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This paper addresses the challenge of rank estimation in the presence of noisy ordinal labels by reformulating the problem as a stochastic ordering issue, allowing for multiple plausible ranks for each instance. The proposed Stochastic Order Learning (SOL) framework utilizes a discriminative loss to structure instance-centroid interactions and a stochastic order loss to maintain probabilistic ordering relations. Experimental results across various datasets show that SOL significantly improves rank estimation reliability even when faced with different types and levels of label noise.
Rank estimation can be reliably achieved even in the presence of structured label noise by embracing the inherent uncertainty of ordinal annotations.
Rank estimation under label noise poses a fundamental challenge, as ordinal annotations often exhibit structured uncertainty rather than simple label corruption. In this paper, we reformulate rank estimation with noisy ordinal labels as a stochastic ordering problem, in which each instance is inherently associated with multiple plausible ranks instead of a single deterministic label. Based on this view, we propose stochastic order learning (SOL), a learning framework that captures ordinal label uncertainty and learns an embedding space through two complementary objectives: a discriminative loss that structures instance--centroid interactions and a stochastic order loss that enforces probabilistic ordering relations between instances. Extensive experiments across diverse datasets demonstrate that SOL enables reliable rank estimation under various types and levels of label noise. The source code is available at https://github.com/cwlee00/SOL.
