# Technical Program

## Paper Detail

 Paper ID SPTM-14.1 Paper Title OUTLIER-ROBUST KERNEL HIERARCHICAL-OPTIMIZATION RLS ON A BUDGET WITH AFFINE CONSTRAINTS Authors Konstantinos Slavakis, University at Buffalo, State University of New York, United States; Masahiro Yukawa, Keio University, Japan Session SPTM-14: Models, Methods and Algorithms 2 Location Gather.Town Session Time: Thursday, 10 June, 13:00 - 13:45 Presentation Time: Thursday, 10 June, 13:00 - 13:45 Presentation Poster Topic Signal Processing Theory and Methods: [ASP] Adaptive Signal Processing IEEE Xplore Open Preview Click here to view in IEEE Xplore Virtual Presentation Click here to watch in the Virtual Conference Abstract This paper introduces a non-parametric learning framework to combat outliers in online, multi-output, and nonlinear regression tasks. A hierarchical-optimization problem underpins the learning task: Search in a reproducing kernel Hilbert space (RKHS) for a function that minimizes a sample average $\ell_p$-norm ($1 \leq p \leq 2$) error loss defined on data contaminated by noise and outliers, under affine constraints defined as the set of minimizers of a quadratic loss on a finite number of faithful data devoid of noise and outliers (side information). To surmount the computational obstacles inflicted by the choice of loss and the potentially infinite dimensional RKHS, approximations of the $\ell_p$-norm loss, as well as a novel twist of the criterion of approximate linear dependency are devised to keep the computational-complexity footprint of the proposed algorithm bounded over time. Numerical tests on datasets showcase the robust behavior of the advocated framework against different types of outliers, under a low computational load, while satisfying at the same time the affine constraints, in contrast to the state-of-the-art methods which are constraint agnostic.