Kernel Density Network for Quantifying Regression Uncertainty in Face Alignment

For deep neural networks, it is important to quantify the uncertainty in its predictions. So a probabilistic neural network with a Gaussian assumption was widely used. However, in real data especially image data, the Gaussian assumption typically cannot hold. We are interested in modeling a more general distribution, e.g. multi-modal or asymmetric distribution. Therefore, a kernel density neural network is proposed. We adopt state-of-the-art neural network architecture and propose a new loss function based on maximizing the conditional log likelihood. And we show its application in face alignment. The proposed loss function achieves comparable or better performance than state-of-the-art end-to-end trainable deep learning based methods in terms of both the predicted labels and uncertainty in predictions. Moreover, it can be generally extended to many other regression problems such as Action Unit intensity estimation and face age estimation.