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Cross-validation is a technique used to assess how the results of a statistical analysis will generalize to an independent data set. In the context of Lasso Regression, which is commonly used for both variable selection and regularization, cross-validation plays a crucial role in determining the optimal value of lambda.

Lambda, also referred to as the regularization parameter, controls the strength of the penalty applied to the size of the coefficients in Lasso regression. By systematically partitioning the training data into subsets, fitting the model on these subsets, and evaluating it on the remaining data, cross-validation helps identify the lambda value that minimizes prediction error. This is essential for achieving a balance between fitting the model closely to the training data while maintaining its ability to generalize to new data, thus avoiding overfitting.

Finding the optimal lambda using cross-validation ensures that the model retains important predictors while effectively shrinking coefficients of less relevant variables, leading to a more interpretable and efficient model structure. Other parameters, such as alpha and beta, do not specifically relate to what cross-validation targets within Lasso regression. Lambda is the critical parameter that directly influences model performance through regularization.