Distance-Based Independence Screening for Canonical Analysis

This paper introduces a new method named Distance-based Independence Screening for Canonical Analysis (DISCA) to reduce dimensions of two random vectors with arbitrary dimensions. The objective of our method is to identify the low dimensional linear projections of two random vectors, such that any dimension reduction based on linear projection with lower dimensions will surely affect some dependent structure -- the removed components are not independent. The essence of DISCA is to use the distance correlation to eliminate the "redundant" dimensions until infeasible. Unlike the existing canonical analysis methods, DISCA does not require the dimensions of the reduced subspaces of the two random vectors to be equal, nor does it require certain distributional assumption on the random vectors. We show that under mild conditions, our approach does undercover the lowest possible linear dependency structures between two random vectors, and our conditions are weaker than some sufficient linear subspace-based methods. Numerically, DISCA is to solve a non-convex optimization problem. We formulate it as a difference-of-convex (DC) optimization problem, and then further adopt the alternating direction method of multipliers (ADMM) on the convex step of the DC algorithms to parallelize/accelerate the computation. Some sufficient linear subspace-based methods use potentially numerically-intensive bootstrap method to determine the dimensions of the reduced subspaces in advance; our method avoids this complexity. In simulations, we present cases that DISCA can solve effectively, while other methods cannot. In both the simulation studies and real data cases, when the other state-of-the-art dimension reduction methods are applicable, we observe that DISCA performs either comparably or better than most of them. Codes and an R package can be found in GitHub https://github.com/ChuanpingYu/DISCA

FSRNet: End-to-End Learning Face Super-Resolution with Facial Priors

Face Super-Resolution (SR) is a domain-specific super-resolution problem. The specific facial prior knowledge could be leveraged for better super-resolving face images. We present a novel deep end-to-end trainable Face Super-Resolution Network (FSRNet), which makes full use of the geometry prior, i.e., facial landmark heatmaps and parsing maps, to super-resolve very low-resolution (LR) face images without well-aligned requirement. Specifically, we first construct a coarse SR network to recover a coarse high-resolution (HR) image. Then, the coarse HR image is sent to two branches: a fine SR encoder and a prior information estimation network, which extracts the image features, and estimates landmark heatmaps/parsing maps respectively. Both image features and prior information are sent to a fine SR decoder to recover the HR image. To further generate realistic faces, we propose the Face Super-Resolution Generative Adversarial Network (FSRGAN) to incorporate the adversarial loss into FSRNet. Moreover, we introduce two related tasks, face alignment and parsing, as the new evaluation metrics for face SR, which address the inconsistency of classic metrics w.r.t. visual perception. Extensive benchmark experiments show that FSRNet and FSRGAN significantly outperforms state of the arts for very LR face SR, both quantitatively and qualitatively. Code will be made available upon publication.Comment: Chen and Tai contributed equally to this pape