Editor
Jordan Anaya
Complete recovery of values in Diophantine systems (CORVIDS) (2018)
Sean Wilner, Katherine Wood, Daniel J. Simons
DOI: 10.17605/osf.io/7shr8 DOI: 10.31234/osf.io/7shr8
This article presents a deterministic method for reconstructing discrete, bounded data. Previously the only methods for doing so were by brute force which quickly becomes untenable as sample size or scale increases, or by a heuristic method (SPRITE) which only gives 1 of potentially many solutions.
Reconstructing data is valuable for multiple reasons. Sometimes there may be only a few possible, or even 1 possible reconstruction, in which case lost or unshared data can be recovered. Just because the summary statistics pass the GRIM and GRIMMER tests, that does not mean the data is mathematically possible when the scale is taken into account, and even if the data is possible it may be so unusual that fraud (or error) is suspected. Furthermore, not all test statistics can be recalculated by only knowing the summary statistics, so a data reconstruction would be needed to recalculate these.
While I don't understand all of the math or code in the paper, I have thoroughly tested CORVIDS version 1, and can confirm it accurately reproduces data sets, albeit slowly for complex data sets. CORVIDS version 2 introduces a method to restrict the mean-variance pairs, i.e. a solution to the GRIMMER patterns, and I am excited to test the performance of the most recent version.
One downside to CORVIDS is that there is not a web application for the test, so users have to download either the Windows or Mac standalones, or the Python scripts.
Again, I have not checked the speed of CORVIDS version 2, but it seems in most cases users will probably want to run SPRITE given the ease and speed of use. In the case that SPRITE doesn't find a solution, SPRITE cannot guarantee there is no solution (unless the data fails the GRIM or GRIMMER tests), so CORVIDS will be needed to say with 100% certainty there is no solution. In addition, SPRITE may preferably return biased distributions, i.e. unusual distributions, concerning the researcher, whereas CORVIDS will return every distribution, some of which may be more normal in appearance.
Due to both the mathematical and computational feats of this publication, I am proud to accept it.
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