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Poster
Flexible Modeling of Diversity with Strongly Log-Concave Distributions
Joshua Robinson · Suvrit Sra · Stefanie Jegelka

Thu Dec 12 05:00 PM -- 07:00 PM (PST) @ East Exhibition Hall B + C #65
in Algorithms -- Unsupervised Learning »

Strongly log-concave (SLC) distributions are a rich class of discrete probability distributions over subsets of some ground set. They are strictly more general than strongly Rayleigh (SR) distributions such as the well-known determinantal point process. While SR distributions offer elegant models of diversity, they lack an easy control over how they express diversity. We propose SLC as the right extension of SR that enables easier, more intuitive control over diversity, illustrating this via examples of practical importance. We develop two fundamental tools needed to apply SLC distributions to learning and inference: sampling and mode finding. For sampling we develop an MCMC sampler and give theoretical mixing time bounds. For mode finding, we establish a weak log-submodularity property for SLC functions and derive optimization guarantees for a distorted greedy algorithm.

Keywords: Graphical Models · Unsupervised Learning · Algorithms · Probabilistic Methods; Probabilistic Methods
[ Paper]  [ Slides] 

Author Information

Joshua Robinson (MIT)
Suvrit Sra (MIT)

Suvrit Sra is a faculty member within the EECS department at MIT, where he is also a core faculty member of IDSS, LIDS, MIT-ML Group, as well as the statistics and data science center. His research spans topics in optimization, matrix theory, differential geometry, and probability theory, which he connects with machine learning --- a key focus of his research is on the theme "Optimization for Machine Learning” (http://opt-ml.org)

Stefanie Jegelka (MIT)

Stefanie Jegelka is an X-Consortium Career Development Assistant Professor in the Department of EECS at MIT. She is a member of the Computer Science and AI Lab (CSAIL), the Center for Statistics and an affiliate of the Institute for Data, Systems and Society and the Operations Research Center. Before joining MIT, she was a postdoctoral researcher at UC Berkeley, and obtained her PhD from ETH Zurich and the Max Planck Institute for Intelligent Systems. Stefanie has received a Sloan Research Fellowship, an NSF CAREER Award, a DARPA Young Faculty Award, the German Pattern Recognition Award and a Best Paper Award at the International Conference for Machine Learning (ICML). Her research interests span the theory and practice of algorithmic machine learning.

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