Efficient learning with combinatorial structure

Learning from complex data such as images, text or biological measurements invariably relies on capturing long-range, latent structure. But the combinatorial structure inherent in real-world data can pose significant computational challenges for modeling, learning and inference.

In this talk, I will view these challenges through the lens of submodular set functions. Considered a "discrete analog of convexity", the combinatorial concept of submodularity captures intuitive yet nontrivial dependencies between variables and underlies many widely used concepts in machine learning. Practical use of submodularity, however, requires care. My first example illustrates how to efficiently handle the important class of submodular composite models. The second example combines submodularity and graphs for a new family of combinatorial models that express long-range interactions while still admitting very efficient inference procedures. As a concrete application, our results enable effective realization of combinatorial sparsity priors on real data, significantly improving image segmentation results in settings where state-of-the-art methods fail. Motivated by good empirical results, we provide a detailed theoretical analysis and identify practically relevant properties that affect complexity and approximation quality of submodular optimization and learning problems.  

Stefanie Jegelka is a postdoctoral researcher at UC Berkeley, working with Michael I. Jordan and Trevor Darrell. She received a Ph.D. in Computer Science from ETH Zurich in 2012, in collaboration with the Max Planck Institute for Intelligent Systems, and completed her studies for a Diploma in Bioinformatics with distinction at the University of Tuebingen (Germany) and the University of Texas at Austin. She was a fellow of the German National Academic Foundation (Studienstiftung) and its scientific college for life sciences, and has received a Google Anita Borg Europe Fellowship and an ICML Best Paper Award. She has also been a research visitor at Georgetown University Medical Center and Microsoft Research and has held workshops and tutorials on submodularity in machine learning.