Mixed-Prior Decision Risk for Open-Set Recognition

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

cs.CVSep 28, 2026

Mixed-Prior Decision Risk for Open-Set Recognition

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

Organizations: Skolkovo Institute of Science and Technology (Skoltech), Moscow, Russia · Risk Management, Sber, Moscow, Russia · The Institute for Information Transmission Problems (IITP RAS), Moscow, Russia

Abstract

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 ranking; no nonlinear supervised model is required. Across nine image, audio, and text benchmarks, MPRisk achieves the best or tied-best Prediction Rejection Ratio at every operating point on the image and audio benchmarks and on most text operating points, with bootstrap-confirmed gains over HolUE on five benchmarks (up to $+0.19$ PRR) at comparable or lower runtime.

Figures & tables

Рис. 1: MPRisk overview. (a) Embedding space of a fixed OSR system with $K$ gallery classes (prototypes $\bullet$ , samples $\blacksquare$ ) under the mixed prior: unknown identities form a continuous component $c\in(K,K{+}1]$ (tinted reject region); dashed lines are decision boundaries; blue shading shows the decision-risk field $1-\max_{a}p(a\mid\mathbf{x})$ . Markers show the three error types: false acceptance ( $\bigstar$ ), misidentification ( $\blacklozenge$ ), and false rejection ( $\boldsymbol{\times}$ ) — a corrupted known probe whose diffuse embedding distribution (green density, low $\kappa_{\mathbf{x}}$ ) yields a non-specific unknown posterior, i.e., high $\mathcal{N}_{0}(\mathbf{x})$ . (b) Top: the KL summary measures information gain and can invert the risk ordering of two posteriors (A vs. B), which is why KL features require the nonlinear calibration of HolUE. Bottom: MPRisk scores the selected decision with four components $r_{\mathrm{FA}}$ , $r_{\mathrm{ID}}$ , $r_{\mathrm{FR}}$ , and $r_{\mathrm{NS}}=P_{0}\,\mathcal{N}_{0}$ ; stacked bars show the components at the three marked probes — for the confidently rejected corrupted probe only $r_{\mathrm{NS}}$ flags the error. The final score $u_{\lambda}$ combines the components with four nonnegative validation-tuned weights.

Dataset	Spearman	Inv. rate	KL AUROC	KL AUPRC
IJB-C	-0.03	0.55	0.45	0.04
Yahoo Answers	-0.47	0.81	0.18	0.15

Таблица 1: Disagreement between the raw (uncalibrated) KL summary and the error-risk ordering. Spearman: rank correlation between the KL summary and the per-probe error indicator. Inv. rate: fraction of (erroneous, correct) probe pairs ordered incorrectly by the KL summary. KL AUROC/AUPRC: any-error detection quality of the raw KL summary used directly as an uncertainty score.

Method	IJB-C			IJB-B			Whale			VB-Eval-L-5
	$0.05$	$0.1$	$0.2$	$0.05$	$0.1$	$0.2$	$0.05$	$0.1$	$0.2$	$0.01$	$0.05$	$0.1$
SCF	0.40	0.31	0.23	0.29	0.25	0.22	0.16	0.02	-0.06	0.55	0.26	0.12
AccScr	0.73	0.72	0.66	0.65	0.68	0.62	0.77	0.75	0.66	0.66	0.76	0.72
MSP	0.74	0.75	0.70	0.66	0.70	0.65	0.77	0.77	0.70	0.38	0.88	0.86
Margin	0.74	0.75	0.70	0.66	0.70	0.66	0.77	0.77	0.70	0.68	0.88	0.86
GalUE	0.74	0.74	0.67	0.66	0.69	0.60	0.78	0.76	0.70	0.69	0.89	0.87

Таблица 2: Prediction Rejection Ratios (PRR,

\uparrow

) for

F_{1}

filtering on image, Whale, and audio open-set recognition benchmarks. HolUE uses its validation-trained calibration; MPRisk uses validation-tuned component weights; both receive identical validation data. Best results in bold, second-best underlined.

	IJB-C (FPIR $0.05$ )				Whale (FPIR $0.1$ )
Method	Any	FA	FR	ID	Any	FA	FR	ID
SCF	0.70	0.61	0.77	0.91	0.61	0.55	0.84	0.86
AccScr	0.87	0.91	0.80	0.85	0.88	0.87	0.86	0.81
MSP	0.87	0.91	0.80	0.88	0.88	0.88	0.85	0.88
GalUE	0.88	0.92	0.80	0.90	0.89	0.88	0.86	0.90
HolUE	0.87	0.96	0.70	0.97	0.93	0.93	0.85	0.90

Таблица 10: Error-type detection quality on IJB-C at FPIR

0.05

and Whale at FPIR

0.1

. AUROC is reported for detecting any OSR error (Any), false acceptance (FA), false rejection (FR), and misidentification (ID).

	Yahoo Answers (FPIR $0.1$ )				PAN-20-AV (FPIR $0.1$ )
Method	Any	FA	FR	ID	Any	FA	FR	ID
SCF	0.45	0.66	0.41	–	0.50	0.37	0.56	0.36
AccScr	0.59	0.77	0.54	–	0.61	0.89	0.48	0.83
MSP	0.54	0.76	0.48	–	0.64	0.82	0.53	0.86
GalUE	0.58	0.77	0.53	–	0.61	0.88	0.48	0.90
HolUE	0.89	0.58	0.92	–	0.59	0.75	0.52	0.70

Таблица 11: Error-type detection quality on Yahoo Answers and PAN-20-AV, both at FPIR

0.1

. AUROC is reported for detecting any OSR error (Any), false acceptance (FA), false rejection (FR), and misidentification (ID); misidentification is absent in the Yahoo Answers protocol at this operating point.

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Open-set recognition systems face a neglected failure mode: high-confidence near-known unknowns, which lie outside the known label set but are close enough to known classes that a closed-set classifier accepts them with high confidence. We show that this failure is widespread across scalar-threshold methods, including recent post-hoc detectors, and that stronger encoders can amplify rather than remove the risk. We propose EGUR-A, which changes the decision from is this sample's score high enough?'' to does this predicted known class have sufficient evidence to accept this sample?'' EGUR-A combines class-conditional local acceptance evidence with global residual evidence, and selects their relative weight from known-sample statistics without unknown validation data. Across CUB, FGVC-Aircraft, and ImageNet-hard, EGUR-A substantially reduces high-confidence false known acceptance at matched known-rejection operating points. The result is not a stronger threshold; it is a different question: whether a known class is entitled to accept a sample.

Abstract

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