{"id":2126,"date":"2025-02-28T07:05:25","date_gmt":"2025-02-28T07:05:25","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/02\/28\/2502-19825\/"},"modified":"2025-02-28T07:05:25","modified_gmt":"2025-02-28T07:05:25","slug":"2502-19825","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/02\/28\/2502-19825\/","title":{"rendered":"Fast Debiasing of the LASSO Estimator"},"content":{"rendered":"

Fast Debiasing of the LASSO Estimator
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arXiv:2502.19825v1 Announce Type: new
\nAbstract: In high-dimensional sparse regression, the textsc{Lasso} estimator offers excellent theoretical guarantees but is well-known to produce biased estimates. To address this, cite{Javanmard2014} introduced a method to “debias” the textsc{Lasso} estimates for a random sub-Gaussian sensing matrix $boldsymbol{A}$. Their approach relies on computing an “approximate inverse” $boldsymbol{M}$ of the matrix $boldsymbol{A}^top boldsymbol{A}\/n$ by solving a convex optimization problem. This matrix $boldsymbol{M}$ plays a critical role in mitigating bias and allowing for construction of confidence intervals using the debiased textsc{Lasso} estimates. However the computation of $boldsymbol{M}$ is expensive in practice as it requires iterative optimization. In the presented work, we re-parameterize the optimization problem to compute a “debiasing matrix” $boldsymbol{W} := boldsymbol{AM}^{top}$ directly, rather than the approximate inverse $boldsymbol{M}$. This reformulation retains the theoretical guarantees of the debiased textsc{Lasso} estimates, as they depend on the emph{product} $boldsymbol{AM}^{top}$ rather than on $boldsymbol{M}$ alone. Notably, we provide a simple, computationally efficient, closed-form solution for $boldsymbol{W}$ under similar conditions for the sensing matrix $boldsymbol{A}$ used in the original debiasing formulation, with an additional condition that the elements of every row of $boldsymbol{A}$ have uncorrelated entries. Also, the optimization problem based on $boldsymbol{W}$ guarantees a unique optimal solution, unlike the original formulation based on $boldsymbol{M}$. We verify our main result with numerical simulations.<\/div>\n

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\n Shuvayan Banerjee, James Saunderson, Radhendushka Srivastava, Ajit Rajwade
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Fast Debiasing of the LASSO Estimator arXiv:2502.19825v1 Announce Type: new Abstract: In high-dimensional sparse regression, the textsc{Lasso} estimator offers excellent theoretical guarantees but is well-known to produce biased estimates. To address this, cite{Javanmard2014} introduced a method to “debias” the textsc{Lasso} estimates for a random sub-Gaussian sensing matrix $boldsymbol{A}$. Their approach relies on computing an “approximate […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,113,112],"tags":[1883,1150,419],"class_list":["post-2126","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-stat-ml","tag-boldsymbol","tag-lasso","tag-matrix"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/2126"}],"collection":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/comments?post=2126"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/2126\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=2126"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=2126"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=2126"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}