Recent Developments on Factor Models and its Applications in Econometric Learning

The recent decade has witnessed a blossom of developments on statistical learning theories and practice, embraced with the exciting progresses on large-scale optimizations and dimension reduction techniques. Factor models, as one of the central machinery on summarizing and extracting information from large scale datasets, have received much attention in this revolutionary era of data science, and many breakthrough methodologies and applications have been developed in this exciting area. This paper makes a selective overview on the recent developments of the factor model and its applications on econometric learning. Our review focuses on the perspective of the low-rank structure of factor models, and draws particular attentions to estimating the model from the low-rank recovery point of view. A central focus in the progress of this literature is the understanding and recovering low-rank structures of high-dimensional models. Many new learning theories and methods have been developed, which have revolutionized the modern understanding of econometric modeling. Meanwhile, the low-rank structure is one of the key properties of factor models. While this structure has long been aware of by researchers, studying the factor model from the perspective of low-rank matrix recovery is relatively new, and has led to many exciting new discoveries and understanding. The survey mainly consists of three parts: the first part is a review on new factor estimation based on modern techniques on recovering low-rank structures of high-dimensional models.