# Learning Deep Structured Models

arXiv: https://arxiv.org/abs/1407.2538 · HTML: https://mlsanity.com/paper/1407.2538/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jul 2014.

## Built on by (most cited first, 21 of 21)

- [Multi-Label Classification Neural Networks with Hard Logical Constraints](https://mlsanity.com/paper/2103.13427/) (2021)
- [Learning to Predict Graphs with Fused Gromov-Wasserstein Barycenters](https://mlsanity.com/paper/2202.03813/) (2022)
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- [Combinatorial Optimization for Panoptic Segmentation: A Fully Differentiable Approach](https://mlsanity.com/paper/2106.03188/) (2021)
- [CARE: Certifiably Robust Learning with Reasoning via Variational Inference](https://mlsanity.com/paper/2209.05055/) (2022)
- [Neural Weighted A*: Learning Graph Costs and Heuristics with Differentiable Anytime A*](https://mlsanity.com/paper/2105.01480/) (2021)
- [An MRF-UNet Product of Experts for Image Segmentation](https://mlsanity.com/paper/2104.05495/) (2021)
- [Structured Convolutional Kernel Networks for Airline Crew Scheduling](https://mlsanity.com/paper/2105.11646/) (2021)
- [Multi-Label Out-of-Distribution Detection with Spectral Normalized Joint Energy](https://mlsanity.com/paper/2405.04759/) (2024)
- [SOInter: A Novel Deep Energy Based Interpretation Method for Explaining Structured Output Models](https://mlsanity.com/paper/2202.09914/) (2022)
- [Machine Learning for Combinatorial Optimisation of Partially-Specified Problems: Regret Minimisation as a Unifying Lens](https://mlsanity.com/paper/2205.10157/) (2022)
- [Deep Dependency Networks for Multi-Label Classification](https://mlsanity.com/paper/2302.00633/) (2023)
- [OVeNet: Offset Vector Network for Semantic Segmentation](https://mlsanity.com/paper/2303.14516/) (2023)
- [Heatmap Regression without Soft-Argmax for Facial Landmark Detection](https://mlsanity.com/paper/2508.14929/) (2025)
- [Content-aware Directed Propagation Network with Pixel Adaptive Kernel Attention](https://mlsanity.com/paper/2107.13144/) (2021)
- [Spatial Parsing and Dynamic Temporal Pooling networks for Human-Object Interaction detection](https://mlsanity.com/paper/2206.03061/) (2022)
- [Convergence of Some Convex Message Passing Algorithms to a Fixed Point](https://mlsanity.com/paper/2403.07004/) (2024)
- [Deep Dependency Networks and Advanced Inference Schemes for Multi-Label Classification](https://mlsanity.com/paper/2404.11667/) (2024)
- [Coalitions of AI-based Methods Predict 15-Year Risks of Breast Cancer Metastasis Using Real-World Clinical Data with AUC up to 0.9](https://mlsanity.com/paper/2408.16256/) (2024)

## Abstract (arXiv)

Many problems in real-world applications involve predicting several random variables which are statistically related. Markov random fields (MRFs) are a great mathematical tool to encode such relationships. The goal of this paper is to combine MRFs with deep learning algorithms to estimate complex representations while taking into account the dependencies between the output random variables. Towards this goal, we propose a training algorithm that is able to learn structured models jointly with deep features that form the MRF potentials. Our approach is efficient as it blends learning and inference and makes use of GPU acceleration. We demonstrate the effectiveness of our algorithm in the tasks of predicting words from noisy images, as well as multi-class classification of Flickr photographs. We show that joint learning of the deep features and the MRF parameters results in significant performance gains.