Joint Energy-based Models for Deep Probabilistic Regression

It is desirable that a deep neural network trained on a regression task not only achieves high prediction accuracy, but its prediction posteriors are also well-calibrated, especially in safety-critical settings. Recently, energy-based models specifically to enrich regression posteriors have been proposed and achieve state-of-art results in object detection tasks. However, applying these models at prediction time is not straightforward as the resulting inference methods require to minimize an underlying energy function. Furthermore, these methods empirically do not provide accurate prediction uncertainties. Inspired by recent joint energy-based models for classification, in this work, we propose to utilize a joint energy model for regression tasks and describe architectural differences needed in this setting. Within this framework, we apply our methods to three computer vision regression tasks. We demonstrate that joint energy-based models for deep probabilistic regression improve the calibration property, do not require expensive inference, and yield competitive accuracy in terms of the mean absolute error (MAE).