Bias-Variance Tradeoff in $L_p$ Regularized Regression

External question — Cross Validated Stack Exchange Author: Valentina Original post: https://stats.stackexchange.com/questions/660240 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. In regularized linear regression with $L_p$ norm penalties $(||w||^p)$ , where $p ≥ 1$ , how does increasing the value of $p$ , especially when the model weights are relatively large ( $>1$ ), affect the model's bias and variance? In the case of $p=1,p=2$ we get LASSO and Ridge Regression, respectively which as I understand aims to minimize overfitting by introducing bias and lowering the variance. Does the same hold for larger values of $p$ ? What is the relationship between p and the bias-variance trade-off?.