Before revision:  We use l1-regularized methods to learn approximations to the regression function and the linear representer, in settings where dimension of (possibly overcomplete) dictionary of basis functions P is much larger than N. We then estimate the linear functional by the solution to the empirical analog of the orthogonal equations. Our key result is that under weak assumptions the estimator of the functional concentrates in a L/ root(n) neighborhood of the target with deviations controlled by the Gaussian law , provided L/root(n) 0;
After revision:  Under weak assumptions, the estimator of the functional concentrates in a L/ root(n) neighborhood of the target with deviations controlled by the Gaussian law , provided L/root(n) 0;