Scikit-Learn OrthogonalMatchingPursuit Model

Orthogonal Matching Pursuit (OMP) is a greedy algorithm used for linear regression, particularly effective for sparse data. It iteratively selects the best features to use in the model.

The key hyperparameters of OrthogonalMatchingPursuit include n_nonzero_coefs (number of non-zero coefficients in the solution) and tol (tolerance for the stopping condition).

The algorithm is appropriate for regression problems, especially when the number of features is large and sparsity is desired.

from sklearn.datasets import make_regression
from sklearn.model_selection import train_test_split
from sklearn.linear_model import OrthogonalMatchingPursuit
from sklearn.metrics import mean_squared_error

# generate regression dataset
X, y = make_regression(n_samples=100, n_features=10, noise=0.1, random_state=1)

# 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=1)

# create model
model = OrthogonalMatchingPursuit(n_nonzero_coefs=5)

# fit model
model.fit(X_train, y_train)

# evaluate model
yhat = model.predict(X_test)
mse = mean_squared_error(y_test, yhat)
print('Mean Squared Error: %.3f' % mse)

# make a prediction
row = [[-0.92693047, 0.64508501, -0.28279068, -0.79252074, 1.83671608, -0.16487948, 0.60939325, 0.70126755, -0.12130892, -0.49103754]]
yhat = model.predict(row)
print('Predicted: %.3f' % yhat[0])

Running the example gives an output like:

Mean Squared Error: 3701.863
Predicted: -12.001

The steps are as follows:

1. First, a synthetic regression dataset is generated using the make_regression() function. This creates a dataset with a specified number of samples (n_samples), features (n_features), and a fixed random seed (random_state) for reproducibility. The dataset is split into training and test sets using train_test_split().

2. Next, an OrthogonalMatchingPursuit model is instantiated with the n_nonzero_coefs parameter set to 5, specifying the number of non-zero coefficients in the model. The model is then fit on the training data using the fit() method.

3. The performance of the model is evaluated by comparing the predictions (yhat) to the actual values (y_test) using the mean squared error metric.

4. A single prediction can be made by passing a new data sample to the predict() method.

This example demonstrates how to quickly set up and use an OrthogonalMatchingPursuit model for regression tasks, showcasing the simplicity and effectiveness of this algorithm in scikit-learn. The model can handle a large number of features and automatically selects the most important ones, making it a powerful tool for sparse data scenarios.