# Regularization Trade-offs with Fake Features

arXiv: https://arxiv.org/abs/2212.00433 · HTML: https://mlsanity.com/paper/2212.00433/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 19 references that are in the map.
- First posted on arXiv 1 Dec 2022.

## Builds on (most cited first, 13 of 13)

- [Reconciling modern machine learning practice and the bias-variance trade-off](https://mlsanity.com/paper/1812.11118/) (2018)
- [Benign Overfitting in Linear Regression](https://mlsanity.com/paper/1906.11300/) (2019)
- [Surprises in High-Dimensional Ridgeless Least Squares Interpolation](https://mlsanity.com/paper/1903.08560/) (2019)
- [Two models of double descent for weak features](https://mlsanity.com/paper/1903.07571/) (2019)
- [Benign overfitting in ridge regression](https://mlsanity.com/paper/2009.14286/) (2020)
- [Optimal Regularization Can Mitigate Double Descent](https://mlsanity.com/paper/2003.01897/) (2020)
- [Double Trouble in Double Descent : Bias and Variance(s) in the Lazy Regime](https://mlsanity.com/paper/2003.01054/) (2020)
- [A Random Matrix Analysis of Random Fourier Features: Beyond the Gaussian Kernel, a Precise Phase Transition, and the Corresponding Double Descent](https://mlsanity.com/paper/2006.05013/) (2020)
- [Optimal ridge penalty for real-world high-dimensional data can be zero or negative due to the implicit ridge regularization](https://mlsanity.com/paper/1805.10939/) (2018)
- [Multiple Descent: Design Your Own Generalization Curve](https://mlsanity.com/paper/2008.01036/) (2020)
- [On the Universality of the Double Descent Peak in Ridgeless Regression](https://mlsanity.com/paper/2010.01851/) (2020)
- [Robust Prediction when Features are Missing](https://mlsanity.com/paper/1912.07226/) (2019)
- [Estimation under Model Misspecification with Fake Features](https://mlsanity.com/paper/2203.03398/) (2022)

## Abstract (arXiv)

Recent successes of massively overparameterized models have inspired a new line of work investigating the underlying conditions that enable overparameterized models to generalize well. This paper considers a framework where the possibly overparametrized model includes fake features, i.e., features that are present in the model but not in the data. We present a non-asymptotic high-probability bound on the generalization error of the ridge regression problem under the model misspecification of having fake features. Our highprobability results provide insights into the interplay between the implicit regularization provided by the fake features and the explicit regularization provided by the ridge parameter. Numerical results illustrate the trade-off between the number of fake features and how the optimal ridge parameter may heavily depend on the number of fake features.