dscr-enet

A simulation study of large-scale regression methods as described in Zou & Hastie (2005)

Background

For a general introduction to DSCs, see here.

In this simulation study, we aim to compare several methods for fitting a linear model of the form Y=XB+e, where y is a n by 1 vector of responses, X is a n by p matrix of predictors, B is a p by 1 vector of unknown coefficients and e is a n by 1 vector of iid Gaussian noise. Although the problem as described is a generic one, the methods in this study aim to provide some level of variable selection, and the vector B typically contains a substantial number of zeroes.

The simulation schemes all contain a training set and a test set. The models are trained on the training set and an estimated vector of coefficients Bhat is returned. The performance of a method is then determined by the quantity E((X* Bhat-X* B)^2), where X* are the predictors in the test set.

Input, meta and output formats

This DSC uses the following formats:

input: an ntrain by p+1 matrix of training data [matrix] #ntrain is the number of observations in the training set, and p is the number of predictors. The first column of the matrix contains the Y values in the training set, and the rest of the matrix contains the X values.

meta: list(testset [matrix], betatrue [vector]) #testset is an ntest by p+1 matrix of test data, where ntest is the number of observations in the test set, and p is the number of predictors. The first column of the matrix contains the Y values in the test set, and the rest of the matrix contains the X values. betatrue is a p by 1 vector, which is simply the true B from whence the observations are generated from.

output: an estimated vector of coefficients for B [vector]

Scores

The performance of a method is scored by the quantity median(Ehat((X* Bhat-X* B)^2)). Here X* are the predictors in the test set, Ehat denotes the sample average, and the median is computed over all runs of a given simulation scheme (ie different seeds).

See score.R.

To add a method

To add a method there are two steps.

• add a .R file containing an R function implenting that method to the methods/ subdirectory
• add the method to the list of methods in the methods.R file.

Each method function must take arguments (input,args) where input is a list with the correct format (defined above), and args is a list containing any additional arguments the method requires.

Each method function must return output, where output is a list with the correct format (defined above).

To add a scenario

To add a scenario there are two steps, the first of which can be skipped if you are using an existing datamaker function

• add a .R file containing an R function implenting a datamaker to the datamakers/ subdirectory
• add the scenario to the list of scenarios in the scenarios.R file.

Each datamaker function must return a list(meta,input) where meta and input are each lists with the correct format (defined above).