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

06/20/2016
by   Pierre C. Bellec, et al.
0

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.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
08/03/2020

On Dantzig and Lasso estimators of the drift in a high dimensional Ornstein-Uhlenbeck model

In this paper we present new theoretical results for the Dantzig and Las...
research
08/06/2019

Debiasing Linear Prediction

Standard methods in supervised learning separate training and prediction...
research
04/09/2012

Non-asymptotic Oracle Inequalities for the High-Dimensional Cox Regression via Lasso

We consider the finite sample properties of the regularized high-dimensi...
research
11/30/2009

Sparse Empirical Bayes Analysis (SEBA)

We consider a joint processing of n independent sparse regression proble...
research
08/01/2016

Oracle Inequalities for High-dimensional Prediction

The abundance of high-dimensional data in the modern sciences has genera...
research
10/16/2022

Dimension free ridge regression

Random matrix theory has become a widely useful tool in high-dimensional...
research
07/29/2021

CAD: Debiasing the Lasso with inaccurate covariate model

We consider the problem of estimating a low-dimensional parameter in hig...

Please sign up or login with your details

Forgot password? Click here to reset