Bias detection between two histograms can be done by checking a random subset of bins, with a PAC guarantee that depends on the fraction of violating bins.
A kernel two-sample test,
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Sample Complexity of Bias Detection with Subsampled Point-to-Subspace Distances
Bias detection between two histograms can be done by checking a random subset of bins, with a PAC guarantee that depends on the fraction of violating bins.