# Error Correcting Algorithms for Sparsely Correlated Regressors

## TL;DR

This paper explores error correction in regression models using compressed sensing, enabling machines to estimate errors without ground truth, especially when regressors are sparsely correlated, by applying $ ext{l}_1$-minimization.

## Contribution

It introduces a novel approach combining compressed sensing and $ ext{l}_1$-minimization to recover regression errors without ground truth, handling correlated regressors.

## Key findings

- Compressed sensing can recover error signals without ground truth.
- Error correction is feasible with sparsely correlated regressors.
- Adding $ ext{l}_1$-minimization ensures correct solution recovery.

## Abstract

Autonomy and adaptation of machines requires that they be able to measure their own errors. We consider the advantages and limitations of such an approach when a machine has to measure the error in a regression task. How can a machine measure the error of regression sub-components when it does not have the ground truth for the correct predictions? A compressed sensing approach applied to the error signal of the regressors can recover their precision error without any ground truth. It allows for some regressors to be \emph{strongly correlated} as long as not too many are so related. Its solutions, however, are not unique - a property of ground truth inference solutions. Adding $\ell_1$--minimization as a condition can recover the correct solution in settings where error correction is possible. We briefly discuss the similarity of the mathematics of ground truth inference for regressors to that for classifiers.