Error Correcting Algorithms for Sparsely Correlated Regressors
This work addresses the challenge of autonomous error measurement in regression tasks for machines, representing an incremental advancement in error correction methods.
The paper tackles the problem of machines measuring their own regression errors without ground truth by using a compressed sensing approach on the error signal, which can recover precision errors under conditions of sparse correlation among regressors, and adding ℓ1-minimization ensures correct solutions where error correction is feasible.
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.