  Exact ground truth invariant polynomial systems can be written for
arbitrarily correlated binary classifiers. Their solutions give estimates for
sample statistics that require knowledge of the ground truth of the correct
labels in the sample. Of these polynomial systems, only a few have been solved
in closed form. Here we discuss the exact solution for independent binary
classifiers - resolving an outstanding problem that has been presented at this
conference and others. Its practical applicability is hampered by its sole
remaining assumption - the classifiers need to be independent in their sample
errors. We discuss how to use the closed form solution to create a
self-consistent test that can validate the independence assumption itself
absent the correct labels ground truth. It can be cast as an algebraic geometry
conjecture for binary classifiers that remains unsolved. A similar conjecture
for the ground truth invariant algebraic system for scalar regressors is
solvable, and we present the solution here. We also discuss experiments on the
Penn ML Benchmark classification tasks that provide further evidence that the
conjecture may be true for the polynomial system of binary classifiers.
