An overview of computational sparse models and their applications in artificial intelligence

Computational sparse models are drawing more and more attentions in a wide range of scientific communities including statistic signal processing and machine learning. The prominent goal of them aims at revealing the sparse structure or correlation among redundant data in terms of computational approaches, e.g. convex optimization and probability inference. The main scope of this chapter concentrates on reviewing the state-of-the-art sparse models and discussing their applications in the field of artificial intelligence. After a brief introduction to the the general idea of sparse computation, the bulk of the chapter will be split into three core sections on sparse signal optimization, low rank matrix completion and low rank structure learning. These three parts respectively correspond to the sparse models for vector case, matrix case and the combination of both. In order to effectively solve the sparse models reviewed in this chapter, we will unify the solutions to all of them in the general framework of proximal gradient algorithm which is a benchmark method for convex optimization with quadratic term. Besides, in each section, after theoretical discussions, some interesting applications of the model will be presented and introduced. Some of these applications are from other researchers' and our previous publications and some of them are novelly proposed in this book chapter.