hows a further comparison through a numeric simulation. It can

hat when ݓଵ increases, the decrease of ݓଶ in a Lasso model is in

curve while the decrease of ݓଶ in a ridge model is in a quadratic

ecause of this, the decay of the regression coefficients of the less

t variables in a Lasso model will be faster.

(a) (b)

A comparison of regression coefficient shrinkage between RLR and Lasso. (a)

atic comparison. (b) The numerical simulation comparison.

s small, more regression coefficients are shrunk to zero. This

at unimportant variables are penalised while important variables

nced in a model. A Lasso model is generally not analytically

and the quadratic programming approach [Garey and Johnson,

used to estimate the parameters for a Lasso model. In

matics, Lasso has been used to derive the parsimonious models or

se models. For instance, it has been used for building the

ious Cox proportional hazards models [Sohn, et al., 2009], for

ing more parsimonious gene networks through exploring the

lationships between genes [Gustafsson, et al., 2009; Shimamura,

07], and for detecting the causative genes of diseases [Shi, et al.,

R package glmnet can be used for the Lasso regression, where

ha parameter is set one. The following code is used to construct a

odel for a data set, where x is an input matrix and y is an output