# On the prediction loss of the lasso in the partially labeled setting

arXiv: https://arxiv.org/abs/1606.06179 · HTML: https://mlsanity.com/paper/1606.06179/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jun 2016.

## Built on by (most cited first, 3 of 3)

- [Mixed Semi-Supervised Generalized-Linear-Regression with Applications to Deep-Learning and Interpolators](https://mlsanity.com/paper/2302.09526/) (2023)
- [Statistical Inference for High-Dimensional Linear Regression with Blockwise Missing Data](https://mlsanity.com/paper/2106.03344/) (2021)
- [Convex Estimation of Gaussian Graphical Regression Models with Covariates](https://mlsanity.com/paper/2410.06326/) (2024)

## Abstract (arXiv)

In this paper we revisit the risk bounds of the lasso estimator in the context of transductive and semi-supervised learning. In other terms, the setting under consideration is that of regression with random design under partial labeling. The main goal is to obtain user-friendly bounds on the off-sample prediction risk. To this end, the simple setting of bounded response variable and bounded (high-dimensional) covariates is considered. We propose some new adaptations of the lasso to these settings and establish oracle inequalities both in expectation and in deviation. These results provide non-asymptotic upper bounds on the risk that highlight the interplay between the bias due to the mis-specification of the linear model, the bias due to the approximate sparsity and the variance. They also demonstrate that the presence of a large number of unlabeled features may have significant positive impact in the situations where the restricted eigenvalue of the design matrix vanishes or is very small.