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Screening Tests for Lasso Problems

机译：套索问题的筛选测试

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摘要

This paper is a survey of dictionary screening for the lasso problem. The lasso problem seeks a sparse linear combination of the columns of a dictionary to best match a given target vector. This sparse representation has proven useful in a variety of subsequent processing and decision tasks. For a given target vector, dictionary screening quickly identifies a subset of dictionary columns that will receive zero weight in a solution of the corresponding lasso problem. These columns can be removed from the dictionary prior to solving the lasso problem without impacting the optimality of the solution obtained. This has two potential advantages: it reduces the size of the dictionary, allowing the lasso problem to be solved with less resources, and it may speed up obtaining a solution. Using a geometrically intuitive framework, we provide basic insights for understanding useful lasso screening tests and their limitations. We also provide illustrative numerical studies on several datasets.
机译：本文是针对套索问题的字典筛选的一项调查。套索问题寻求字典的列的稀疏线性组合以最佳地匹配给定的目标向量。这种稀疏表示已被证明可用于各种后续处理和决策任务。对于给定的目标向量，字典筛选可以快速识别字典列的子集，该子集将在对应套索问题的解决方案中获得零权重。在解决套索问题之前，可以将这些列从字典中删除，而不会影响所获得解决方案的最优性。这有两个潜在的优点：减小字典的大小，允许套索问题用更少的资源解决，并且可以加快获得解决方案的速度。使用几何直观的框架，我们为了解有用的套索筛选测试及其局限性提供了基本见解。我们还提供了一些数据集的说明性数值研究。

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