# Complementary to Multiple Labels: A Correlation-Aware Correction Approach

arXiv: https://arxiv.org/abs/2302.12987 · HTML: https://mlsanity.com/paper/2302.12987/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 56 references that are in the map.
- First posted on arXiv 25 Feb 2023.

## Builds on (most cited first, 17 of 17)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Generalized Cross Entropy Loss for Training Deep Neural Networks with Noisy Labels](https://mlsanity.com/paper/1805.07836/) (2018)
- [Making Deep Neural Networks Robust to Label Noise: a Loss Correction Approach](https://mlsanity.com/paper/1609.03683/) (2016)
- [Robust Loss Functions under Label Noise for Deep Neural Networks](https://mlsanity.com/paper/1712.09482/) (2017)
- [Are Anchor Points Really Indispensable in Label-Noise Learning?](https://mlsanity.com/paper/1906.00189/) (2019)
- [Progressive Identification of True Labels for Partial-Label Learning](https://mlsanity.com/paper/2002.08053/) (2020)
- [Learning with Biased Complementary Labels](https://mlsanity.com/paper/1711.09535/) (2017)
- [Learning from Complementary Labels](https://mlsanity.com/paper/1705.07541/) (2017)
- [Complementary-Label Learning for Arbitrary Losses and Models](https://mlsanity.com/paper/1810.04327/) (2018)
- [Learning with Multiple Complementary Labels](https://mlsanity.com/paper/1912.12927/) (2019)
- [Improving Pairwise Ranking for Multi-label Image Classification](https://mlsanity.com/paper/1704.03135/) (2017)
- [Unbiased Risk Estimators Can Mislead: A Case Study of Learning with Complementary Labels](https://mlsanity.com/paper/2007.02235/) (2020)
- [Generative-Discriminative Complementary Learning](https://mlsanity.com/paper/1904.01612/) (2019)
- [Bridging Ordinary-Label Learning and Complementary-Label Learning](https://mlsanity.com/paper/2002.02158/) (2020)
- [HOT-VAE: Learning High-Order Label Correlation for Multi-Label Classification via Attention-Based Variational Autoencoders](https://mlsanity.com/paper/2103.06375/) (2021)
- [Multi-Instance Partial-Label Learning: Towards Exploiting Dual Inexact Supervision](https://mlsanity.com/paper/2212.08997/) (2022)

## Built on by (most cited first, 1 of 1)

- [Rethinking Consistent Multi-Label Classification Under Inexact Supervision](https://mlsanity.com/paper/2510.04091/) (2025)

## Abstract (arXiv)

textitComplementary label learning (CLL) requires annotators to give irrelevant labels instead of relevant labels for instances. Currently, CLL has shown its promising performance on multi-class data by estimating a transition matrix. However, current multi-class CLL techniques cannot work well on multi-labeled data since they assume each instance is associated with one label while each multi-labeled instance is relevant to multiple labels. Here, we show theoretically how the estimated transition matrix in multi-class CLL could be distorted in multi-labeled cases as they ignore co-existing relevant labels. Moreover, theoretical findings reveal that calculating a transition matrix from label correlations in textitmulti-labeled CLL (ML-CLL) needs multi-labeled data, while this is unavailable for ML-CLL. To solve this issue, we propose a two-step method to estimate the transition matrix from candidate labels. Specifically, we first estimate an initial transition matrix by decomposing the multi-label problem into a series of binary classification problems, then the initial transition matrix is corrected by label correlations to enforce the addition of relationships among labels. We further show that the proposal is classifier-consistent, and additionally introduce an MSE-based regularizer to alleviate the tendency of BCE loss overfitting to noises. Experimental results have demonstrated the effectiveness of the proposed method.