Energy-Based Models for Deep Probabilistic Regression (1909.12297v4)

Abstract: 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 https://github.com/fregu856/ebms_regression.

• The paper introduces a novel approach using energy-based models to directly learn un-normalized log densities for regression tasks.
• It employs Monte Carlo importance sampling to optimize the estimation of conditional target densities, outperforming standard baselines.
• The method achieved notable improvements on COCO object detection and set new benchmarks in visual tracking tasks.

Overview of "Energy-Based Models for Deep Probabilistic Regression"

The paper "Energy-Based Models for Deep Probabilistic Regression" by Gustafsson et al. introduces a novel approach to supervised regression tasks in computer vision using energy-based models (EBMs). While traditional deep learning models tend to apply standardized strategies for classification, regression tasks often necessitate a wider array of methodologies. The authors address limitations in confidence-based regression techniques by proposing a more universally applicable probabilistic regression framework with EBMs, which can predict the conditional target density directly from feature-target pairs without the need for pseudo-labels.

Methodology

The core innovation of this work is the utilization of energy-based models to learn an un-normalized representation of the conditional target density, $p(y | x)$, using deep neural networks. Rather than restricting the modeling to specific distribution forms such as Gaussian or Laplace, the authors employ a flexible EBM framework where the output scalar value from a neural network is interpreted as un-normalized log densities. The model is trained by minimizing the negative log-likelihood of the target given the input, approximated using Monte Carlo importance sampling. By maximizing these learned densities, the method provides precise predictions even in multimodal or complex conditional target landscapes.

Training the model involves generating proposals from a distribution centered around true targets, which are then refined through gradient ascent at inference time. The authors emphasize the conceptual simplicity and probabilistic clarity of this approach over existing methods like confidence-based regression, which require task-specific pseudo-labels and lack probabilistic interpretation.

Experimental Evaluation

The approach was thoroughly evaluated across several computer vision tasks, demonstrating superior performance over both direct regression methods and advanced state-of-the-art techniques like IoU-Net. Specifically, notable improvements were observed in object detection tasks on the COCO dataset, where the proposed model surpassed the Faster-RCNN baseline by 2.2% Average Precision (AP) and established a new standard for visual tracking benchmarks by improving upon the ATOM tracker.

Additionally, the generality of the proposed method was validated on age estimation and head-pose estimation tasks. These experiments consistently showed that the energy-based model outperformed conventional baselines, reinforcing the versatility of this approach for a variety of regression problems beyond traditional bounding box tasks.

Implications and Future Directions

This paper provides a significant contribution to the field of deep probabilistic regression in computer vision by offering a method that is applicable across a diverse set of tasks without cumbersome task-specific adaptations. It opens doors to further research into refined EBM architectures, potentially expanding the expressiveness and efficiency. Future research might also explore the theoretical underpinnings of energy-based models in handling aleatoric uncertainty and broader applications beyond regression to classification or even unsupervised learning domains.

In conclusion, the work by Gustafsson et al. represents a well-founded, probabilistically meaningful stride forward in handling regression tasks within computer vision, potentially establishing a new paradigm for researchers and practitioners aiming for sophisticated model interpretations and performance in real-world scenarios.