Mixed-Prior Decision Risk for Open-Set Recognition

L. A. Erlygin, P. D. Proskura, A. A. Zaytsev

In open-set recognition (OSR), a probe must either be identified as one of the known gallery classes or rejected as unknown, so three error types coexist: false acceptance, false rejection, and misidentification. An uncertainty score for selective recognition should rank probes by the risk of the decision the system has made. Bayesian gallery-aware models such as Holistic Uncertainty Estimation (HolUE) summarize the posterior over known and unknown classes by Kullback--Leibler (KL) divergence components and map them to an uncertainty score with a supervised nonlinear calibrator. We show that the KL summary is not generally monotone in decision risk: linear fusion of the KL components tuned on validation data yields negative filtering quality on several benchmarks. We propose MPRisk, a mixed-prior posterior decision-risk score that keeps the same Bayesian posterior but directly scores the error events associated with the selected decision: false-acceptance, misidentification, and false-rejection risks, plus a non-specificity penalty for rejections, enabled by modeling unknown identities as a continuous component. Four nonnegative weights tuned on a validation set suffice for…