Robust kernel-based distribution regression

Regularization schemes for regression have been widely studied in learning theory and inverse problems. In this paper, we study distribution (DR) which involves two stages of sampling, aims at regressing from probability measures to real-valued responses over a reproducing kernel Hilbert space (RKHS). Recently, theoretical analysis on DR has carried out via ridge several behaviors observed. However, the topic not explored understood beyond least square based DR. By introducing robust loss function $l_{\sigma}$ two-stage sampling problems, present novel (RDR) scheme. With windowing $V$ scaling parameter $\sigma$ can be appropriately chosen, include wide range popular used functions that enrich theme Moreover, is necessarily convex, hence largely improving former class (least square) literature The rates under different regularity ranges $f_{\rho}$ are comprehensively derived integral operator techniques. shown crucial providing robustness satisfactory RDR.