# A study on tuning parameter selection for the high-dimensional lasso

arXiv: https://arxiv.org/abs/1602.01522 · HTML: https://mlsanity.com/paper/1602.01522/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Feb 2016.

## Built on by (most cited first, 1 of 1)

- [Strong Screening Rules for Group-based SLOPE Models](https://mlsanity.com/paper/2405.15357/) (2024)

## Abstract (arXiv)

High-dimensional predictive models, those with more measurements than observations, require regularization to be well defined, perform well empirically, and possess theoretical guarantees. The amount of regularization, often determined by tuning parameters, is integral to achieving good performance. One can choose the tuning parameter in a variety of ways, such as through resampling methods or generalized information criteria. However, the theory supporting many regularized procedures relies on an estimate for the variance parameter, which is complicated in high dimensions. We develop a suite of information criteria for choosing the tuning parameter in lasso regression by leveraging the literature on high-dimensional variance estimation. We derive intuition showing that existing information-theoretic approaches work poorly in this setting. We compare our risk estimators to existing methods with an extensive simulation and derive some theoretical justification. We find that our new estimators perform well across a wide range of simulation conditions and evaluation criteria.