Tomasz Malisiewicz and
I recently gave a
tutorial on Learning and Inference in Vision:
from Features to Scene Understanding at the
MLD Student Research Symposium on November 13.
[slides].
My research goals revolve around developing efficient
probabilistic reasoning algorithms. I am currently
interested in reasoning with uncertainty over permutations.
Permutations appear in a variety of real world problems ranging from
data association problems in multiobject tracking, to ranking/voting applications.
Unlike most discrete problems, permutations
present a much more challenging problem for inference due to the fact
that there are n! permutations.
Due to the enormous domain sizes involved, many approaches are
inspired by methods for working with continuous distributions.
In my thesis work, I have been developing Fourier
theoretic methods which have led to principled and efficient
approximate algorithms for reasoning with permutations.
Finally, I am also interested in a number of related areas such
as learning and inference in graphical models and dynamical systems,
nonparametric Hilbert space embeddings of probability distributions,
as well as computer vision applications of machine learning.
For your viewing pleasure, here is a
wordle generated from abstracts
of my recent papers:
(LDA) Latent Dirichlet Allocation
Jonathan Huang and
Tomasz Malisiewicz,
An implementation of the mean field inference/learning
algorithms from
Blei et al. (2003)
Sperner's Lemma
,
Jonathan Huang,
Some theorems/corollaries of Sperner's Lemma that I collected for a
combinatorics class. Sperner is an easy combinatorial fact about labelings
on a simplicial complex, but it has several surprising applications in
topology and analysis. The famous
Brouwer fixed point
theorem, and the fundamental theorem of algebra are two of the examples
that I discuss. [typos]
Cup Products in Computational Topology
,
Jonathan Huang,
Senior Honors Thesis (advisor: Gunnar Carlsson). We
show an application of topological persistence to computing invariants
related to the cohomology (cup product structure) of a finite simplicial
complex.
I am co-organizing a NIPS 2009 workshop
on Learning with Orderings!
