A key challenge in today's Big Data world is that the methods we have come to rely and interpret so fluently are not easily extendable to many real-world scenarios. This leaves a big gap in interpretability, and seems to ask for a tradeoff between methods that perform well on very large datasets, and methods that are reliable and well-understood. The goal of my research is to extend the well-understood topics in convex optimization to large-scale ``messy" machine learning problems.
This talk will focus on generalizations of sparse optimization over large datasets. First, we show that almost all proximal methods identify a sparse support in a finite number of iterations, as a result of a simple and geometrically interpretable observation. Next, we generalize the notion of sparsity itself, and show how sparse optimization can be interpreted as satisfying a Holder-like alignment condition, which can then be exploited to obtain generalized support recovery and inspire the use of fast and scalable dual methods.