How does the concept of bias-variance tradeoff apply to lasso regression?

The bias-variance tradeoff is a fundamental concept in statistical modeling that describes the balance needed to achieve a model that generalizes well to unseen data. In the context of lasso regression, which is a type of linear regression that incorporates L1 regularization, the correct understanding of its behavior in terms of bias and variance is central.

Lasso regression works by adding a penalty to the loss function that is proportional to the absolute values of the coefficients. This regularization technique helps to shrink some of the coefficients towards zero, which effectively reduces the complexity of the model. While this shrinking can lead to greater bias—because the model may not fit the training data as closely due to some coefficients being set to zero—it also leads to a significant reduction in variance.

Higher variance in a model indicates that it is highly sensitive to fluctuations in the training data, which can cause overfitting. By introducing a regularization term, lasso regression constrains the model more, allowing it to perform better on unseen data even if it comes at the cost of a higher bias. In scenarios where a model fails to generalize well, the introduction of bias often results in more robust predictions across different datasets, making lasso useful for high-dimensional datasets where variables may be correlated