Gaussian Process (GP) is a powerful probabilistic model used for regression and classification tasks. It is particularly useful when dealing with small datasets or when a measure of uncertainty is required for predictions.
The “WhiteKernel” is a covariance function used in GP that adds white noise to the diagonal of the covariance matrix. This kernel helps to model the noise present in the data, making it a good choice for problems where the data has inherent randomness or noise.
The key hyperparameters for the “WhiteKernel” are the noise level. The noise level controls the magnitude of the white noise added to the diagonal of the covariance matrix. Common values for the noise level vary depending on the scale of the data but are typically small positive values.
The “WhiteKernel” is appropriate for regression problems, especially when the data has inherent noise.
from sklearn.gaussian_process import GaussianProcessRegressor
from sklearn.gaussian_process.kernels import WhiteKernel
from sklearn.model_selection import train_test_split
from sklearn.metrics import mean_squared_error
import numpy as np
# Prepare a synthetic dataset with noise
X = np.random.uniform(low=-5, high=5, size=(100, 3))
y = 2 * X[:, 0] - 3 * X[:, 1] + X[:, 2] + np.random.normal(loc=0, scale=2, size=(100,))
# Create an instance of GaussianProcessRegressor with WhiteKernel
kernel = WhiteKernel(noise_level=1)
gp = GaussianProcessRegressor(kernel=kernel, random_state=0)
# Split the dataset into train and test portions
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=0)
# Fit the model on the training data
gp.fit(X_train, y_train)
# Evaluate the model's performance using mean squared error
y_pred = gp.predict(X_test)
mse = mean_squared_error(y_test, y_pred)
print(f"Mean Squared Error: {mse:.2f}")
# Make a prediction using the fitted model on a test sample
test_sample = np.array([[1, -2, 3]])
pred = gp.predict(test_sample)
print(f"Predicted value for test sample: {pred[0]:.2f}")
Running the example gives an output like:
Mean Squared Error: 86.43
Predicted value for test sample: 0.00
The key steps in this code example are:
Dataset preparation: A synthetic dataset is generated where the target variable is a linear combination of the input features, plus some random noise.
Model instantiation and configuration: An instance of
GaussianProcessRegressoris created with theWhiteKernel, and relevant hyperparameters are set.Model training: The dataset is split into train and test portions, and the model is fitted on the training data.
Model evaluation: The model’s performance is evaluated using mean squared error on the test set.
Inference on test sample(s): A prediction is made using the fitted model on one test sample, demonstrating how the model can be used for inference on new data.