transformed.ineq: Transform Data to Fit PaC Implementation for Inequality... In PACLasso: Penalized and Constrained Lasso Optimization

Description

This function is called internally by `lars.c` to compute the transformed versions of the X, Y, and constraint matrix data, as shown in the PaC paper.

Usage

 `1` ```transformed.ineq(x, y, C.full, b, lambda, beta0, eps = 10^-8) ```

Arguments

 `x` independent variable matrix of data to be used in calculating PaC coefficient paths `y` response vector of data to be used in calculating PaC coefficient paths `C.full` complete constraint matrix C (with inequality constraints of the form `C.full`*`beta` >= `b`)) `b` constraint vector b `lambda` value of lambda `beta0` initial guess for beta coefficient vector `eps` value close to zero used to verify SVD decomposition. Default is 10^-8

Value

`x` transformed x data to be used in the PaC algorithm

`y` transformed y data to be used in the PaC algorithm

`Y_star` transformed Y* value to be used in the PaC algorithm

`a2` index of A used in the calculation of beta2 (the non-zero coefficients)

`beta1` beta1 values

`beta2` beta2 values

`C` constraint matrix

`C2` subset of constraint matrix corresponding to non-zero coefficients

`active.beta` index of non-zero coefficient values

`beta2.index` index of non-zero coefficient values

References

Gareth M. James, Courtney Paulson, and Paat Rusmevichientong (JASA, 2019) "Penalized and Constrained Optimization." (Full text available at http://www-bcf.usc.edu/~gareth/research/PAC.pdf)

Examples

 ```1 2 3 4 5 6 7``` ```random_data = generate.data(n = 500, p = 20, m = 10) transform_fit = transformed.ineq(random_data\$x, random_data\$y, random_data\$C.full, random_data\$b, lambda = 0.01, beta0 = rep(0,20)) dim(transform_fit\$x) head(transform_fit\$y) dim(transform_fit\$C) transform_fit\$active.beta ```

PACLasso documentation built on May 2, 2019, 2:29 p.m.