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Elastic Net Regularization
Combination of L1 and L2 regularizations that uses a mixing parameter to simultaneously benefit from variable selection (L1) and coefficient stabilization (L2).
Regularization Hyperparameter (λ)
Scalar parameter that controls the intensity of penalization in regularization methods, balancing data fitting and model complexity.
Regularization Factor
Multiplicative coefficient applied to the regularization term in the objective function, determining the relative weight of the penalty compared to the approximation error.
Regularization Bias
Systematic bias introduced by regularization in parameter estimates, necessary to reduce variance and improve generalization.
Frobenius Penalty
Matrix regularization term based on the Frobenius norm, penalizing the sum of squares of all matrix elements to control its complexity.
Nuclear Regularization
Penalization based on the nuclear norm (sum of singular values) that promotes low-rank matrices, particularly useful in matrix completion.
Cross-Validation for λ
Systematic evaluation procedure using different data partitions to select the optimal value of the regularization hyperparameter λ.
Factor Degeneracy
Problem where latent factors become arbitrarily large in amplitude without improving approximation quality, requiring regularization to constrain their norm.
Trace regularization
Penalty term based on the trace (sum of diagonal elements) of a matrix, used to control the global scale of factors in decomposition.
Sparsity coefficient
Parameter controlling the intensity of L1 regularization, determining the desired level of sparsity in the representation of latent factors.
Tikhonov penalty
Generalized form of L2 regularization applied to inverse problems, stabilizing the solution by penalizing the norm of parameters according to a predefined weighting matrix.
Adaptive regularization adjustment
Method where the regularization parameter varies dynamically based on the local structure of the data, applying differentiated penalties according to regions of the space.