Scikit-Learn GridSearchCV NuSVR

Hyperparameter tuning is a crucial step in optimizing machine learning models for best performance. In this example, we’ll demonstrate how to use scikit-learn’s GridSearchCV to perform hyperparameter tuning for NuSVR, a variant of Support Vector Regression (SVR) that handles non-linear relationships.

Grid search is a method for evaluating different combinations of model hyperparameters to find the best performing configuration. It exhaustively searches through a specified parameter grid, trains and evaluates the model for each combination using cross-validation, and selects the hyperparameters that yield the best performance metric.

NuSVR is a type of Support Vector Regression that uses a parameter nu to control the number of support vectors. This allows for a more flexible model that can be fine-tuned for different types of data. The model maps inputs into high-dimensional feature spaces using a kernel function.

The key hyperparameters for NuSVR include the regularization parameter C, which controls the trade-off between achieving a low error on the training data and minimizing model complexity; the nu parameter, which controls the number of support vectors and thus affects model flexibility; and the kernel, which defines the type of kernel used to map inputs into feature spaces.

from sklearn.datasets import make_regression
from sklearn.model_selection import train_test_split, GridSearchCV
from sklearn.svm import NuSVR

# Generate synthetic regression dataset
X, y = make_regression(n_samples=1000, n_features=10, noise=0.1, random_state=42)

# Split into train and test sets
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

# Define parameter grid
param_grid = {
    'C': [0.1, 1, 10],
    'nu': [0.25, 0.5, 0.75],
    'kernel': ['linear', 'rbf']
}

# Perform grid search
grid_search = GridSearchCV(estimator=NuSVR(),
                           param_grid=param_grid,
                           cv=5,
                           scoring='r2')
grid_search.fit(X_train, y_train)

# Report best score and parameters
print(f"Best score: {grid_search.best_score_:.3f}")
print(f"Best parameters: {grid_search.best_params_}")

# Evaluate on test set
best_model = grid_search.best_estimator_
r2_score = best_model.score(X_test, y_test)
print(f"Test set R2 score: {r2_score:.3f}")

Running the example gives an output like:

Best score: 1.000
Best parameters: {'C': 10, 'kernel': 'linear', 'nu': 0.5}
Test set R2 score: 1.000

The steps are as follows:

1. Generate a synthetic regression dataset using scikit-learn’s make_regression function.
2. Split the dataset into train and test sets using train_test_split.
3. Define the parameter grid with different values for C, nu, and kernel hyperparameters.
4. Perform grid search using GridSearchCV, specifying the NuSVR model, parameter grid, 5-fold cross-validation, and R2 scoring metric.
5. Report the best cross-validation score and best set of hyperparameters found by grid search.
6. Evaluate the best model on the hold-out test set and report the R2 score.

By using GridSearchCV, we can easily explore different hyperparameter settings and find the combination that maximizes the model’s performance. This automated approach saves time and effort compared to manual hyperparameter tuning and helps ensure we select the best configuration for our NuSVR model.