | |
Linear regression | fit_intercept: True | MSE = 4.12 [3.24–5.02] | MSE = 4.28 [2.64–6.07] |
copy_X: True | RMSE = 2.03 [1.80–2.24] | RMSE = 2.06 [1.62–2.46] | |
n_jobs: -1 | R2 = 0.31 [0.21–0.41] | R2 = 0.20 [-0.13–0.51] | |
positive: True | MAE = 1.71 [1.49–1.91] | MAE = 1.56 [1.31–1.78] | |
Support vector machine | C: 1 | MSE = 4.06 [3.09–5.16] | MSE = 2.84 [2.38–3.34] |
kernel: rbf | RMSE = 2.01 [1.76–2.27] | RMSE = 1.68 [1.54–1.83] | |
degree: 2 | R2 = 0.32 [0.14–0.49] | R2 = 0.47 [0.37–0.55] | |
MAE = 1.62 [1.40–1.83] | MAE = 1.33 [1.20–1.47] | ||
K-nearest neighbors | n_neighbors: 9 | MSE = 3.94 [3.02–4.98] | MSE = 2.97 [2.45–3.55] |
p: 1 | RMSE = 1.98 [1.74–2.23] | RMSE = 1.72 [1.57–1.88] | |
weights: uniform | R2 = 0.34 [0.17–0.49] | R2 = 0.45 [0.34–0.54] | |
MAE = 1.62 [1.42–1.83] | MAE = 1.37 [1.23–1.51] | ||
Random forest | max_depth: None | MSE = 3.81 [2.81–4.92] | MSE = 2.29 [1.91–2.71] |
max_features: sqrt | RMSE = 1.95 [1.68–2.22] | RMSE = 1.51 [1.38–1.65] | |
min_samples_leaf: 4 | R2 = 0.36 [0.19–0.52] | R2 = 0.57 [0.48–0.65] | |
min_samples_split: 10 | MAE = 1.55 [1.33–1.77] | MAE = 1.18 [1.06–1.29] | |
n_estimators: 200 | |||
AdaBoost | learning_rate: 0.1 | MSE = 4.01 [3.00–5.14] | MSE = 2.58 [2.17–3.02] |
loss: linear | RMSE = 2.00 [1.73–2.27] | RMSE = 1.60 [1.47–1.74] | |
n_estimators: 100 | R2 = 0.33 [0.16–0.49] | R2 = 0.52 [0.42–0.60] | |
MAE = 1.61 [1.39–1.82] | MAE = 1.30 [1.19–1.42] | ||
Decision tree | max_depth: 10 | MSE = 4.83 [3.65–6.12] | MSE = 2.94 [2.31–3.65] |
max_features: sqrt | RMSE = 2.19 [1.91–2.47] | RMSE = 1.71 [1.52–1.91] | |
min_samples_leaf: 4 | R2 = 0.19 [-0.02–0.40] | R2 = 0.45 [0.31–0.57] | |
min_samples_split: 10 | MAE = 1.74 [1.50–1.99] | MAE = 1.29 [1.14–1.45] | |
MLP regressor | activation: relu | MSE = 4.11 [3.18–5.12] | MSE = 3.02 [2.52–3.65] |
alpha: 0.001 | RMSE = 2.02 [1.78–2.26] | RMSE = 1.73 [1.59–1.91] | |
hidden_layer_sizes: (100,) | R2 = 0.31 [0.14–0.47] | Rv = 0.44 [0.31–0.53] | |
learning_rate: constant | MAE = 1.65 [1.44–1.87] | MAE = 1.40 [1.27–1.53] | |
solver: adam |
