Overfitting and Underfitting

A trained model should be evaluated beyond the examples used to fit it. Under comparable training and held-out conditions, high training performance with much weaker held-out performance can indicate overfitting to training-specific patterns. Poor performance on both sets can be consistent with underfitting, although failed optimization, unsuitable data, and other causes also need consideration. The labels therefore guide diagnosis rather than substitute for it. Changing relevant features or model capacity can be worth testing when the representation is too limited, while regularization and data choices can affect how flexibly a model fits. Bias and variance describe another view of prediction error: bias concerns systematic deviation of the estimated predictor, and variance concerns sensitivity to the sampled training data. Small models are not automatically biased, and large models are not automatically high-variance in every task. The data-generating relationship and fitting procedure matter. Validation and final testing also have different roles. Validation data can help choose a model, hyperparameters, or stopping point. Repeatedly using the final test set for those choices can make the reported final estimate optimistic, so final testing should remain separate when possible. Modern research includes double-descent curves where test error rises near an interpolation regime and falls again as capacity increases. Such observations do not make that curve universal. Assess the actual task, information available, data splits, and fitting procedure rather than infer reliability solely from parameter count.