# Deep Neural Networks for Rank-Consistent Ordinal Regression Based On Conditional Probabilities

arXiv: https://arxiv.org/abs/2111.08851 · HTML: https://mlsanity.com/paper/2111.08851/

## Key facts

- Cited by 59 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 29 references that are in the map.
- First posted on arXiv 17 Nov 2021.

## Builds on (most cited first, 7 of 7)

- [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)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Rank consistent ordinal regression for neural networks with application to age estimation](https://mlsanity.com/paper/1901.07884/) (2019)
- [Differentiable Sorting Networks for Scalable Sorting and Ranking Supervision](https://mlsanity.com/paper/2105.04019/) (2021)
- [An Image is Worth More than a Thousand Favorites: Surfacing the Hidden Beauty of Flickr Pictures](https://mlsanity.com/paper/1505.03358/) (2015)

## Built on by (most cited first, 30 of 59)

- [Rank-N-Contrast: Learning Continuous Representations for Regression](https://mlsanity.com/paper/2210.01189/) (2022)
- [Class Distance Weighted Cross-Entropy Loss for Ulcerative Colitis Severity Estimation](https://mlsanity.com/paper/2202.05167/) (2022)
- [Unsupervised Contrast-Consistent Ranking with Language Models](https://mlsanity.com/paper/2309.06991/) (2023)
- [Class Distance Weighted Cross Entropy Loss for Classification of Disease Severity](https://mlsanity.com/paper/2412.01246/) (2024)
- [The Shape of Attraction in UMAP: Exploring the Embedding Forces in Dimensionality Reduction](https://mlsanity.com/paper/2503.09101/) (2025)
- [ADSNet: Cross-Domain LTV Prediction with an Adaptive Siamese Network in Advertising](https://mlsanity.com/paper/2406.10517/) (2024)
- [Learning What To Hear: Boosting Sound-Source Association For Robust Audiovisual Instance Segmentation](https://mlsanity.com/paper/2509.22740/) (2025)
- [Ordinal-Aware Calibration for Ordinal Classification](https://mlsanity.com/paper/2410.15658/) (2024)
- [Detecting respiratory motion artefacts for cardiovascular MRIs to ensure high-quality segmentation](https://mlsanity.com/paper/2209.09678/) (2022)
- [Dual input stream transformer for vertical drift correction in eye-tracking reading data](https://mlsanity.com/paper/2311.06095/) (2023)
- [TabTreeFormer: Tabular Data Generation Using Hybrid Tree-Transformer](https://mlsanity.com/paper/2501.01216/) (2025)
- [Parameterized Diffusion Optimization enabled Autoregressive Ordinal Regression for Diabetic Retinopathy Grading](https://mlsanity.com/paper/2507.04978/) (2025)
- [Spinal Osteophyte Detection via Robust Patch Extraction on minimally annotated X-rays](https://mlsanity.com/paper/2402.19263/) (2024)
- [Multi-Channel Hypergraph Contrastive Learning for Matrix Completion](https://mlsanity.com/paper/2411.01376/) (2024)
- [ACCon: Angle-Compensated Contrastive Regularizer for Deep Regression](https://mlsanity.com/paper/2501.07045/) (2025)
- [Learning Disease State from Noisy Ordinal Disease Progression Labels](https://mlsanity.com/paper/2503.10440/) (2025)
- [Extreme Cardiac MRI Analysis under Respiratory Motion: Results of the CMRxMotion Challenge](https://mlsanity.com/paper/2507.19165/) (2025)
- [Uncertainty-Aware Longitudinal Forecasting of Alzheimer's Disease Progression Using Deep Learning](https://mlsanity.com/paper/2606.24604/) (2026)
- [Reliable Conformal Prediction for Ordinal Classification Using the Ranked Probability Score](https://mlsanity.com/paper/2606.24959/) (2026)
- [Decoding Children's Gait Behavior](https://mlsanity.com/paper/2608.00371/) (2026)
- [Robust Capped lp-Norm Support Vector Ordinal Regression](https://mlsanity.com/paper/2404.16616/) (2024)
- [Weakly-supervised Autism Severity Assessment in Long Videos](https://mlsanity.com/paper/2407.09159/) (2024)
- [SurvCORN: Survival Analysis with Conditional Ordinal Ranking Neural Network](https://mlsanity.com/paper/2409.19901/) (2024)
- [AI-Assisted Decision-Making for Clinical Assessment of Auto-Segmented Contour Quality](https://mlsanity.com/paper/2505.00308/) (2025)
- [XTransfer: Modality-Agnostic Few-Shot Model Transfer for Human Sensing at the Edge](https://mlsanity.com/paper/2506.22726/) (2025)
- [Ordinality in Discrete-level Question Difficulty Estimation: Introducing Balanced DRPS and OrderedLogitNN](https://mlsanity.com/paper/2507.00736/) (2025)
- [Granular feedback merits sophisticated aggregation](https://mlsanity.com/paper/2507.12041/) (2025)
- [Ordinal Adaptive Correction: A Data-Centric Approach to Ordinal Image Classification with Noisy Labels](https://mlsanity.com/paper/2509.02351/) (2025)
- [Functional effects models: Accounting for preference heterogeneity in panel data with machine learning](https://mlsanity.com/paper/2509.18047/) (2025)
- [BRIQA: Balanced Reweighting in Image Quality Assessment of Pediatric Brain MRI](https://mlsanity.com/paper/2510.26661/) (2025)

## Abstract (arXiv)

In recent times, deep neural networks achieved outstanding predictive performance on various classification and pattern recognition tasks. However, many real-world prediction problems have ordinal response variables, and this ordering information is ignored by conventional classification losses such as the multi-category cross-entropy. Ordinal regression methods for deep neural networks address this. One such method is the CORAL method, which is based on an earlier binary label extension framework and achieves rank consistency among its output layer tasks by imposing a weight-sharing constraint. However, while earlier experiments showed that CORAL's rank consistency is beneficial for performance, it is limited by a weight-sharing constraint in a neural network's fully connected output layer, which may restrict the expressiveness and capacity of a network trained using CORAL. We propose a new method for rank-consistent ordinal regression without this limitation. Our rank-consistent ordinal regression framework (CORN) achieves rank consistency by a novel training scheme. This training scheme uses conditional training sets to obtain the unconditional rank probabilities through applying the chain rule for conditional probability distributions. Experiments on various datasets demonstrate the efficacy of the proposed method to utilize the ordinal target information, and the absence of the weight-sharing restriction improves the performance substantially compared to the CORAL reference approach. Additionally, the suggested CORN method is not tied to any specific architecture and can be utilized with any deep neural network classifier to train it for ordinal regression tasks.