import numpy as np
[docs]class base_optimizer:
"""
Base class to define the methods, which are to implemented
"""
def __init__(self):
pass
[docs] def solve(self):
raise NotImplementedError
[docs]class lstsqrs(base_optimizer):
"""
Least squares optimizer.
This optimizer pipes the training data to numpy.linalg.lstsq. This can be understood as the most simple optimizer. Use with strong caution because no regularization is applied, which poses the risk of overfitting and bad out-of-sample predictions
"""
def __init__(self):
pass
[docs] def solve(self, feature_matrix, target_matrix):
"""
Solver, which is invoked by derrom's fit method.
Parameters:
-----------
feature_matrix : 2D numpy.ndarray
Feature matrix with the feature vectors stored in the rows. The feature matrix is automatically generated by derrom's fit method
target_matrix : 2D numpy.ndarray
Target matrix with the target vectors stored in the rows. The target matrix is automatically generated by derrom's fit method
"""
return np.asarray( np.linalg.lstsq(feature_matrix, target_matrix, rcond = -1)[0] )
[docs]class ridge(base_optimizer):
"""
Regularized least squares optimizer. Rigde regression.
This optimizer applies L2/Thikonov regularization to the regression weights. This approach counters overfitting and helps to improve out-of-sample predictions. It can be understood as sacrificing the models specificity to improve its ability to generalize. A balance between these two, i.e., an optimal alpha must be found to optimize the regression performance.
Parameters:
-----------
alpha : float
Regularization parameter. Larger values impose a stronger regularization. alpha = 0 eliminates the regularization und yields the least-squares estimator.
"""
def __init__(self, alpha = 1e-6):
self.alpha = alpha
[docs] def solve(self, feature_matrix, target_matrix):
"""
Solver, which is invoked by derrom's fit method.
Parameters:
-----------
feature_matrix : 2D numpy.ndarray
Feature matrix with the feature vectors stored in the rows. The feature matrix is automatically generated by derrom's fit method
target_matrix : 2D numpy.ndarray
Target matrix with the target vectors stored in the rows. The target matrix is automatically generated by derrom's fit method
"""
return np.linalg.inv(feature_matrix.T @ feature_matrix + self.alpha * np.identity(feature_matrix.shape[1])) @ feature_matrix.T @ target_matrix