Which statement about the tuning parameter λ in the lasso model-fitting procedure is true?

In the context of the lasso (Least Absolute Shrinkage and Selection Operator) model-fitting procedure, the tuning parameter λ plays a crucial role in determining the characteristics of the model. As λ increases, the lasso introduces a stronger penalty for including predictors in the model, leading to more coefficients being driven exactly to zero. This means that the complexity of the model is reduced, often resulting in a model that captures the essence of the data without the noise contributed by many predictors.

When λ increases, the penalty effectively tightens around the coefficient estimates, leading to greater bias in those estimates. This occurs because, with higher values of λ, the model becomes less prone to overfitting the training data, which is especially beneficial in situations with high-dimensional data or where multicollinearity among predictors is a concern. The trade-off here is that, although the bias increases, the variance of the predictions typically decreases, resulting in a more stable model when applied to new data. Thus, the correct interpretation aligns with the notion that increasing λ tends to inflate bias, as it shrinks coefficients towards zero and potentially overlooks useful predictors.

The correctness of this statement hinges on the fundamental nature of lasso regression, where controlling model complexity through regularization alters bias