The optimal ridge penalty for real-world high-dimensional data can be zero or negative due to the implicit ridge regularization

Dmitry Kobak, Jonathan Lomond, Benoit Sanchez
https://jmlr.org/papers/v21/19-844.html (previously https://arxiv.org/abs/1805.10939)
Journal of Machine Learning Research, 21(169):1−16, 2020.

The entire code is contained within the single Python notebook.