Learning Deep Structured Models
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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.
Key facts. Cited by 21 papers in the map (data through 14 Oct 2026). First posted on arXiv 9 Jul 2014.
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Citing papers per year: 2021: 7; 2022: 5; 2023: 4; 2024: 4; 2025: 1.
21 papers.
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- 2021Multi-Label Classification Neural Networks with Hard Logical Constraintscited by 36
- 2022Learning to Predict Graphs with Fused Gromov-Wasserstein Barycenterscited by 22
- 2021Deep Structured Reactive Planningcited by 19
- 2023ReMaX: Relaxing for Better Training on Efficient Panoptic Segmentationcited by 18
- 2023Factor Graph Neural Networkscited by 15
- 2021Combinatorial Optimization for Panoptic Segmentation: A Fully Differentiable Approachcited by 10
- 2022CARE: Certifiably Robust Learning with Reasoning via Variational Inferencecited by 10
- 2021Neural Weighted A*: Learning Graph Costs and Heuristics with Differentiable Anytime A*cited by 3
- 2021An MRF-UNet Product of Experts for Image Segmentationcited by 2
- 2021Structured Convolutional Kernel Networks for Airline Crew Schedulingcited by 2
- 2024Multi-Label Out-of-Distribution Detection with Spectral Normalized Joint Energycited by 2
- 2022SOInter: A Novel Deep Energy Based Interpretation Method for Explaining Structured Output Modelscited by 1
9 more
- 2022Machine Learning for Combinatorial Optimisation of Partially-Specified Problems: Regret Minimisation as a Unifying Lenscited by 1
- 2023Deep Dependency Networks for Multi-Label Classificationcited by 1
- 2023OVeNet: Offset Vector Network for Semantic Segmentationcited by 1
- 2025Heatmap Regression without Soft-Argmax for Facial Landmark Detectioncited by 1
- 2021Content-aware Directed Propagation Network with Pixel Adaptive Kernel Attentioncited by 0
- 2022Spatial Parsing and Dynamic Temporal Pooling networks for Human-Object Interaction detectioncited by 0
- 2024Convergence of Some Convex Message Passing Algorithms to a Fixed Pointcited by 0
- 2024Deep Dependency Networks and Advanced Inference Schemes for Multi-Label Classificationcited by 0
- 2024Coalitions of AI-based Methods Predict 15-Year Risks of Breast Cancer Metastasis Using Real-World Clinical Data with AUC up to 0.9cited by 0
- 2025Heatmap Regression without Soft-Argmax for Facial Landmark Detection19 Aug 2025
- 2024Coalitions of AI-based Methods Predict 15-Year Risks of Breast Cancer Metastasis Using Real-World Clinical Data with AUC up to 0.929 Aug 2024
- 2024Multi-Label Out-of-Distribution Detection with Spectral Normalized Joint Energy8 May 2024
- 2024Deep Dependency Networks and Advanced Inference Schemes for Multi-Label Classification17 Apr 2024
- 2024Convergence of Some Convex Message Passing Algorithms to a Fixed Point7 Mar 2024
- 2023Factor Graph Neural Networks2 Aug 2023
- 2023ReMaX: Relaxing for Better Training on Efficient Panoptic Segmentation29 Jun 2023
- 2023OVeNet: Offset Vector Network for Semantic Segmentation25 Mar 2023
- 2023Deep Dependency Networks for Multi-Label Classification1 Feb 2023
- 2022CARE: Certifiably Robust Learning with Reasoning via Variational Inference12 Sep 2022
- 2022Spatial Parsing and Dynamic Temporal Pooling networks for Human-Object Interaction detection7 Jun 2022
- 2022Machine Learning for Combinatorial Optimisation of Partially-Specified Problems: Regret Minimisation as a Unifying Lens20 May 2022
9 more
- 2022SOInter: A Novel Deep Energy Based Interpretation Method for Explaining Structured Output Models20 Feb 2022
- 2022Learning to Predict Graphs with Fused Gromov-Wasserstein Barycenters8 Feb 2022
- 2021Content-aware Directed Propagation Network with Pixel Adaptive Kernel Attention28 Jul 2021
- 2021Combinatorial Optimization for Panoptic Segmentation: A Fully Differentiable Approach6 Jun 2021
- 2021Structured Convolutional Kernel Networks for Airline Crew Scheduling25 May 2021
- 2021Neural Weighted A*: Learning Graph Costs and Heuristics with Differentiable Anytime A*4 May 2021
- 2021An MRF-UNet Product of Experts for Image Segmentation12 Apr 2021
- 2021Multi-Label Classification Neural Networks with Hard Logical Constraints24 Mar 2021
- 2021Deep Structured Reactive Planning18 Jan 2021
- 2021Multi-Label Classification Neural Networks with Hard Logical Constraintscited by 36
- 2022Learning to Predict Graphs with Fused Gromov-Wasserstein Barycenterscited by 22
- 2021Deep Structured Reactive Planningcited by 19
- 2023ReMaX: Relaxing for Better Training on Efficient Panoptic Segmentationcited by 18
- 2023Factor Graph Neural Networkscited by 15
- 2021Combinatorial Optimization for Panoptic Segmentation: A Fully Differentiable Approachcited by 10
- 2022CARE: Certifiably Robust Learning with Reasoning via Variational Inferencecited by 10
- 2021Neural Weighted A*: Learning Graph Costs and Heuristics with Differentiable Anytime A*cited by 3
- 2021An MRF-UNet Product of Experts for Image Segmentationcited by 2
- 2021Structured Convolutional Kernel Networks for Airline Crew Schedulingcited by 2
- 2024Multi-Label Out-of-Distribution Detection with Spectral Normalized Joint Energycited by 2
- 2022SOInter: A Novel Deep Energy Based Interpretation Method for Explaining Structured Output Modelscited by 1
12 most cited of 21 All 21 (JSON)
- 2025Heatmap Regression without Soft-Argmax for Facial Landmark Detection19 Aug 2025
- 2024Coalitions of AI-based Methods Predict 15-Year Risks of Breast Cancer Metastasis Using Real-World Clinical Data with AUC up to 0.929 Aug 2024
- 2024Multi-Label Out-of-Distribution Detection with Spectral Normalized Joint Energy8 May 2024
- 2024Deep Dependency Networks and Advanced Inference Schemes for Multi-Label Classification17 Apr 2024
- 2024Convergence of Some Convex Message Passing Algorithms to a Fixed Point7 Mar 2024
- 2023Factor Graph Neural Networks2 Aug 2023
- 2023ReMaX: Relaxing for Better Training on Efficient Panoptic Segmentation29 Jun 2023
- 2023OVeNet: Offset Vector Network for Semantic Segmentation25 Mar 2023
- 2023Deep Dependency Networks for Multi-Label Classification1 Feb 2023
- 2022CARE: Certifiably Robust Learning with Reasoning via Variational Inference12 Sep 2022
- 2022Spatial Parsing and Dynamic Temporal Pooling networks for Human-Object Interaction detection7 Jun 2022
- 2022Machine Learning for Combinatorial Optimisation of Partially-Specified Problems: Regret Minimisation as a Unifying Lens20 May 2022
12 newest of 21 All 21 (JSON)