Error Correcting Algorithms for Sparsely Correlated Regressors

May 16, 2019 Blind Submission readers: everyone
• Keywords: ground truth inference, compressed sensing, errors, sample statistics, correlation, regressors
• TL;DR: A non-parametric method to measure the error moments of regressors without ground truth can be used with biased regressors
• 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 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.
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