[Colloquium] Reminder: Fraser/Dissertation Defense/Jul 12, 2013

[Margaret Jaffey]

This is a reminder about Maia's defense tomorrow morning.

       Department of Computer Science/The University of Chicago

                     *** Dissertation Defense ***


Candidate:  Maia Fraser

Date:  Friday, July 12, 2013

Time:  10:00 AM

Place:  Ryerson 276

Title: Group Actions in Topological Data Analysis and Hierarchical
Learning

Abstract:
In broad terms this thesis focuses on underlying structure in data and
its relevance to hierarchical and/or semi-supervised learning. Of
special interest is structure given by group actions on data.

Our primary theoretical contribution is a notion of complexity of a
class of statistical models which we use to evaluate advantages of
multi-step (hierarchical) and/or semi-supervised learning strategies
under certain conditions on underlying structure in the data.
Essentially, we consider statistical models on X x Y in which the
marginal p_X determines a representation t_{p_X}(x) such that (y,
t_{p_X}(x)) is sufficient for the regression of interest. The measure
of complexity of a statistical model on X x Y which we define, the
``uniform shattering dimension", serves as a measure of variability of
the class of conditionals p(y|x) traded off against uniformity of the
marginals p_X and we use it to obtain lower bounds on the worst case
expected error of learning algorithms. With additional conditions we
derive a gap between purely supervised and semi-supervised learning
rates. The setup we propose holds in many practical settings,
including (but not restricted to) settings where data are concentrated
near an underlying submanifold or subject to a suitable group action.
Our proof generalizes an unpublished argument of Niyogi (2008) in
support of manifold regularization. The example of Castelli and Cover
(1996) which first compared the value of labeled vs. unlabeled data,
also falls into our framework but they did not derive lower bounds for
purely supervised learning rates.

Our experimental work is divided into two parts. Both are focused on
spaces of images and deal with underlying structure in data. In one,
we use topological analysis (TDA) to investigate S^1-actions in spaces
of images. In the other, we look at hierarchical learning and
investigate the performance of certain novel hierarchical
ISO_+(2)-invariant features for image classification. As well we make
several theoretical contributions to TDA.

Maia's advisor is Prof. Risi Kondor

Login to the Computer Science Department website for details,
including a draft copy of the dissertation:

 https://www.cs.uchicago.edu/phd/phd_announcements#maia

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Margaret P. Jaffey            margaret at cs.uchicago.edu
Department of Computer Science
Student Support Rep (Ry 156)               (773) 702-6011
The University of Chicago      http://www.cs.uchicago.edu
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