Jonathan Huang is an NSF Computing Innovation (CI) postdoctoral fellow at the geometric computing group at Stanford University. He completed his Ph.D. in 2011 with the School of Computer Science at Carnegie Mellon University where he also received a Masters degree in 2008.  He received his B.S. degree in Mathematics from  Stanford University in 2005.  His research interests lie primarily in statistical machine learning and reasoning with combinatorially structured data with applications
such as analyzing real world education data.  His research has resulted in a number of publications in premier machine learning conferences and journals, receiving a paper award in NIPS 2007 for his work on applying group theoretic Fourier analysis to probabilistic reasoning with permutations.

AG 1, AG 2, AG 3, AG 4, AG 5, RG1, SWS, MMCI   Info

MPI Audience

English

45 Minutes

Saarbrücken

Probabilistic reasoning and learning with permutation data arises as a
fundamental problem in myriad applications such as modeling preference
rankings over objects (such as webpages), tracking multiple moving
objects, reconstructing the temporal ordering of events from multiple
imperfect accounts, and more. Since the number of permutations scales
factorially with the number of objects being ranked or tracked,
however, it is not feasible to represent and reason with arbitrary
probability distributions on permutations. Consequently, many
approaches to probabilistic reasoning problems on the group of
permutations have been either ad-hoc, unscalable, and/or relied on
rigid and unrealistic assumptions. For example, common factorized
probability distribution representations, such as graphical models,
are inefficient due to the mutual exclusivity constraints that are
typically associated with permutations.

In this talk, I'll talk about an algebraic approach which we have
developed to combat this combinatorial explosion and
its implications for multi target tracking.  Our approach is based on
the idea of projecting a distribution onto a group theoretic
generalization of the Fourier basis. I'll discuss how the
probabilistic decomposition leads to compact representations for
distributions over permutations and that one can formulate efficient
probabilistic inference algorithms by taking advantage of the
combinatorial structure of the Fourier representation.

Time permitting, I will also touch on some of my more recent
projects related to massive open online courses (MOOCs) which
have become popular in the last two years and have much to gain
from large scale data analysis and machine learning.

Michael Wand

4008

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