# Computationally Efficient Wasserstein Loss for Structured Labels

arXiv: https://arxiv.org/abs/2103.00899 · HTML: https://mlsanity.com/paper/2103.00899/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 31 references that are in the map.
- First posted on arXiv 1 Mar 2021.

## Builds on (most cited first, 16 of 16)

- [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)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Enriching Word Vectors with Subword Information](https://mlsanity.com/paper/1607.04606/) (2016)
- [Bag of Tricks for Efficient Text Classification](https://mlsanity.com/paper/1607.01759/) (2016)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [Learning with a Wasserstein Loss](https://mlsanity.com/paper/1506.05439/) (2015)
- [Label Distribution Learning](https://mlsanity.com/paper/1408.6027/) (2014)
- [Deep Label Distribution Learning with Label Ambiguity](https://mlsanity.com/paper/1611.01731/) (2016)
- [Large-Scale Multi-Label Text Classification on EU Legislation](https://mlsanity.com/paper/1906.02192/) (2019)
- [Comparative Study of CNN and RNN for Natural Language Processing](https://mlsanity.com/paper/1702.01923/) (2017)
- [Stabilized Sparse Scaling Algorithms for Entropy Regularized Transport Problems](https://mlsanity.com/paper/1610.06519/) (2016)
- [Tree-Sliced Variants of Wasserstein Distances](https://mlsanity.com/paper/1902.00342/) (2019)
- [Fast Unbalanced Optimal Transport on a Tree](https://mlsanity.com/paper/2006.02703/) (2020)
- [An Entropic Optimal Transport Loss for Learning Deep Neural Networks under Label Noise in Remote Sensing Images](https://mlsanity.com/paper/1810.01163/) (2018)

## Built on by (most cited first, 2 of 2)

- [Meta Optimal Transport](https://mlsanity.com/paper/2206.05262/) (2022)
- [An Empirical Study of Self-supervised Learning with Wasserstein Distance](https://mlsanity.com/paper/2310.10143/) (2023)

## Abstract (arXiv)

The problem of estimating the probability distribution of labels has been widely studied as a label distribution learning (LDL) problem, whose applications include age estimation, emotion analysis, and semantic segmentation. We propose a tree-Wasserstein distance regularized LDL algorithm, focusing on hierarchical text classification tasks. We propose predicting the entire label hierarchy using neural networks, where the similarity between predicted and true labels is measured using the tree-Wasserstein distance. Through experiments using synthetic and real-world datasets, we demonstrate that the proposed method successfully considers the structure of labels during training, and it compares favorably with the Sinkhorn algorithm in terms of computation time and memory usage.