Theoretical Analysis of Leave-one-out Cross Validation for
Non-differentiable Penalties under High-dimensional Settings
- URL: http://arxiv.org/abs/2402.08543v2
- Date: Wed, 14 Feb 2024 16:28:59 GMT
- Title: Theoretical Analysis of Leave-one-out Cross Validation for
Non-differentiable Penalties under High-dimensional Settings
- Authors: Haolin Zou, Arnab Auddy, Kamiar Rahnama Rad, Arian Maleki
- Abstract summary: We provide finite sample upper bounds on the expected squared error of leave-one-out cross-validation (LO) in estimating the out-of-sample risk.
The theoretical framework presented here provides a solid foundation for elucidating empirical findings that show the accuracy of LO.
- Score: 12.029919627622954
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Despite a large and significant body of recent work focused on estimating the
out-of-sample risk of regularized models in the high dimensional regime, a
theoretical understanding of this problem for non-differentiable penalties such
as generalized LASSO and nuclear norm is missing. In this paper we resolve this
challenge. We study this problem in the proportional high dimensional regime
where both the sample size n and number of features p are large, and n/p and
the signal-to-noise ratio (per observation) remain finite. We provide finite
sample upper bounds on the expected squared error of leave-one-out
cross-validation (LO) in estimating the out-of-sample risk. The theoretical
framework presented here provides a solid foundation for elucidating empirical
findings that show the accuracy of LO.
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