# Learning Probabilistic Ordinal Embeddings for Uncertainty-Aware Regression

arXiv: https://arxiv.org/abs/2103.13629 · HTML: https://mlsanity.com/paper/2103.13629/

## Key facts

- Cited by 58 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 61 references that are in the map.
- First posted on arXiv 25 Mar 2021.

## Builds on (most cited first, 27 of 27)

- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semantics](https://mlsanity.com/paper/1705.07115/) (2017)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Deep Variational Information Bottleneck](https://mlsanity.com/paper/1612.00410/) (2016)
- [Wasserstein GAN](https://mlsanity.com/paper/1701.07875/) (2017)
- [Towards Principled Methods for Training Generative Adversarial Networks](https://mlsanity.com/paper/1701.04862/) (2017)
- [Probabilistic Face Embeddings](https://mlsanity.com/paper/1904.09658/) (2019)
- [Fine-Grained Head Pose Estimation Without Keypoints](https://mlsanity.com/paper/1710.00925/) (2017)
- [Bounding Box Regression with Uncertainty for Accurate Object Detection](https://mlsanity.com/paper/1809.08545/) (2018)
- [Data Uncertainty Learning in Face Recognition](https://mlsanity.com/paper/2003.11339/) (2020)
- [Photo Aesthetics Ranking Network with Attributes and Content Adaptation](https://mlsanity.com/paper/1606.01621/) (2016)
- [Deep Label Distribution Learning with Label Ambiguity](https://mlsanity.com/paper/1611.01731/) (2016)
- [Lightweight Probabilistic Deep Networks](https://mlsanity.com/paper/1805.11327/) (2018)
- [SDE-Net: Equipping Deep Neural Networks with Uncertainty Estimates](https://mlsanity.com/paper/2008.10546/) (2020)
- [Modeling Uncertainty with Hedged Instance Embedding](https://mlsanity.com/paper/1810.00319/) (2018)
- [Efficient Uncertainty Estimation for Semantic Segmentation in Videos](https://mlsanity.com/paper/1807.11037/) (2018)
- [BridgeNet: A Continuity-Aware Probabilistic Network for Age Estimation](https://mlsanity.com/paper/1904.03358/) (2019)
- [Deep Regression Forests for Age Estimation](https://mlsanity.com/paper/1712.07195/) (2017)
- [Mixture Dense Regression for Object Detection and Human Pose Estimation](https://mlsanity.com/paper/1912.00821/) (2019)
- [Label Distribution Learning Forests](https://mlsanity.com/paper/1702.06086/) (2017)
- [An Image is Worth More than a Thousand Favorites: Surfacing the Hidden Beauty of Flickr Pictures](https://mlsanity.com/paper/1505.03358/) (2015)
- [Graph-Based Social Relation Reasoning](https://mlsanity.com/paper/2007.07453/) (2020)
- [Graph-based Kinship Reasoning Network](https://mlsanity.com/paper/2004.10375/) (2020)

## Built on by (most cited first, 30 of 58)

- [Rank-N-Contrast: Learning Continuous Representations for Regression](https://mlsanity.com/paper/2210.01189/) (2022)
- [Moving Window Regression: A Novel Approach to Ordinal Regression](https://mlsanity.com/paper/2203.13122/) (2022)
- [OrdinalCLIP: Learning Rank Prompts for Language-Guided Ordinal Regression](https://mlsanity.com/paper/2206.02338/) (2022)
- [FaceXFormer: A Unified Transformer for Facial Analysis](https://mlsanity.com/paper/2403.12960/) (2024)
- [DARE-GRAM : Unsupervised Domain Adaptation Regression by Aligning Inverse Gram Matrices](https://mlsanity.com/paper/2303.13325/) (2023)
- [Label2Label: A Language Modeling Framework for Multi-Attribute Learning](https://mlsanity.com/paper/2207.08677/) (2022)
- [COLD Fusion: Calibrated and Ordinal Latent Distribution Fusion for Uncertainty-Aware Multimodal Emotion Recognition](https://mlsanity.com/paper/2206.05833/) (2022)
- [Learning-to-Rank Meets Language: Boosting Language-Driven Ordering Alignment for Ordinal Classification](https://mlsanity.com/paper/2306.13856/) (2023)
- [Teach CLIP to Develop a Number Sense for Ordinal Regression](https://mlsanity.com/paper/2408.03574/) (2024)
- [Ord2Seq: Regarding Ordinal Regression as Label Sequence Prediction](https://mlsanity.com/paper/2307.09004/) (2023)
- [RICA2: Rubric-Informed, Calibrated Assessment of Actions](https://mlsanity.com/paper/2408.02138/) (2024)
- [CLOC: Contrastive Learning for Ordinal Classification with Multi-Margin N-pair Loss](https://mlsanity.com/paper/2504.17813/) (2025)
- [Stating Comparison Score Uncertainty and Verification Decision Confidence Towards Transparent Face Recognition](https://mlsanity.com/paper/2210.10354/) (2022)
- [Robust Image Ordinal Regression with Controllable Image Generation](https://mlsanity.com/paper/2305.04213/) (2023)
- [Trustworthy Multimodal Fusion for Sentiment Analysis in Ordinal Sentiment Space](https://mlsanity.com/paper/2404.08923/) (2024)
- [Introspective Deep Metric Learning](https://mlsanity.com/paper/2309.09982/) (2023)
- [Ordinal Learning: Longitudinal Attention Alignment Model for Predicting Time to Future Breast Cancer Events from Mammograms](https://mlsanity.com/paper/2409.06887/) (2024)
- [Ordinal Multiple-instance Learning for Ulcerative Colitis Severity Estimation with Selective Aggregated Transformer](https://mlsanity.com/paper/2411.14750/) (2024)
- [A Survey on Ordinal Regression: Applications, Advances and Prospects](https://mlsanity.com/paper/2503.00952/) (2025)
- [DIOR-ViT: Differential Ordinal Learning Vision Transformer for Cancer Classification in Pathology Images](https://mlsanity.com/paper/2407.08503/) (2024)
- [Uncertainty-Guided Alignment for Unsupervised Domain Adaptation in Regression](https://mlsanity.com/paper/2401.13721/) (2024)
- [Aligning Vision Models with Human Aesthetics in Retrieval: Benchmarks and Algorithms](https://mlsanity.com/paper/2406.09397/) (2024)
- [Contrastive Learning with Adaptive Neighborhoods for Brain Age Prediction on 3D Stiffness Maps](https://mlsanity.com/paper/2408.00527/) (2024)
- [Self-supervised Auxiliary Learning for Texture and Model-based Hybrid Robust and Fair Featuring in Face Analysis](https://mlsanity.com/paper/2409.19582/) (2024)
- [Ordinal-Aware Calibration for Ordinal Classification](https://mlsanity.com/paper/2410.15658/) (2024)
- [OrderChain: Towards General Instruct-Tuning for Stimulating the Ordinal Understanding Ability of MLLM](https://mlsanity.com/paper/2504.04801/) (2025)
- [FaceInsight: A Multimodal Large Language Model for Face Perception](https://mlsanity.com/paper/2504.15624/) (2025)
- [IMG: Calibrating Diffusion Models via Implicit Multimodal Guidance](https://mlsanity.com/paper/2509.26231/) (2025)
- [Uncertainty Estimation for 3D Dense Prediction via Cross-Point Embeddings](https://mlsanity.com/paper/2209.14602/) (2022)
- [Probabilistic Deep Metric Learning for Hyperspectral Image Classification](https://mlsanity.com/paper/2211.08349/) (2022)

## Abstract (arXiv)

Uncertainty is the only certainty there is. Modeling data uncertainty is essential for regression, especially in unconstrained settings. Traditionally the direct regression formulation is considered and the uncertainty is modeled by modifying the output space to a certain family of probabilistic distributions. On the other hand, classification based regression and ranking based solutions are more popular in practice while the direct regression methods suffer from the limited performance. How to model the uncertainty within the present-day technologies for regression remains an open issue. In this paper, we propose to learn probabilistic ordinal embeddings which represent each data as a multivariate Gaussian distribution rather than a deterministic point in the latent space. An ordinal distribution constraint is proposed to exploit the ordinal nature of regression. Our probabilistic ordinal embeddings can be integrated into popular regression approaches and empower them with the ability of uncertainty estimation. Experimental results show that our approach achieves competitive performance. Code is available at https://github.com/Li-Wanhua/POEs.