The ℓ¹-regularized empirical risk minimizer achieves minimax-optimal convergence rate n^{-r/(1+b-br)} for nonlinear statistical inverse learning under variational source conditions and polynomial effective-dimension decay.
Nonlinear approximation and the space bv(r2).American Journal of Mathematics, 121(3):587–628, 1999
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Statistical inverse learning and $\ell^1$-regularization
The ℓ¹-regularized empirical risk minimizer achieves minimax-optimal convergence rate n^{-r/(1+b-br)} for nonlinear statistical inverse learning under variational source conditions and polynomial effective-dimension decay.