Outlier Robust Multivariate Polynomial Regression

arXiv:2403.09465v1 Announce Type: cross
Abstract: We study the problem of robust multivariate polynomial regression: let $p\colon\mathbb{R}^n\to\mathbb{R}$ be an unknown $n$-variate polynomial of degree at most $d$ in each variable. We are given as input a set of random samples $(\mathbf{x}_i,y_i) \in [-1,1]^n \times \mathbb{R}$ that are noisy versions of $(\mathbf{x}_i,p(\mathbf{x}_i))$. More precisely, each $\mathbf{x}_i$ is sampled independently from some distribution $\chi$ on $[-1,1]^n$, and for each $i$ independently, $y_i$ is arbitrary (i.e., an outlier) with probability at most $\rho < …

abstract arxiv cs.ds cs.lg multivariate outlier polynomial random regression robust samples set study type versions