Shrinkage methods in regression include [[ridge regression]], [[lasso regression]], and [[elastic net]]. Shrinkage methods can overcome [[multicollinearity]] and the [[curse of dimensionality]], help with [[feature selection]], and are often used in place of [[best subset selection]] for finding a [[base/Linear Regression/linear regression|linear regression]] model. An alternative to shrinkage methods are [[dimension reduction]] methods. Shrinkage methods are so named because they shrink the estimates of the coefficients $\vec \beta$ towards zero using a **shrinkage penalty**. Where the number of parameters $p$ is greater than the number of observations $n$, there will be no single solution to the [[least squares estimator]], however shrinkage methods can overcome this. Because shrinkage methods will shrink the values of some coefficients, they can be used for feature selection. Lasso regression is better in this case than ridge regression as it will produce estimates of zero for some coefficients while ridge regression will not. In this sense, lasso regression can be thought of as a computationally feasible solution for best subset selection when $p$ is large.