# Label Distribution Learning using the Squared Neural Family on the Probability Simplex

arXiv: https://arxiv.org/abs/2412.07324 · HTML: https://mlsanity.com/paper/2412.07324/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 49 references that are in the map.
- First posted on arXiv 10 Dec 2024.

## Builds on (most cited first, 9 of 9)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Label Distribution Learning](https://mlsanity.com/paper/1408.6027/) (2014)
- [Diverse mini-batch Active Learning](https://mlsanity.com/paper/1901.05954/) (2019)
- [A Comparative Survey of Deep Active Learning](https://mlsanity.com/paper/2203.13450/) (2022)
- [Label Distribution Learning Forests](https://mlsanity.com/paper/1702.06086/) (2017)
- [Squared Neural Families: A New Class of Tractable Density Models](https://mlsanity.com/paper/2305.13552/) (2023)
- [Label Information Bottleneck for Label Enhancement](https://mlsanity.com/paper/2303.06836/) (2023)
- [RankMatch: A Novel Approach to Semi-Supervised Label Distribution Learning Leveraging Inter-label Correlations](https://mlsanity.com/paper/2312.06343/) (2023)

## Abstract (arXiv)

Label distribution learning (LDL) provides a framework wherein a distribution over categories rather than a single category is predicted, with the aim of addressing ambiguity in labeled data. Existing research on LDL mainly focuses on the task of point estimation, i.e., finding an optimal distribution in the probability simplex conditioned on the given sample. In this paper, we propose a novel label distribution learning model SNEFY-LDL, which estimates a probability distribution of all possible label distributions over the simplex, by unleashing the expressive power of the recently introduced Squared Neural Family (SNEFY), a new class of tractable probability models. As a way to summarize the fitted model, we derive the closed-form label distribution mean, variance and covariance conditioned on the given sample, which can be used to predict the ground-truth label distributions, construct label distribution confidence intervals, and measure the correlations between different labels. Moreover, more information about the label distribution prediction uncertainties can be acquired from the modeled probability density function. Extensive experiments on conformal prediction, active learning and ensemble learning are conducted, verifying SNEFY-LDL's great effectiveness in LDL uncertainty quantification. The source code of this paper is available at https://github.com/daokunzhang/SNEFY-LDL.