Deciding global fairness of the COMPAS neural network within a specific confidence interval

Determine whether the feed-forward deep neural network trained on the COMPAS recidivism dataset is globally fair under the paper’s confidence-based global 2-safety definition when Ethnicity is used as the sensitive attribute for confidence thresholds in the interval [0.969, 0.999]. Specifically, ascertain if for all input pairs that differ only in Ethnicity and satisfy the non-sensitive attribute tolerance constraints, the predicted classes coincide whenever one input’s softmax confidence exceeds a threshold c in [0.969, 0.999].

Background

The paper verifies confidence-based global fairness by self-composition and a novel softmax abstraction. For three-output networks, including their COMPAS model, the softmax approximation introduces an error bound (~0.171), which they account for when certifying fairness at a given confidence threshold.

Empirically, for COMPAS with Ethnicity as the sensitive attribute, they found counterexamples at lower confidence thresholds (e.g., 0.99) but proved fairness at 0.999. Running the reported counterexample on the real network produced a true confidence of 0.969, leading the authors to conclude the model is fair for confidence higher than 0.999, unfair for confidence lower than 0.969, and that the interval [0.969, 0.999] remains undecided due to approximation-induced uncertainty.