Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the prediction loss of the lasso in the partially labeled setting   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.

34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin