Stochastic Order Learning: An Approach to Rank Estimation Using Noisy Data
For practitioners dealing with ordinal labels that have structured uncertainty, SOL provides a robust rank estimation method that outperforms existing approaches under label noise.
The paper reformulates rank estimation under label noise as a stochastic ordering problem and proposes a learning framework (SOL) that captures ordinal label uncertainty, achieving reliable rank estimation across diverse datasets under various noise types and levels.
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.