Energy-Based Models for Deep Probabilistic Regression

While deep learning-based classification is generally tackled using standardized approaches, a wide variety of techniques are employed for regression. In computer vision, one particularly popular such technique is that of confidence-based regression, which entails predicting a confidence value for each input-target pair (x,y). While this approach has demonstrated impressive results, it requires important task-dependent design choices, and the predicted confidences lack a natural probabilistic meaning. We address these issues by proposing a general and conceptually simple regression method with a clear probabilistic interpretation. In our proposed approach, we create an energy-based model of the conditional target density p(y|x), using a deep neural network to predict the un-normalized density from (x,y). This model of p(y|x) is trained by directly minimizing the associated negative log-likelihood, approximated using Monte Carlo sampling. We perform comprehensive experiments on four computer vision regression tasks. Our approach outperforms direct regression, as well as other probabilistic and confidence-based methods. Notably, our model achieves a 2.2% AP improvement over Faster-RCNN for object detection on the COCO dataset, and sets a new state-of-the-art on visual tracking when applied for bounding box estimation. In contrast to confidence-based methods, our approach is also shown to be directly applicable to more general tasks such as age and head-pose estimation. Code is available at

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Results from the Paper

 Ranked #1 on Object Detection on COCO test-dev (Hardware Burden metric)

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Task Dataset Model Metric Name Metric Value Global Rank Result Benchmark
Object Detection COCO test-dev IoU-Net+EnergyRegression AP50 58.5 # 145
AP75 41.8 # 143
Hardware Burden None # 1
Operations per network pass None # 1
Visual Object Tracking TrackingNet ATOM(Resnet18)+EnergyRegression Precision 69.7 # 21
Normalized Precision 80.1 # 23
Success Rate 74.5 # 1
Visual Object Tracking UAV123 ATOM(Resnet18)+EnergyRegression AUC 0.672 # 11


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