Abstract
The lasso is a popular tool for sparse linear regression, especially for problems in which the number of variables
A second important question is: how can we manage the case of non-uniqueness in lasso solutions? In light of the aforementioned result, this case really only arises when some of the predictor variables are discrete, or when some post-processing has been performed on continuous predictor measurements. Though we certainly cannot claim to provide a complete answer to such a broad question, we do present progress towards understanding some aspects of non-uniqueness. First, we extend the LARS algorithm for computing the lasso solution path to cover the non-unique case, so that this path algorithm works for any predictor matrix. Next, we derive a simple method for computing the component-wise uncertainty in lasso solutions of any given problem instance, based on linear programming. Finally, we review results from the literature on some of the unifying properties of lasso solutions, and also point out particular forms of solutions that have distinctive properties.
Citation
Ryan J. Tibshirani. "The lasso problem and uniqueness." Electron. J. Statist. 7 1456 - 1490, 2013. https://doi.org/10.1214/13-EJS815
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