Abstract: Submodular functions capture a wide spectrum of discrete problems in machine learning, signal processing and computer vision. They are characterized by intuitive notions of diminishing returns and economies of scale, and often lead to practical algorithms with theoretical guarantees.
In the first part of this talk, I will give a general introduction to the concept of submodular functions, their optimization and example applications in machine learning.
In the second part, I will demonstrate how the close connection of submodularity to convexity leads to fast algorithms for minimizing a subclass of submodular functions - those decomposing as a sum of submodular functions. Using a specific relaxation, the algorithms solve the discrete submodular optimization problem as a "best approximation" problem. They are easy to use and parallelize, and solve both the convex relaxation and the original discrete problem. Their convergence analysis combines elements of geometry and spectral graph theory.
This is joint work with Robert Nishihara, Francis Bach, Suvrit Sra and Michael I. Jordan.
Watch the full talk on the WNCG YouTube Channel: