# Probabilistic Label Relation Graphs with Ising Models

arXiv: https://arxiv.org/abs/1503.01428 · HTML: https://mlsanity.com/paper/1503.01428/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Mar 2015.

## Built on by (most cited first, 5 of 5)

- [Joining datasets via data augmentation in the label space for neural networks](https://mlsanity.com/paper/2106.09260/) (2021)
- [pRSL: Interpretable Multi-label Stacking by Learning Probabilistic Rules](https://mlsanity.com/paper/2105.13850/) (2021)
- [Introducing instance label correlation in multiple instance learning. Application to cancer detection on histopathological images](https://mlsanity.com/paper/2310.19359/) (2023)
- [Cleaning and Structuring the Label Space of the iMet Collection 2020](https://mlsanity.com/paper/2106.00815/) (2021)
- [Inverted Semantic-Index for Image Retrieval](https://mlsanity.com/paper/2206.12623/) (2022)

## Abstract (arXiv)

We consider classification problems in which the label space has structure. A common example is hierarchical label spaces, corresponding to the case where one label subsumes another (e.g., animal subsumes dog). But labels can also be mutually exclusive (e.g., dog vs cat) or unrelated (e.g., furry, carnivore). To jointly model hierarchy and exclusion relations, the notion of a HEX (hierarchy and exclusion) graph was introduced in [7]. This combined a conditional random field (CRF) with a deep neural network (DNN), resulting in state of the art results when applied to visual object classification problems where the training labels were drawn from different levels of the ImageNet hierarchy (e.g., an image might be labeled with the basic level category "dog", rather than the more specific label "husky"). In this paper, we extend the HEX model to allow for soft or probabilistic relations between labels, which is useful when there is uncertainty about the relationship between two labels (e.g., an antelope is "sort of" furry, but not to the same degree as a grizzly bear). We call our new model pHEX, for probabilistic HEX. We show that the pHEX graph can be converted to an Ising model, which allows us to use existing off-the-shelf inference methods (in contrast to the HEX method, which needed specialized inference algorithms). Experimental results show significant improvements in a number of large-scale visual object classification tasks, outperforming the previous HEX model.