Scikit-Learn RandomizedSearchCV NuSVR

Hyperparameter tuning is essential for optimizing machine learning models. In this example, we’ll demonstrate how to use scikit-learn’s RandomizedSearchCV for hyperparameter tuning of a Nu-Support Vector Regression (NuSVR) model, commonly used for regression tasks.

Random search is a method for evaluating different combinations of model hyperparameters. Unlike grid search, it samples a fixed number of hyperparameter combinations from a specified distribution, making it more efficient when searching over a large hyperparameter space.

NuSVR is a regression model from the Support Vector Machines family, designed to predict continuous values. It allows controlling the number of support vectors via the nu parameter.

Key hyperparameters for NuSVR include the regularization parameter (C), which controls model complexity and helps prevent overfitting; the nu parameter, which is an upper bound on the fraction of margin errors; and the kernel, which specifies the kernel type to be used (e.g., linear, polynomial, RBF).

from sklearn.datasets import make_regression
from sklearn.model_selection import train_test_split, RandomizedSearchCV
from sklearn.svm import NuSVR
from scipy.stats import uniform

# Generate synthetic regression dataset
X, y = make_regression(n_samples=100, 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 the model
model = NuSVR()

# Define hyperparameter distribution
param_dist = {
    'C': uniform(loc=0, scale=4),
    'nu': uniform(loc=0, scale=1),
    'kernel': ['linear', 'rbf']
}

# Perform random search
random_search = RandomizedSearchCV(estimator=model,
                                   param_distributions=param_dist,
                                   n_iter=50,
                                   cv=5,
                                   scoring='neg_mean_squared_error',
                                   random_state=42)
random_search.fit(X_train, y_train)

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

# Evaluate on test set
best_model = random_search.best_estimator_
mse = -best_model.score(X_test, y_test)
print(f"Test set MSE: {mse:.3f}")

Running the example gives an output like:

Best score: -2592.826
Best parameters: {'C': 3.8950220753658367, 'kernel': 'linear', 'nu': 0.45606998421703593}
Test set MSE: -0.994

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 NuSVR model and the hyperparameter distributions for C, nu, and kernel.
4. Perform random search using RandomizedSearchCV, specifying the NuSVR model, hyperparameter distribution, 100 iterations, 5-fold cross-validation, and negative mean squared error as the scoring metric.
5. Report the best cross-validation score and best set of hyperparameters found by random search.
6. Evaluate the best model on the hold-out test set and report the mean squared error.

By using RandomizedSearchCV, we can efficiently 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.