How does lasso regression compare to ordinary least squares regarding flexibility and prediction accuracy?

Lasso regression, which stands for Least Absolute Shrinkage and Selection Operator, applies L1 regularization to the regression process. This regularization technique encourages sparsity in the model by penalizing the absolute size of the coefficients attached to the predictor variables. As a result, lasso regression can lead to simpler models that utilize only the most relevant predictors, effectively performing variable selection in addition to coefficient estimation.

When we say that lasso regression is less flexible compared to ordinary least squares (OLS), we refer to its characteristic of shrinking coefficients, which can lead to higher bias. This bias arises from the model being less able to capture the true relationships in the data due to the restrictions imposed by the L1 penalty. However, this trade-off between bias and variance is what allows lasso regression to improve prediction accuracy in certain situations, especially when dealing with high-dimensional data or when multicollinearity exists among predictors.

In scenarios where the true underlying model is indeed sparse (i.e., only a few predictors are truly relevant while others contribute noise), lasso regression performs well as it effectively reduces overfitting by ignoring irrelevant predictors. This aspect helps enhance the prediction accuracy when the model complexity is curtailed, leading to more generalizable models compared to O