Penalized empirical risk minimization over Besov spaces

• We revisit the Ellipsoid method (Bland et al., 1981) to design screening test for samples, when the objec- tive is convex and its dual admits a sparse solution.. • We propose a

We study the performance of empirical risk minimization (ERM), with re- spect to the quadratic risk, in the context of convex aggregation, in which one wants to construct a

The problem of convex aggregation is to construct a procedure having a risk as close as possible to the minimal risk over conv(F).. Consider the bounded regression model with respect

We have shown in Section 2 that the small-ball condition is satis…ed for linear models such as histograms, piecewise polynomials or compactly supported wavelets, but with constants

We prove that, if all the M classifiers are binary, the (penalized) Empirical Risk Minimization procedures are suboptimal (even under the margin/low noise condition) when the

Although statistical learning theory mainly focuses on establishing universal rate bounds (i.e., which hold for any distribution of the data) for the accuracy of a decision rule

In this paper, we argue that for such problems, Empirical Risk Minimization can be implemented using statistical counterparts of the risk based on much less terms (picked randomly

The l 1 –based penalizer is known as the lasso (least absolute shrinkage and selection operator) [2]. The lasso estimates a vector of linear regression coefficients by minimizing