[CSEE Talk] talk: Learning from High-Dimensional Data via Transformations, 12pm 2/29, ITE325b

[Tim Finin]

              Computer Science and Electrical Engineering
                University of Maryland, Baltimore County

        Learning from High-Dimensional Data via Transformations

                        Dr. Hossein Mobahi, MIT

               12:00pm Monday 29, February 2016, ITE325b

High-dimensional data is ubiquitous in the modern world, arising
in images, movies, biomedical measurements, documents, and many
other contexts. The "curse of dimensionality" tells us that
learning in such regimes is generally intractable. However,
practical problems often exhibit special simplifying structures
which, when identified and exploited, can render learning in high
dimensions tractable. This is a great prospect however, but how
to get there in not trivial. In this talk, I will address two
challenges associated with high-dimensional learning and discuss
my proposed solution.

First, parsimony (sparsity, low rank, etc.) is one of the most
prevalent structures in high-dimensional learning
applications. However, its presence is often implicit and it
reveals itself only after a transformation of the data. Studying
the space of such transformations and the associated algorithms
for their inference constitute an important class of problems in
high-dimensional learning. I will present some of my work in this
direction related to image segmentation. I will show how low-rank
structures become abundant in images when certain spatial and
geometric transformations are considered. This work resulted in a
state of the art algorithm for segmentation of natural images.

Second, important scenarios such as deep learning involve
high-dimensional nonconvex optimization. Such optimization is
generally intractable. However, I show how some properties in the
optimization landscape, such as smoothness and stability, can be
exploited to transform the objective function to simpler
subproblems and allow obtaining reasonable solutions
efficiently. The theory is derived by combining the notion of
convex envelopes with differential equations. This results in
algorithms involving high-dimensional convolution with the
Gaussian kernel, which I show has a closed form in many practical
scenarios. I will present applications of this work in image
alignment, image matching, and deep learning. Furthermore, I will
discuss how this theory justifies heuristics currently used in
deep learning and suggests new training algorithms that offer a
significant speedup.


Hossein Mobahi (http://people.csail.mit.edu/hmobahi) is a
postdoctoral researcher in the Computer Science and Artificial
Intelligence Lab at the Massachusetts Institute of Technology
(MIT). His research interests include machine learning, computer
vision, optimization, and especially the intersection of the
three. He obtained his PhD from the University of Illinois at
Urbana-Champaign in Dec 2012. He is the recipient of
Computational Science & Engineering Fellowship, Cognitive Science
& AI Award, and Mavis Memorial Scholarship. His recent work on
machine learning and optimization have been covered by the MIT
news.

Host: Tim Finin, finin at umbc.edu

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