I am interested in solving the following problem
$$ \min_{\boldsymbol{\beta}} \left( \mathbf{y}-\mathbf{X}\boldsymbol{\beta} \right)^T W \left( \mathbf{y}-\mathbf{X}\boldsymbol{\beta} \right) + \lambda \left|\boldsymbol{\beta}\right|_1 $$
$\mathbf{y}$ is the vector of observations for each dataset.
$\mathbf{X}$ is the matrix of predictors.
$\boldsymbol{\beta}$ is the set of regression coefficients.
$\mathbf{W}$ is a diagonal matrix filled with positive real numbers.
using the LARS-Lasso approach. Is there any existing package that does this, meaning that it accepts weights for each as an input?
With all the normalizing of the datasets (centering and scaling) that need to be done, I am hesitant to pre-process my data and multiply both the observation and the predictors with $\sqrt{W}$ and feed it in to the algorithm.
R
package? Are you wondering about anything other than the name of a package that would do this for you? If not, this question is probably best asked on the r-help-listserve; it would be off-topic here (please see our FAQ). $\endgroup$