Preconditioning the Lasso for sign consistency

By Jinzhu Jia, Karl Rohe. 2015

53 citations recorded by the source corpus.

: Sign consistency of the Lasso requires the stringent irrepre- sentable condition. This paper examines whether preconditioning can circumvent this condition. Let X ∈ R n × p and Y ∈ R n satisfy the standard linear regression equation. Instead of computing the Lasso with ( X ,Y ), preconditioning ﬁrst left multiplies by F ∈ R n × n and then computes the Lasso with ( F X ,FY ). While others have proposed preconditioning for other purposes, we provide the ﬁrst results that show F X can satisfy the irrepresentable condi- tion even when X fails to satisfy the condition. Preconditioning the Lasso creates a new estimator that is sign consistent in a wider variety of set- tings. Importantly, left multiplying the regression equation by F does not change β , the vector of unknown coeﬃcients. However, left multiplying this equation by F often inﬂates the variance of the errors. We propose a class of preconditioners to balance these costs and beneﬁts.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/815e0f2e2b4884da7decf29d1a9a0f6e60ac67e0

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Citations in the corpus

Spectral Deconfounding and Perturbed Sparse Linear Models (2018, methodology): “The algorithm is analyzed in [15] as a pre-conditioning method for the variable selection problem when there is no coeﬃcient perturbation present.”