The False Positive Control Lasso
Erik Drysdale, Yingwei Peng, Timothy P. Hanna, Paul Nguyen, Anna, Goldenberg

TL;DR
This paper introduces a novel method for controlling false positives in high-dimensional regression using a generalized Lasso approach, applicable across various models and compatible with existing solvers, with theoretical guarantees.
Contribution
It recasts the SQRT-Lasso as a false positive control method, extends it to all generalized linear models, and provides finite-sample guarantees with practical efficiency.
Findings
Method effectively controls false positives in simulations.
Applicable to all generalized linear models.
Compatible with existing Lasso optimization algorithms.
Abstract
In high dimensional settings where a small number of regressors are expected to be important, the Lasso estimator can be used to obtain a sparse solution vector with the expectation that most of the non-zero coefficients are associated with true signals. While several approaches have been developed to control the inclusion of false predictors with the Lasso, these approaches are limited by relying on asymptotic theory, having to empirically estimate terms based on theoretical quantities, assuming a continuous response class with Gaussian noise and design matrices, or high computation costs. In this paper we show how: (1) an existing model (the SQRT-Lasso) can be recast as a method of controlling the number of expected false positives, (2) how a similar estimator can used for all other generalized linear model classes, and (3) this approach can be fit with existing fast Lasso…
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Taxonomy
TopicsStatistical Methods and Inference · Statistical Methods and Bayesian Inference · Bayesian Methods and Mixture Models
