# Oracle Inequalities for High-dimensional Prediction

arXiv: https://arxiv.org/abs/1608.00624 · HTML: https://mlsanity.com/paper/1608.00624/

## Key facts

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

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

- [Statistical guarantees for sparse deep learning](https://mlsanity.com/paper/2212.05427/) (2022)
- [Learning the Dynamics of Sparsely Observed Interacting Systems](https://mlsanity.com/paper/2301.11647/) (2023)
- [Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data](https://mlsanity.com/paper/2509.00924/) (2025)
- [Covariance-Driven Regression Trees: Reducing Overfitting in CART](https://mlsanity.com/paper/2601.07281/) (2026)

## Abstract (arXiv)

The abundance of high-dimensional data in the modern sciences has generated tremendous interest in penalized estimators such as the lasso, scaled lasso, square-root lasso, elastic net, and many others. In this paper, we establish a general oracle inequality for prediction in high-dimensional linear regression with such methods. Since the proof relies only on convexity and continuity arguments, the result holds irrespective of the design matrix and applies to a wide range of penalized estimators. Overall, the bound demonstrates that generic estimators can provide consistent prediction with any design matrix. From a practical point of view, the bound can help to identify the potential of specific estimators, and they can help to get a sense of the prediction accuracy in a given application.