Blind Polynomial Regression

TL;DR

This paper introduces the blind polynomial regression problem, addressing the challenge of fitting polynomials when input data is partially or completely unknown, and proposes algorithms with practical applications like jitter correction.

Contribution

It formally defines the blind regression problem, explores its theoretical properties, and develops algorithms to solve it, demonstrated through a jitter-correction case study.

Findings

Algorithms effectively solve blind regression problems

Successful application to jitter-correction task

Theoretical insights into problem properties

Abstract

Fitting a polynomial to observed data is an ubiquitous task in many signal processing and machine learning tasks, such as interpolation and prediction. In that context, input and output pairs are available and the goal is to find the coefficients of the polynomial. However, in many applications, the input may be partially known or not known at all, rendering conventional regression approaches not applicable. In this paper, we formally state the (potentially partial) blind regression problem, illustrate some of its theoretical properties, and propose algorithmic approaches to solve it. As a case-study, we apply our methods to a jitter-correction problem and corroborate its performance.