Optimal rates of convergence for convex set estimation from support functions

TL;DR

This paper introduces a minimax optimal method for estimating convex sets from noisy support function measurements, utilizing regularized least squares, applicable to both fixed and random data designs.

Contribution

It provides the first minimax optimal estimator for convex set estimation from support functions with regularization techniques.

Findings

Achieves minimax optimal convergence rates.

Works for both fixed and random measurement designs.

Uses regularized least squares for improved estimation.

Abstract

We present a minimax optimal solution to the problem of estimating a compact, convex set from finitely many noisy measurements of its support function. The solution is based on appropriate regularizations of the least squares estimator. Both fixed and random designs are considered.