Blind Polynomial Regression
This addresses a limitation in signal processing and machine learning where traditional regression fails due to unknown inputs, but it appears incremental as it builds on existing regression frameworks.
The paper tackles the problem of polynomial regression when inputs are partially or completely unknown, formalizing the blind regression problem and proposing algorithmic solutions. It demonstrates the method's performance on a jitter-correction task, though no concrete numerical results are provided in the 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.