# Fractional ridge regression: a fast, interpretable reparameterization of ridge regression

arXiv: https://arxiv.org/abs/2005.03220 · HTML: https://mlsanity.com/paper/2005.03220/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 May 2020.

## Built on by (most cited first, 4 of 4)

- [NeuroGen: activation optimized image synthesis for discovery neuroscience](https://mlsanity.com/paper/2105.07140/) (2021)
- [Personalized visual encoding model construction with small data](https://mlsanity.com/paper/2202.02245/) (2022)
- [Visual representations in the human brain are aligned with large language models](https://mlsanity.com/paper/2209.11737/) (2022)
- [Optimized two-stage AI-based Neural Decoding for Enhanced Visual Stimulus Reconstruction from fMRI Data](https://mlsanity.com/paper/2412.13237/) (2024)

## Abstract (arXiv)

Ridge regression (RR) is a regularization technique that penalizes the L2-norm of the coefficients in linear regression. One of the challenges of using RR is the need to set a hyperparameter (α) that controls the amount of regularization. Cross-validation is typically used to select the best α from a set of candidates. However, efficient and appropriate selection of α can be challenging, particularly where large amounts of data are analyzed. Because the selected α depends on the scale of the data and predictors, it is not straightforwardly interpretable. Here, we propose to reparameterize RR in terms of the ratio γ between the L2-norms of the regularized and unregularized coefficients. This approach, called fractional RR (FRR), has several benefits: the solutions obtained for different γ are guaranteed to vary, guarding against wasted calculations, and automatically span the relevant range of regularization, avoiding the need for arduous manual exploration. We provide an algorithm to solve FRR, as well as open-source software implementations in Python and MATLAB (https://github.com/nrdg/fracridge). We show that the proposed method is fast and scalable for large-scale data problems, and delivers results that are straightforward to interpret and compare across models and datasets.