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ProHOC: Probabilistic Hierarchical Out-of-Distribution Classification via Multi-Depth Networks

CVPR 2025 · Label-efficient and robust learning › OOD and anomaly detection · approach: Spurious-aware OOD detection · 2 citations (OpenAlex)

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Proposes ProHOC, which classifies in-distribution and OOD samples to nodes of a class hierarchy by factorizing a probabilistic tree model over networks trained at each hierarchy depth.

Problem

Standard OOD detection is binary and ignores semantic relations between OOD samples and ID classes; the goal is to assign OOD samples to their correct internal nodes of a known class hierarchy.

Approach

Factorize the predictive distribution over a hierarchy with an OOD child node at each internal node, and approximate the conditionals with separately trained multi-depth classifiers using complementary probability plus child-prediction entropy as the OOD score; predictions minimize expected hierarchical distance.

Key results

• ProHOC with EntCompProb reaches MixBAcc 50.3 on FGVC-Aircraft vs 46.1 for HSC, and 46.4 vs 42.3 on SimpleHierImageNet.
• On iNaturalist19, ProHOC (EntCompProb) attains MixBMHD 0.94 vs 1.28 for HSC.
• Multi-depth networks beat marginalized leaf predictions on OOD samples at ground-truth depth by +1.6 to +17.0 accuracy points.

Measured effects reported in the paper

Surprising findings

• The HSC baseline was given thresholds tuned on test OOD data, yet ProHOC still outperforms it.

Limitations

• Performance is bounded by the underlying multi-depth networks, which were not optimized (ResNet50, standard training).
• Assumes the class hierarchy reflects observable visual similarity; fails when ID and OOD siblings share no visual features.

Experimental setup

Datasets: FGVC-Aircraft iNaturalist19 SimpleHierImageNet tieredImageNet

Benchmarks: FGVC-Aircraft iNaturalist19 SimpleHierImageNet Office31 PACS

Metrics: BMHD MixBMHD balanced accuracy MixBAcc F1 Dirty F1 accuracy on out-of-hierarchy OOD

Baselines: Depth oracle Leaf model HSC

Builds on: HSC hierarchical OOD classification maximum softmax probability OOD detection entropy-based OOD scoring

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