# Unimodal-Concentrated Loss: Fully Adaptive Label Distribution Learning for Ordinal Regression arXiv: https://arxiv.org/abs/2204.00309 ยท HTML: https://mlsanity.com/paper/2204.00309/ ## Key facts - Cited by 23 papers in the map (data through 14 Oct 2026). - Builds on 14 of its 40 references that are in the map. - First posted on arXiv 1 Apr 2022. ## Builds on (most cited first, 14 of 14) - [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015) - [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014) - [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014) - [How far are we from solving the 2D & 3D Face Alignment problem? (and a dataset of 230,000 3D facial landmarks)](https://mlsanity.com/paper/1703.07332/) (2017) - [Fine-Grained Head Pose Estimation Without Keypoints](https://mlsanity.com/paper/1710.00925/) (2017) - [Label Distribution Learning](https://mlsanity.com/paper/1408.6027/) (2014) - [Deep Label Distribution Learning with Label Ambiguity](https://mlsanity.com/paper/1611.01731/) (2016) - [An All-In-One Convolutional Neural Network for Face Analysis](https://mlsanity.com/paper/1611.00851/) (2016) - [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) - [Facial Pose Estimation by Deep Learning from Label Distributions](https://mlsanity.com/paper/1904.13102/) (2019) - [Self-Paced Deep Regression Forests with Consideration on Underrepresented Examples](https://mlsanity.com/paper/2004.01459/) (2020) - [Apparent Age Estimation Using Ensemble of Deep Learning Models](https://mlsanity.com/paper/1606.02909/) (2016) - [A Computational Approach to Relative Aesthetics](https://mlsanity.com/paper/1704.01248/) (2017) ## Built on by (most cited first, 23 of 23) - [Learning-to-Rank Meets Language: Boosting Language-Driven Ordering Alignment for Ordinal Classification](https://mlsanity.com/paper/2306.13856/) (2023) - [A Call to Reflect on Evaluation Practices for Age Estimation: Comparative Analysis of the State-of-the-Art and a Unified Benchmark](https://mlsanity.com/paper/2307.04570/) (2023) - [Trustworthy Multimodal Fusion for Sentiment Analysis in Ordinal Sentiment Space](https://mlsanity.com/paper/2404.08923/) (2024) - [Label Distribution Learning via Implicit Distribution Representation](https://mlsanity.com/paper/2209.13824/) (2022) - [A Survey on Ordinal Regression: Applications, Advances and Prospects](https://mlsanity.com/paper/2503.00952/) (2025) - [From Age Estimation to Age-Invariant Face Recognition: Generalized Age Feature Extraction Using Order-Enhanced Contrastive Learning](https://mlsanity.com/paper/2501.01760/) (2025) - [Ordinal-Aware Calibration for Ordinal Classification](https://mlsanity.com/paper/2410.15658/) (2024) - [SVLDL: Improved Speaker Age Estimation Using Selective Variance Label Distribution Learning](https://mlsanity.com/paper/2210.09524/) (2022) - [URL: Combating Label Noise for Lung Nodule Malignancy Grading](https://mlsanity.com/paper/2308.08772/) (2023) - [Underage Detection through a Multi-Task and MultiAge Approach for Screening Minors in Unconstrained Imagery](https://mlsanity.com/paper/2506.10689/) (2025) - [Enhancing User-Centric Privacy Protection: An Interactive Framework through Diffusion Models and Machine Unlearning](https://mlsanity.com/paper/2409.03326/) (2024) - [Stage-wise Adaptive Label Distribution for Facial Age Estimation](https://mlsanity.com/paper/2509.00450/) (2025) - [Learning Ordinal Probabilistic Reward from Preferences](https://mlsanity.com/paper/2602.12660/) (2026) - [DiffoR: A Unified Continuous Generative Framework for Universal Ordinal Regression](https://mlsanity.com/paper/2606.07599/) (2026) - [FedAR+: A Federated Learning Approach to Appliance Recognition with Mislabeled Data in Residential Buildings](https://mlsanity.com/paper/2209.01338/) (2022) - [Robust Capped lp-Norm Support Vector Ordinal Regression](https://mlsanity.com/paper/2404.16616/) (2024) - [JAM: A Comprehensive Model for Age Estimation, Verification, and Comparability](https://mlsanity.com/paper/2410.04012/) (2024) - [UAKNN: Label Distribution Learning via Uncertainty-Aware KNN](https://mlsanity.com/paper/2504.01508/) (2025) - [Latent label distribution grid representation for modeling uncertainty](https://mlsanity.com/paper/2505.21180/) (2025) - [Ordinal Adaptive Correction: A Data-Centric Approach to Ordinal Image Classification with Noisy Labels](https://mlsanity.com/paper/2509.02351/) (2025) - [Multi-View Semi-Supervised Label Distribution Learning with Local Structure Complementarity](https://mlsanity.com/paper/2510.13917/) (2025) - [From Kellgren-Lawrence to Calcium Pyrophosphate Crystal Deposition: A Soft-Labelling Framework for Knee Osteoarthritis Assessmen](https://mlsanity.com/paper/2605.28176/) (2026) - [Stochastic Order Learning: An Approach to Rank Estimation Using Noisy Data](https://mlsanity.com/paper/2607.08103/) (2026) ## Abstract (arXiv) Learning from a label distribution has achieved promising results on ordinal regression tasks such as facial age and head pose estimation wherein, the concept of adaptive label distribution learning (ALDL) has drawn lots of attention recently for its superiority in theory. However, compared with the methods assuming fixed form label distribution, ALDL methods have not achieved better performance. We argue that existing ALDL algorithms do not fully exploit the intrinsic properties of ordinal regression. In this paper, we emphatically summarize that learning an adaptive label distribution on ordinal regression tasks should follow three principles. First, the probability corresponding to the ground-truth should be the highest in label distribution. Second, the probabilities of neighboring labels should decrease with the increase of distance away from the ground-truth, i.e., the distribution is unimodal. Third, the label distribution should vary with samples changing, and even be distinct for different instances with the same label, due to the different levels of difficulty and ambiguity. Under the premise of these principles, we propose a novel loss function for fully adaptive label distribution learning, namely unimodal-concentrated loss. Specifically, the unimodal loss derived from the learning to rank strategy constrains the distribution to be unimodal. Furthermore, the estimation error and the variance of the predicted distribution for a specific sample are integrated into the proposed concentrated loss to make the predicted distribution maximize at the ground-truth and vary according to the predicting uncertainty. Extensive experimental results on typical ordinal regression tasks including age and head pose estimation, show the superiority of our proposed unimodal-concentrated loss compared with existing loss functions.