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arXiv · 2004.11554

Estimating the Lasso's Effective Noise

Johannes Lederer·Michael Vogt
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Abstract

Much of the theory for the lasso in the linear model $Y = X \beta^* + \varepsilon$ hinges on the quantity $2 \| X^\top \varepsilon \|_{\infty} / n$, which we call the lasso's effective noise. Among other things, the effective noise plays an important role in finite-sample bounds for the lasso, the calibration of the lasso's tuning parameter, and inference on the parameter vector $\beta^*$. In this paper, we develop a bootstrap-based estimator of the quantiles of the effective noise. The estimator is fully data-driven, that is, does not require any additional tuning parameters. We equip our estimator with finite-sample guarantees and apply it to tuning parameter calibration for the lasso and to high-dimensional inference on the parameter vector $\beta^*$.

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Johannes Lederer, Michael Vogt. 2020-04-24. Estimating the Lasso's Effective Noise. https://arxiv.org/abs/2004.11554

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