Some new phenomena in high-dimensional statistics and optimization
Statistical models in which the ambient dimension is of the same order or larger than the sample size arise frequently in different areas of science and engineering. Examples include sparse regression in genomics; graph selection in social network analysis; and low-rank matrix estimation in video segmentation. Although high-dimensional models of this type date back to seminal work of Kolmogorov and others, they have been the subject of especially intensive study over the past decade, and have interesting connections to many branches of applied mathematics and computer science, including random matrices and algorithms, concentration of measure, convex geometry, and information theory. In this talk, we discuss various issues in high-dimensional statistics, including vignettes on phase transitions in high-dimensional graph recovery, and randomized sketching for large-scale optimization.