Before revision:  We use L1-regularized methods to learn approximations to the regression function and the Riesz representer, and construct the estimator for the linear functionals as the solution to the orthogonal estimating equations.
After 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 orthogonal estimating equations.