Learning Curves and Validation Curves

A learning curve plots model performance against the amount of training data or, in other settings, training time or optimization steps. A common version repeatedly fits on larger training subsets and evaluates both training and validation performance. Label the horizontal axis because adding examples and running more epochs answer different questions. When training and validation performance are both poor and close, the model may be underfitting. More data of the same kind may not solve the problem; a more expressive model, better features, or less restrictive regularization may be needed. When training performance is much better than validation performance, the gap points to overfitting. More representative data, stronger regularization, a simpler model, or better data handling may reduce it. The curve is diagnostic, not a verdict. If validation performance continues to improve at the largest sample size, additional data may help, but benefit depends on whether new examples resemble the target population. A plateau can indicate diminishing returns, limited model capacity, label noise, or a mismatch between training and evaluation distributions. Repeated splits or error bars help show whether trends are stable. A validation curve varies a hyperparameter and plots validation performance against its values. It can reveal that a model is too constrained at one end and overfits at the other. A shallow tree may miss structure, while an excessively deep tree can memorize training cases. Keep other choices and the evaluation protocol fixed when interpreting the result. The validation set guides model selection, so repeated tuning can gradually overfit that set. Reserve a separate test set for final evaluation, and use cross-validation when data is limited. For time-dependent or grouped data, splits must respect chronology or groups. A random split can produce a polished curve that measures leakage instead of generalization.