Stochastic Order Learning: An Approach to Rank Estimation Using Noisy Data

2026-07-09

AI Summary

This work addresses the problem of robust rank estimation under structured ordinal label noise by proposing a stochastic ranking learning framework that explicitly models the uncertainty of ordinal labels as probabilistic ranking relations, thereby moving beyond the conventional assumption of deterministic labels. The method jointly optimizes a discriminative loss and a stochastic ranking loss, integrating discriminative instance-to-centroid interactions with probabilistic ranking constraints in the embedding space to effectively capture the distribution over multiple plausible rankings. Experimental results demonstrate that the proposed framework significantly enhances both the robustness and accuracy of rank estimation across diverse datasets and noise configurations.

Abstract

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.

Problem

• rank estimation
• label noise
• ordinal labels
• stochastic ordering
• structured uncertainty

Innovation

• stochastic ordering
• ordinal label noise
• rank estimation
• probabilistic ranking
• embedding learning