Shogun is an open source ML library that provides a wide range of unified ML algorithms. The Shogun library has the CLinearRidgeRegression class for solving simple linear regression problems. This class solves problems with standard Cholesky matrix decomposition in a noniterative way, as illustrated in the following code block:

auto x = some<CDenseFeatures<float64_t>>(x_values);
auto y= some<CRegressionLabels>(y_values); // real-valued labels
float64_t tau_regularization = 0.0001;
auto lr = some<CLinearRidgeRegression>(tau_regularization, nullptr, nullptr); // regression model with regularization
lr->set_labels(y);
r->train(x)

For new x inputs, we can predict new y values in the following way:

auto new_x = some<CDenseFeatures<float64_t>>(new_x_values);
auto y_predict = lr->apply_regression(new_x);

Also, we can get the calculated parameters (the linear regression task solution) vector, as follows:

auto weights = lr->get_w();

Moreover, we can calculate the value of MSE, as follows:

auto y_predict = lr->apply_regression(x);
auto eval = some<CMeanSquaredError>();
auto mse = eval->evaluate(y_predict , y);