Seminars and Colloquia by Series

Introduction to the h-principle

Series
Other Talks
Time
Friday, January 23, 2009 - 15:00 for 2 hours
Location
Skiles 269
Speaker
Mohammad GhomiSchool of Mathematics, Georgia Tech
h-Principle consists of a powerful collection of tools developed by Gromov and others to solve underdetermined partial differential equations or relations which arise in differential geometry and topology. In these talks I will describe the Holonomic approximation theorem of Eliashberg-Mishachev, and discuss some of its applications including the sphere eversion theorem of Smale. Further I will discuss the method of convex integration and its application to proving the C^1 isometric embedding theorem of Nash.

Learning with Teacher - Learning Using Hidden Information

Series
Other Talks
Time
Friday, January 16, 2009 - 14:00 for 1 hour (actually 50 minutes)
Location
Klaus 2447
Speaker
Vladimir VapnikNEC Laboratories, Columbia University and Royal Holloway University of London

Please Note: You are cordially invited to attend a reception that will follow the seminar to chat informally with faculty and students. Refreshments will be provided.

The existing machine learning paradigm considers a simple scheme: given a set of training examples find in a given collection of functions the one that in the best possible way approximates the unknown decision rule. In such a paradigm a teacher does not play an important role. In human learning, however, the role of a teacher is very important: along with examples a teacher provides students with explanations, comments, comparisons, and so on. In this talk I will introduce elements of human teaching in machine learning. I will consider an advanced learning paradigm called learning using hidden information (LUHI), where at the training stage a teacher gives some additional information x^* about training example x. This information will not be available at the test stage. I will consider the LUHI paradigm for support vector machine type of algorithms, demonstrate its superiority over the classical one and discuss general questions related to this paradigm. For details see FODAVA, Foundations of Data Analysis and Visual Analytics

Model Complexity Optimization

Series
Other Talks
Time
Friday, January 16, 2009 - 13:00 for 1 hour (actually 50 minutes)
Location
Klaus 2447
Speaker
Alexey ChervonenkisRussian Academy of Science and Royal Holloway University of London
It is shown (theoretically and empirically) that a reliable result can be gained only in the case of a certain relation between the capacity of the class of models from which we choose and the size of the training set. There are different ways to measure the capacity of a class of models. In practice the size of a training set is always finite and limited. It leads to an idea to choose a model from the most narrow class, or in other words to use the simplest model (Occam's razor). But if our class is narrow, it is possible that there is no true model within the class or a model close to the true one. It means that there will be greater residual error or larger number of errors even on the training set. So the problem of model complexity choice arises – to find a balance between errors due to limited number of training data and errors due to excessive model simplicity. I shall review different approaches to the problem.

Southeast Geometry Seminar

Series
Other Talks
Time
Friday, December 12, 2008 - 09:00 for 8 hours (full day)
Location
Skiles 243
Speaker
Various SpeakersVarious Universities
The Southeast Geometry Seminar (SGS) is a semiannual series of one day events organized by Vladimir Oliker (Emory), Mohammad Ghomi and John McCuan (Georgia Tech) and Gilbert Weinstein (UAB). See http://www.math.uab.edu/sgs for details

When Biology is Computation

Series
Other Talks
Time
Tuesday, October 21, 2008 - 11:00 for 1 hour (actually 50 minutes)
Location
Klaus Building, 1116E&W
Speaker
Leslie ValiantDivision of Engineering and Applied Sciences, Harvard University
We argue that computational models have an essential role in uncovering the principles behind a variety of biological phenomena that cannot be approached by other means. In this talk we shall focus on evolution. Living organisms function according to complex mechanisms that operate in different ways depending on conditions. Darwin's theory of evolution suggests that such mechanisms evolved through random variation guided by natural selection. However, there has existed no theory that would explain quantitatively which mechanisms can so evolve in realistic population sizes within realistic time periods, and which are too complex. Here we suggest such a theory. Evolution is treated as a form of computational learning from examples in which the course of learning depends only on the aggregate fitness of the current hypothesis on the examples, and not otherwise on individual examples. We formulate a notion of evolvability that distinguishes function classes that are evolvable with polynomially bounded resources from those that are not. For example, we can show that monotone Boolean conjunctions and disjunctions are demonstrably evolvable over the uniform distribution, while Boolean parity functions are demonstrably not. We shall discuss some broader issues in evolution and intelligence that can be addressed via such an approach.

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