资源论文Complexity Analysis of the Lasso Regularization Path

Complexity Analysis of the Lasso Regularization Path

2020-02-28 | |  40 |   38 |   0

Abstract

The regularization path of the Lasso can be shown to be piecewise linear, making it possible to “follow” and explicitly compute the entire path. We analyze in this paper this popular strategy, and prove that its worst case complexity is exponential in the number of variables. We then oppose this pessimistic result to an (optimistic) approximate analysis: We show ? that an approximate path with at most 图片.png linear segments can always be obtained, where every point on the path is guaranteed to be optimal up to a relative ε-duality gap. We complete our theoretical analysis with a practical algorithm to compute these approximate paths.

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