Max-Linear Regression by Convex Programming

arXiv:2103.07020v2 Announce Type: replace-cross
Abstract: We consider the multivariate max-linear regression problem where the model parameters $\boldsymbol{\beta}_{1},\dotsc,\boldsymbol{\beta}_{k}\in\mathbb{R}^{p}$ need to be estimated from $n$ independent samples of the (noisy) observations $y = \max_{1\leq j \leq k} \boldsymbol{\beta}_{j}^{\mathsf{T}} \boldsymbol{x} + \mathrm{noise}$. The max-linear model vastly generalizes the conventional linear model, and it can approximate any convex function to an arbitrary accuracy when the number of linear models $k$ is large enough. However, the inherent nonlinearity of the max-linear model renders the estimation …

abstract arxiv beta cs.it cs.lg function independent linear linear model linear regression math.it math.st max multivariate noise parameters programming regression samples stat.ml stat.th type