Ridgesäännöllistäminen

Ridgesäännöllistäminen is a regularization technique used in statistical modeling, particularly in regression analysis, to address multicollinearity and improve the stability of coefficient estimates. It is a variation of ordinary least squares (OLS) that introduces a penalty term to the loss function. This penalty is proportional to the square of the magnitude of the coefficients.

The core idea behind Ridgesäännöllistäminen is to shrink the regression coefficients towards zero, but not exactly to zero, unlike in Lasso regression. This shrinkage is controlled by a parameter, often denoted as lambda (λ) or alpha (α). A larger value of λ results in more shrinkage, effectively reducing the influence of less important predictors.

By adding this penalty, Ridgesäännöllistäminen effectively reduces the variance of the coefficient estimates at the expense of a small increase in bias. This trade-off can lead to a model with better predictive accuracy, especially when dealing with datasets where independent variables are highly correlated. The technique is particularly useful when the number of predictors is large relative to the number of observations.

The mathematical formulation of Ridgesäännöllistäminen involves minimizing a cost function that combines the residual sum of squares (RSS) with the sum of squared coefficients multiplied by λ. The resulting coefficients are not necessarily zero, meaning that all predictors still contribute to the model, albeit with potentially reduced impact. The selection of an appropriate λ value is crucial and is often done through cross-validation.