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=== Lasso/glmnet, adaptive lasso and FAQs ===
=== Lasso/glmnet, adaptive lasso and FAQs ===
* https://en.wikipedia.org/wiki/Lasso_(statistics). It has a discussion when two covariates are highly correlated. For example if gene <math>i</math> and gene <math>j</math> are identical, then the values of <math>\beta _{j}</math> and <math>\beta _{k}</math> that minimize the lasso objective function are not uniquely determined. Elastic Net has been designed to address this shortcoming.
** Strongly correlated covariates have similar regression coefficients, is referred to as the '''grouping''' effect. From the wikipedia page ''"one would like to find all the associated covariates, rather than selecting only one from each set of strongly correlated covariates, as lasso often does. In addition, selecting only a single covariate from each group will typically result in increased prediction error, since the model is less robust (which is why ridge regression often outperforms lasso)"''.

Revision as of 22:41, 7 September 2019

Lasso/glmnet, adaptive lasso and FAQs

    • Strongly correlated covariates have similar regression coefficients, is referred to as the grouping effect. From the wikipedia page "one would like to find all the associated covariates, rather than selecting only one from each set of strongly correlated covariates, as lasso often does. In addition, selecting only a single covariate from each group will typically result in increased prediction error, since the model is less robust (which is why ridge regression often outperforms lasso)".
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