Supposed that you have applied Decision Tree algorithm to your training set and validation set and you have got the following scenarios by choosing different depth for your algorithm. Which depth you will pick for your final model?[table]
Depth | Training error | Validation error 3 | 30% | 35% 4 | 26% | 30% 5 | 22% | 30% 6 | 15% | 35%
[/table]

Question

BlackTom AI · Accepted Answer

To decide the final depth for the Decision Tree, I will examine how the training and validation errors change across depths. 
Option a (depth 6): Training error is very low (15%), but the validation error rises to 35%. This indicates overfitting: the model fits training data well but generalizes poorly.
Option b (depth 5): Training error is 22% with a validation error of 30%. The validation error is better than depth 6 but still not the best among the options because we can achieve the same or better generalization with a simpler tree.
Option c (depth 4): Training error is 26% and validation error is 30%. Here, the validation error (30%) is the lowest observed among depths 4 and 5, and the training error is not excessively high, suggesting a good bias-variance balance.
Option d (depth 3): Training error is 30% and validation error is 35%. The validation error is worse than at depths 4 and 5, so depth 3 provides poorer generalization.
Now, focusing on validation error as the primary criterion for model performance on unseen data, the smallest validation error occurs at depths 4 and 5, both at 30%. When two depths give the same validation performance, we generally prefer the simpler model to avoid unnecessary complexity and potential overfitting risk. Between depths 4 and 5, depth 4 is the simpler choice with fewer nodes or branches, while achieving the same validation error.
Therefore, the depth you would pick for the final model is depth 4. (This corresponds to option c.)

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