Contents
What is one standard error Rule?
One standard error is a heuristic rule. If one number is within one standard error from the other number, the two numbers can be thought of as statistically equal.
What is cross validation in Lasso?
One feature of the lasso, and its extensions, is the addition of “tuning” parameters that control some aspect of the fitted model such as the amount of shrinkage applied to the coefficients. Cross-validation is the most commonly used method for choosing tuning parameter values in penalized regression.
When K n the cross validation estimator is approximately unbiased for the true prediction error?
With K=N, the cross-validation estimator is approximately unbiased for the true (expected) prediction error, but can have high variance because the N “training sets” are so similar to one another.
When to use the one standard error rule?
The “one standard error rule” is applied when selecting models through cross-validation (or more generally through any randomization-based procedure). Assume we consider models Mτ indexed by a complexity parameter τ ∈ R, such that Mτ is “more complex”…
How is lasso regularization used in generalized linear models?
For a discussion of generalized linear models, see What Are Generalized Linear Models?. Lasso is a regularization technique for estimating generalized linear models. Lasso includes a penalty term that constrains the size of the estimated coefficients. Therefore, it resembles Ridge Regression.
How is lasso different from stepwise regression and ridge regression?
Unlike ridge regression, as the penalty term increases, the lasso technique sets more coefficients to zero. This means that the lasso estimator is a smaller model, with fewer predictors. As such, lasso is an alternative to stepwise regression and other model selection and dimensionality reduction techniques.
Why is Lasso used as shrinkage estimator?
Lasso includes a penalty term that constrains the size of the estimated coefficients. Therefore, it resembles Ridge Regression. Lasso is a shrinkage estimator: it generates coefficient estimates that are biased to be small.