MALBEC

MALBEC seminar, Spring 2009

Here’s the schedule for the MALBEC (”Math, Algorithms, Learning, Brains, Engineering, Computing”) seminar, hosted by the University of Wisconsin Department of Mathematics, Spring 2009. The aim of this lecture series is to create closer ties between mathematicians and scientists around UW doing mathematical work on the foundations of learning, perception, and behavior of people and machines. Please come, participate, and hang around afterwards with the speakers!

More information will be forthcoming — for instance, Michele Basso from physiology has agreed to speak and we’re working on a date. Also, you can expect enticing and nutritious receptions to follow each of these talks — location announced at the lecture. The MALBEC series is presented by the Department of Mathematics, Department of Computer Sciences, the Wisconsin Alumni Research Foundation, the Graduate School, and the Morgridge Institute. Direct all questions to Jordan Ellenberg.

Wednesday, March 4, 4pm:

Van Vleck B102

David Balduzzi (UW, psychiatry, Center for Sleep and Consciousness)

“Measuring consciousness as integrated information”

The integrated information theory (Tononi 2004) starts from phenomenology and makes use of thought experiments to claim that consciousness is integrated information. First: the quantity of consciousness corresponds to the amount of integrated information generated by a system of elements. Information is quantified by taking the current state as a measurement the system performs on itself, which specifies a repertoire of prior states that cause (lead to) the current state. Integrated information (phi) is quantified by computing the repertoire specified by the system as a whole relative to the repertoires specified independently by its parts. Second: the quality of an experience is completely specified by the set of informational relationships generated within that system. The set of all repertoires generated by subsystems of a system is represented in a geometric object, the quale. Informational relationships between points in the quale characterize how the measurements resulting from interactions in the system give structure to a particular experience.

After describing the theory in some detail, I will discuss how several neurobiological observations fall naturally into place in the framework: the association of consciousness with certain neural systems rather than with others; the fact that neural processes underlying consciousness can influence or be influenced by neural processes that remain unconscious; and the reduction of consciousness during dreamless sleep and generalized seizures. Furthermore, features of the quale can be related to features of conscious experience, such as modalities and submodalities, and can explain the distinct roles of different cortical subsystems in affecting the quality of experience.

(A relevant paper is here.)

Friday, April 17, 4pm: Partha Niyogi (U. Chicago, computer science)

Van Vleck B102

"Geometry, Perception, and Learning"

Our perceptual systems (visual and auditory) are confronted with data
in very high dimensional spaces. Yet we are able to learn how to
recognize faces, objects, phonemes, words, and so on without running
into the "curse of dimensionality". How might we get machines to
replicate this ability? What might be plausible principles of learning
in high dimensional spaces and what is its relevance to biological
learning?

I will explore these questions with a geometric point of view.  My
central thesis is this: in high dimensional spaces, natural data
occupies a tiny sliver of the space --- most of the ambient space is
empty.  The geometric structure of the data allows us to build
intrinsic and invariant representations, to define suitable classes of
functions with which to operate, and ultimately to learn effectively.
This point of view motivates new geometrically oriented learning
algorithms, new theoretical questions that surround their analysis,
and new models and metaphors to reason about perceptual systems.

Tuesday, April 21, 4pm Michael Coen (UW, biostatistics and medical informatics, computer sciences)

Computer Science room 1221

"Toward Formalizing "Abstract Nonsense""

When can we say two things are the "same?"  What, if anything, does this imply about their being "different?"

The idea of a category -- a set of objects sharing common properties
-- is a fundamental concept in many fields, including mathematics,
artificial intelligence, and cognitive and neuroscience.  Numerous
frameworks, for example, in machine learning and linguistics, rest
upon the simple presumption that categories are well-defined.  This is
slightly worrisome, as the many attempts formalizing categories have
met with equally many attempts shooting them down.

Instead of approaching this issue head on, I derive a robust theory of
"similarity," from a biologically-inspired approach to perception in
animals.  The very idea of creating categories assumes some implicit
notion of similarity, but it is rarely examined in isolation.
However, doing so is worthwhile, and I demonstrate the theory's
applicability to a variety of natural and artificial learning
problems.  Even when faced with Watanabe's "Ugly Duckling" theorem or
Wolpert's stingy cafeteria (serving the famous "No Free Lunch"
theorems), one can make significant progress toward formalizing a
theory of categories by examining their often unstated properties.

I demonstrate practical applications of this work in several domains,
including unsupervised machine learning, ensemble clustering, image
segmentation, human acquisition of language, and cognitive
neuroscience.

(Joint work with M.H.Ansari)

Wednesday, May 6 4pm  Jerry Zhu (UW, computer sciences)

Van Vleck B102

HAMLET (Human, Animal, and Machine Learning: Experiment and Theory)

Machine learning studies the principles governing all learning systems. Human beings and animals are learning systems too, and can be explored using the same mathematical tools.  This approach has been fruitful in the last few decades with standard tools such as reinforcement learning, artificial neural networks, and non-parametric Bayesian statistics.  We bring the approach one step further with some latest tools in machine learning, and uncover new quantitative findings.  In this talk, I will present three examples: (1) Human semi-supervised learning. Consider a child learning animal names.  Dad occasionally points to an animal and says "Dog!" (labeled data). But mostly the child observes the world by herself without explicit feedback (unlabeled data).  We show that humans learn from both labeled and unlabeled data, and that a simple Gaussian Mixture Model trained using the EM algorithm provides a nice fit to human behaviors.  (2) Human active learning.  The child may ask "What's that?", i.e. actively selecting items to query the target labels.  We show that humans are able to perform good active learning, achieving fast exponential error convergence as predicted by machine learning theory.  In contrast, when passively given i.i.d. training data humans learn much slower (polynomial convergence), also predicted by learning theory.  (3) Monkey online learning.  Rhesus monkeys can learn a "target concept", in the form of a certain shape or color.  What if the target concept keeps changing?  Adversarial online learning model provides a polynomial mistake bound.  Although monkeys perform worse than theory, anecdotal evidence suggests that they follow the concepts better than some graduate students. Finally, I will speculate on a few lessons learned in order to create better machine learning algorithms.

(Note from JE:  if the acronym in the title sounds familiar, it's because it's the name of another Wisconsin interdisciplinary seminar on quantitative and theoretical approaches to cognition --  the HAMLET seminar, which is highly recommended to anyone who likes MALBEC.)