What is a cost associated with regularizing input distributions in regression?

In the context of regression, regularizing input distributions refers to techniques that modify the model to control overfitting and improve generalization. While regularization can lead to benefits such as improved model simplicity and enhanced prediction accuracy, it often introduces challenges in interpreting the model outputs.

When input distributions are regularized, particularly through techniques like Lasso (L1 regularization) or Ridge (L2 regularization), the model may shrink some coefficients towards zero or alter their magnitudes significantly. This leads to a situation where the relationship between predictors and the response variable can become less straightforward, making it difficult for practitioners to understand the influence of each predictor on the outcome. Consequently, while the model may perform better statistically, interpreting how each variable contributes to predictions becomes complex, thus emphasizing the point that regularization often affects model interpretability negatively.

Improved prediction accuracy and model simplicity are advantages that can arise from regularization, while the ability to handle outliers can also be enhanced. However, these benefits do not outweigh the challenges related to interpreting the model—demonstrating the trade-offs involved in using regularization techniques in regression modeling.