I’m trying to work my head around the example of Nested vs. Non-Nested CV in Sklearn. I checked multiple answers but I am still confused on the example.
To my knowledge, a nested CV aims to use a different subset of data to select the best parameters of a classifier (e.g. C in SVM) and validate its performance. Therefore, from a dataset X, the outer 10-folds CV (for simplicity n=10) creates 10 training sets and 10 test sets:
(Tr0, Te0),…, (Tr0, Te9)
Then, the inner 10-CV splits EACH outer training set into 10 training and 10 test sets:
From Tr0: (Tr0_0,Te_0_0), … , (Tr0_9,Te0_9)
From Tr9: (Tr9_0,Te_9_0), … , (Tr9_9,Te9_9)
Now, using the inner CV, we can find the best values of C for every single outer Training set. This is done by testing all the possible values of C with the inner CV. The value providing the highest performance (e.g. accuracy) is chosen for that specific outer Training set. Finally, having discovered the best C values for every outer Training set, we can calculate an unbiased accuracy using the outer Test sets. With this procedure, the samples used to identify the best parameter (i.e. C) are not used to compute the performance of the classifier, hence we have a totally unbiased validation.
The example provided in the Sklearn page is:
inner_cv = KFold(n_splits=4, shuffle=True, random_state=i)
outer_cv = KFold(n_splits=4, shuffle=True, random_state=i)
# Non_nested parameter search and scoring
clf = GridSearchCV(estimator=svm, param_grid=p_grid, cv=inner_cv)
clf.fit(X_iris, y_iris)
non_nested_scores[i] = clf.best_score_
# Nested CV with parameter optimization
nested_score = cross_val_score(clf, X=X_iris, y=y_iris, cv=outer_cv)
nested_scores[i] = nested_score.mean()
From what I understand, the code simply calculates the scores using two different cross-validations (i.e. different splits into training and test set). Both of them used the entire dataset. The GridCV identifies the best parameters using one (of the two CVs), then cross_val_score calculates, with the second CV, the performance when using the best parameters.
Am I interpreting a Nested CV in the wrong way? What am I missing from the example?
Okay, you\’ve got a good grasp of the fundamental idea behind nested cross-validation, but let\’s clarify how it\’s implemented in the scikit-learn example and address your points of confusion. Your understanding of *why* nested CV is used (unbiased performance estimation after hyperparameter tuning) is correct.\n\nHere\’s a breakdown to clear up the confusion:\n\n**Your Understanding (Mostly Correct):**\n\n* You correctly identified that nested CV aims to select the best hyperparameters on one subset of the data and then validate the performance of the model (with those selected hyperparameters) on a completely separate subset. This avoids the bias of evaluating performance on data used for hyperparameter tuning.\n* Your explanation of the inner and outer loops and the purpose of each is accurate.\n* You understand that the inner CV finds the best `C` for each outer training set.\n\n**Where the Confusion Lies & Detailed Explanation of the Sklearn Example:**\n\nThe key is understanding what `cross_val_score` *does* when you pass it a `GridSearchCV` object. It\’s not just *calculating* a score with pre-determined best parameters. It\’s performing the **outer** cross-validation loop of the nested CV, *including* re-running the inner hyperparameter optimization within each outer fold.\n\nLet\’s walk through the code snippet line by line:\n\n“`python\ninner_cv = KFold(n_splits=4, shuffle=True, random_state=i) # Create KFold objects\nouter_cv = KFold(n_splits=4, shuffle=True, random_state=i) # Create KFold objects\n\n# Non_nested parameter search and scoring\nclf = GridSearchCV(estimator=svm, param_grid=p_grid, cv=inner_cv) #Create GridSearchCV with svm and inner_cv\nclf.fit(X_iris, y_iris) # Fit the GridSearchCV with ALL the data using inner_cv splits to find the best parameter for the WHOLE dataset\nnon_nested_scores[i] = clf.best_score_ #The score that we are measuring is calculated using the best_estimator_ over all the possible parameters, inner_cv folds and the WHOLE dataset\n\n# Nested CV with parameter optimization\nnested_score = cross_val_score(clf, X=X_iris, y=y_iris, cv=outer_cv) #Pass a GridSearchCV object and the outer_cv folds, triggers the Nested CV\nnested_scores[i] = nested_score.mean() #Calculate the mean of the nested_score over all the folds\n“`\n\n**Detailed Explanation:**\n\n1. **`inner_cv = KFold(…)` and `outer_cv = KFold(…)`**: These lines define the cross-validation strategies for the inner and outer loops. `KFold` is used in this example, but you could use `StratifiedKFold` for classification tasks to ensure class representation is maintained in each fold. The `random_state=i` is important for reproducibility, ensuring that the same splits are used for each iteration.\n\n2. **`clf = GridSearchCV(estimator=svm, param_grid=p_grid, cv=inner_cv)`**: This creates a `GridSearchCV` object. Crucially, it\’s *not* yet fitted. It\’s just a configuration. The `cv=inner_cv` tells `GridSearchCV` how to perform cross-validation for hyperparameter tuning.\n\n3. **`clf.fit(X_iris, y_iris)`**: This fits the `GridSearchCV` object to the *entire* dataset `X_iris`, `y_iris`. This is where your understanding diverges from the nested CV. This is **NOT** part of the nested CV; it\’s calculating a non-nested score.\n * The `GridSearchCV` explores all combinations of hyperparameters defined in `p_grid` using the cross-validation scheme specified by `inner_cv`.\n * It finds the best hyperparameter combination based on the average score across the inner folds.\n * It then *refits* the *entire* dataset using the best hyperparameter combination found. This is important! The `clf` object now holds a model trained on the entire dataset with the \”best\” hyperparameters (according to the inner CV on the *whole* dataset).\n * **`non_nested_scores[i] = clf.best_score_`**: This stores the best score achieved by the `GridSearchCV` *after* it has been fit to the *entire* dataset and refitted with the best hyperparameters. This score is biased because the same data was used for hyperparameter selection and performance evaluation.\n\n4. **`nested_score = cross_val_score(clf, X=X_iris, y=y_iris, cv=outer_cv)`**: This is the *nested* cross-validation part. This line is more powerful than it appears.\n * `cross_val_score` takes the *unfitted* `GridSearchCV` object (`clf`), the data `X_iris`, `y_iris`, and the outer cross-validation strategy `outer_cv`.\n * **For each fold in `outer_cv`:**\n * `cross_val_score` trains a *new* `GridSearchCV` object (using the *same* `clf` configuration but with a different training/validation split provided by `outer_cv`).\n * This `GridSearchCV` object performs an *inner* cross-validation (using `inner_cv`) on the *current* outer fold\’s training data to find the best hyperparameters for *that* outer fold. **This is the key! The hyperparameter tuning is redone for each outer fold.**\n * The `GridSearchCV` object then trains a model using the best hyperparameters found in the inner CV on the outer fold\’s training data.\n * Finally, the trained model is evaluated on the outer fold\’s test data, and the score is recorded.\n * `cross_val_score` returns an array of scores, one for each outer fold. These scores are unbiased estimates of the model\’s performance because the data used to evaluate the model was never used to select the hyperparameters for that particular fold.\n\n5. **`nested_scores[i] = nested_score.mean()`**: This calculates the average of the scores obtained from the outer folds of the nested cross-validation. This average score is the more reliable, unbiased estimate of the model\’s generalization performance.\n\n**In Summary:**\n\n* The non-nested approach uses the *entire* dataset to find the best hyperparameters and then evaluates performance. This leads to an optimistic (biased) performance estimate.\n* The nested CV performs hyperparameter tuning *independently* for each outer fold, using only the training data within that fold. This results in a more realistic (unbiased) performance estimate. The `cross_val_score` function, when given a `GridSearchCV` object, handles the outer loop of the nested CV and the re-tuning of hyperparameters within each fold.\n\n**Analogy:**\n\nImagine you\’re trying to find the best recipe for chocolate chip cookies and then want to know how good your recipe is.\n\n* **Non-Nested CV:** You try different amounts of sugar and chocolate chips (hyperparameter tuning) using *all* your cookie dough. You find the \”best\” recipe based on tasting all the cookies you made. Then, you use that recipe to make *more* cookies from the same dough and taste those to see how good the recipe is. This is biased because you already used the dough to optimize the recipe.\n* **Nested CV:** You divide your dough into several batches (outer folds). For *each* batch, you try different amounts of sugar and chocolate chips (hyperparameter tuning) *only* using that batch\’s dough. You find the \”best\” recipe for *that* batch. Then, you bake cookies from *that* batch using the best recipe you found for *that* batch and taste them. You repeat this for all the batches. This gives you a more realistic idea of how good your recipe is in general, because you\’re not using the same dough to both optimize and evaluate.\n\n**Key Takeaways:**\n\n* `cross_val_score` is the workhorse for the *outer* loop of nested CV in the scikit-learn example *when given an unfitted `GridSearchCV` object.* It\’s not just calculating a score with pre-determined parameters; it\’s orchestrating the entire nested procedure.\n* The inner CV (handled by `GridSearchCV`) is performed independently for each outer fold.\n* Nested CV provides a more reliable estimate of how well your model will generalize to unseen data, especially when hyperparameter tuning is involved.\n* The `fit` call on the GridSearch before the `cross_val_score` is computing a regular, *non-nested* cross-validation score for comparison.\n\nI hope this clears up your understanding of the example! Let me know if you have any further questions.\n
