Poster
A Comparative Framework for Preconditioned Lasso Algorithms
Fabian L Wauthier · Nebojsa Jojic · Michael Jordan

Sat Dec 7th 07:00 -- 11:59 PM @ Harrah's Special Events Center, 2nd Floor #None
The Lasso is a cornerstone of modern multivariate data analysis, yet its performance suffers in the common situation in which covariates are correlated. This limitation has led to a growing number of \emph{Preconditioned Lasso} algorithms that pre-multiply $X$ and $y$ by matrices $P_X$, $P_y$ prior to running the standard Lasso. A direct comparison of these and similar Lasso-style algorithms to the original Lasso is difficult because the performance of all of these methods depends critically on an auxiliary penalty parameter $\lambda$. In this paper we propose an agnostic, theoretical framework for comparing Preconditioned Lasso algorithms to the Lasso without having to choose $\lambda$. We apply our framework to three Preconditioned Lasso instances and highlight when they will outperform the Lasso. Additionally, our theory offers insights into the fragilities of these algorithms to which we provide partial solutions.

Author Information

Fabian L Wauthier (Amazon)
Nebojsa Jojic (Microsoft Research)
Michael Jordan (UC Berkeley)

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