L2regularisoinnissa

L2 regularization is a technique used in machine learning to prevent overfitting. It works by adding a penalty term to the model's cost function, which is proportional to the square of the magnitude of the model's coefficients. This penalty discourages the model from assigning large weights to any single feature, thus promoting a simpler model with better generalization capabilities. The L2 penalty is often referred to as ridge regression when applied to linear models.

The mathematical formulation of the L2 regularization term is the sum of the squares of all the weights in the model, multiplied by a regularization parameter, lambda. The cost function then becomes the original cost function plus this L2 penalty term. During training, the optimization algorithm aims to minimize this combined cost function. By minimizing the squared weights, L2 regularization effectively shrinks the coefficients towards zero, but it rarely makes them exactly zero. This contrasts with L1 regularization, which can drive coefficients to zero, leading to feature selection.

The strength of the regularization is controlled by the hyperparameter lambda. A larger lambda results in a stronger penalty and more shrinkage of the coefficients, leading to a simpler model. Conversely, a smaller lambda means less regularization and a model that is closer to the unregularized version. Choosing the optimal value of lambda is crucial and is typically done through cross-validation. L2 regularization is widely used in various machine learning algorithms, including linear regression, logistic regression, and neural networks, due to its effectiveness in improving model robustness and preventing overfitting.