  In recent years, Convolutional Neural Networks (CNNs) have enabled
significant advancements to the state-of-the-art in computer vision. For
classification tasks, CNNs have widely employed probabilistic output and have
shown the significance of providing additional confidence for predictions.
However, such probabilistic methodologies are not widely applicable for
addressing regression problems using CNNs, as regression involves learning
unconstrained continuous and, in many cases, multi-variate target variables. We
propose a PRObabilistic Parametric rEgression Loss (PROPEL) that facilitates
CNNs to learn parameters of probability distributions for addressing
probabilistic regression problems. PROPEL is fully differentiable and, hence,
can be easily incorporated for end-to-end training of existing CNN regression
architectures using existing optimization algorithms. The proposed method is
flexible as it enables learning complex unconstrained probabilities while being
generalizable to higher dimensional multi-variate regression problems. We
utilize a PROPEL-based CNN to address the problem of learning hand and head
orientation from uncalibrated color images. Our experimental validation and
comparison with existing CNN regression loss functions show that PROPEL
improves the accuracy of a CNN by enabling probabilistic regression, while
significantly reducing required model parameters by $10 \times$, resulting in
improved generalization as compared to the existing state-of-the-art.
