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Nested Cross-Validation

Model evaluation technique using two nested cross-validation loops to prevent overfitting during hyperparameter optimization. The inner loop selects the best hyperparameters while the outer loop evaluates the performance of the selected model in an unbiased manner.

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Inner Loop

First level of cross-validation in nested cross-validation, responsible for selecting and optimizing model hyperparameters. This loop uses a separate validation set to identify the optimal configuration before final evaluation.

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Outer Loop

Second level of cross-validation in nested cross-validation, providing an unbiased estimate of model performance after hyperparameter selection. The test data from this loop is never used during hyperparameter optimization.

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Hyperparameter Overfitting

Phenomenon where hyperparameters are optimized to perform specifically on the validation set, compromising generalization to new data. This problem occurs when the same cross-validation is used for both hyperparameter selection and final evaluation.

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Selection Bias

Systematic error introduced during model or hyperparameter selection when the test set is implicitly used in the optimization process. This bias leads to an optimistic and unrealistic estimate of model performance in production.

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Nested Grid Search

Method combining nested cross-validation with exhaustive hyperparameter search on a predefined grid. Each grid configuration is evaluated by the inner loop before the best one is tested by the outer loop.

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Estimated Generalization Error

Performance measure obtained by the outer loop of nested cross-validation, representing an approximation of model error on unseen data. This estimate is considered more reliable than that obtained by simple cross-validation.

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Sequential Optimization

Process where hyperparameter selection and model evaluation are performed sequentially but on separate datasets to avoid contamination. This approach is fundamentally implemented in nested cross-validation.

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Nested Cross-Validation

Extension of nested cross-validation adding a third level for selection between different model families. Each level uses disjoint data to ensure a completely unbiased evaluation of the entire pipeline.

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Temporal Information Leakage

Specific problem to serial data where nested cross-validation is essential to maintain chronological order between training, validation, and test sets. This approach prevents the use of future information in optimization.

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Selection Stability

Ability of nested cross-validation to identify robust hyperparameters that perform consistently across different outer validation folds. Low stability indicates strong dependence on specific training data.

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Quadratic Computational Cost

Algorithmic complexity of nested cross-validation, requiring O(k²) trainings where k is the number of folds. This high cost is the necessary compromise to obtain an unbiased evaluation of model performance.

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Nested Monte Carlo Cross-Validation

Variant of nested cross-validation using random sampling with replacement for both inner and outer loops. This approach reduces correlation between estimates while maintaining the impartiality of evaluation.

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Evaluation Pipelining

Software architecture where nested cross-validation is implemented as a complete pipeline integrating preprocessing, feature selection, hyperparameter optimization, and final evaluation. This structure guarantees reproducibility and absence of data leakage.

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Nested Confidence Intervals

Statistical method using the results of the outer loop to calculate confidence intervals on model performance. These intervals reflect uncertainty due to both data variability and the hyperparameter selection process.

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