A Unified Empirical Risk Minimization Framework for Flexible N-Tuples Weak Supervision

TL;DR

This paper introduces a unified empirical risk minimization framework for N-tuples weak supervision, integrating pointwise unlabeled data to improve learning, with theoretical guarantees and extensive validation on benchmark datasets.

Contribution

It provides a general, theoretically grounded N-tuples learning framework that unifies various scenarios and incorporates unlabeled data to enhance performance.

Findings

Unbiased empirical risk estimator derived for N-tuples models.

The framework generalizes multiple existing N-tuples approaches.

Leveraging unlabeled data improves generalization in experiments.

Abstract

To alleviate the annotation burden in supervised learning, N-tuples learning has recently emerged as a powerful weakly-supervised method. While existing N-tuples learning approaches extend pairwise learning to higher-order comparisons and accommodate various real-world scenarios, they often rely on task-specific designs and lack a unified theoretical foundation. In this paper, we propose a general N-tuples learning framework based on empirical risk minimization, which systematically integrates pointwise unlabeled data to enhance learning performance. This paper first unifies the data generation processes of N-tuples and pointwise unlabeled data under a shared probabilistic formulation. Based on this unified view, we derive an unbiased empirical risk estimator that generalizes a broad class of existing N-tuples models. We further establish a generalization error bound for theoretical support. To demonstrate the flexibility of the framework, we instantiate it in four representative weakly supervised scenarios, each recoverable as a special case of our general model. Additionally, to address overfitting issues arising from negative risk terms, we adopt correction functions to adjust the empirical risk. Extensive experiments on benchmark datasets validate the effectiveness of the proposed framework and demonstrate that leveraging pointwise unlabeled data consistently improves generalization across various N-tuples learning tasks.