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L1 Regularization

Regularization technique that adds a penalty equal to the absolute value of the model coefficients, promoting sparsity and automatically eliminating irrelevant features.

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L2 Regularization

Penalization method that adds a term proportional to the square of the coefficients, reducing their magnitude without zeroing them completely to counter overfitting.

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Elastic Net

Linear combination of L1 and L2 regularizations that inherits the variable selection properties of Lasso and the stability of Ridge, particularly effective in the presence of correlated features.

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Lambda hyperparameter

Regularization parameter controlling the intensity of the penalty applied to coefficients, where lambda=0 corresponds to no regularization and high lambda increases the constraint.

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L1 Norm

Vector norm calculated as the sum of the absolute values of the components, used as a penalty term in L1 regularization to induce sparsity.

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L2 Norm

Euclidean norm calculated as the square root of the sum of the squares of the components, used in L2 regularization to penalize large coefficients.

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Shrinkage

Process of systematically reducing the magnitude of model coefficients toward zero to decrease complexity and improve generalization.

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Bias-variance dilemma

Fundamental trade-off in machine learning between reducing bias (systematic error) and reducing variance (sensitivity to data fluctuations).

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Alpha coefficient

Mixing parameter in Elastic Net varying between 0 (pure L2 regularization) and 1 (pure L1 regularization) to adjust the relative proportion of the two penalties.

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Regularization path

Trajectory of model solutions when the regularization parameter varies, allowing analysis of the evolution of coefficients and their progressive selection.

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Weight vector

Set of multiplicative coefficients applied to features in a linear model, whose magnitude is controlled by regularization techniques.

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Group penalty

Extension of L1/L2 regularization that penalizes groups of coefficients simultaneously, useful for handling categorical or structured variables.

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Adaptive regularization

Variant of regularization where each coefficient receives an individualized penalty based on preliminary estimates, allowing finer variable selection.

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Information criterion

Metrics like AIC or BIC that balance model fit and its complexity, often used to select the optimal regularization parameter.

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Regularized gradient descent

Optimization algorithm incorporating L1/L2 penalty terms directly into the objective function to efficiently train regularized models.

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Coordinate descent

Optimization method particularly efficient for L1 regularization that updates coefficients one by one in an analytical manner.

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