NP-hardness of p-adic linear regression

TL;DR

This paper proves that finding optimal solutions for p-adic linear regression is NP-hard by reducing the problem from Max Cut, highlighting computational complexity challenges in p-adic analysis.

Contribution

It establishes the NP-hardness of p-adic linear regression through a polynomial-time reduction from Max Cut, a novel complexity result.

Findings

NP-hardness of p-adic linear regression proven

Reduction from Max Cut used in proof

Highlights computational difficulty in p-adic regression

Abstract

$p$-adic linear regression is the problem of finding coefficients $\beta$ that minimise $\sum_i |y_i - x_i^\top\beta|_p$. We prove that computing an optimal solution is NP-hard via a polynomial-time reduction from Max Cut using a regularisation gadget.