# On the Prediction Performance of the Lasso

arXiv: https://arxiv.org/abs/1402.1700 · HTML: https://mlsanity.com/paper/1402.1700/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Feb 2014.

## Built on by (most cited first, 12 of 12)

- [Semi-Random Sparse Recovery in Nearly-Linear Time](https://mlsanity.com/paper/2203.04002/) (2022)
- [On the Power of Preconditioning in Sparse Linear Regression](https://mlsanity.com/paper/2106.09207/) (2021)
- [Statistical guarantees for sparse deep learning](https://mlsanity.com/paper/2212.05427/) (2022)
- [Feature Adaptation for Sparse Linear Regression](https://mlsanity.com/paper/2305.16892/) (2023)
- [Multivariate Trend Filtering for Lattice Data](https://mlsanity.com/paper/2112.14758/) (2021)
- [On the design-dependent suboptimality of the Lasso](https://mlsanity.com/paper/2402.00382/) (2024)
- [Distributional Hardness Against Preconditioned Lasso via Erasure-Robust Designs](https://mlsanity.com/paper/2203.02824/) (2022)
- [Variance estimation in graphs with the fused lasso](https://mlsanity.com/paper/2207.12638/) (2022)
- [LCEN: A Nonlinear, Interpretable Feature Selection and Machine Learning Algorithm](https://mlsanity.com/paper/2402.17120/) (2024)
- [Non-Asymptotic Uncertainty Quantification in High-Dimensional Learning](https://mlsanity.com/paper/2407.13666/) (2024)
- [Joint estimation of smooth graph signals from partial linear measurements](https://mlsanity.com/paper/2505.23240/) (2025)
- [Sparse Linear Regression is Easy on Random Supports](https://mlsanity.com/paper/2511.06211/) (2025)

## Abstract (arXiv)

Although the Lasso has been extensively studied, the relationship between its prediction performance and the correlations of the covariates is not fully understood. In this paper, we give new insights into this relationship in the context of multiple linear regression. We show, in particular, that the incorporation of a simple correlation measure into the tuning parameter can lead to a nearly optimal prediction performance of the Lasso even for highly correlated covariates. However, we also reveal that for moderately correlated covariates, the prediction performance of the Lasso can be mediocre irrespective of the choice of the tuning parameter. We finally show that our results also lead to near-optimal rates for the least-squares estimator with total variation penalty.