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Asymptotic Geometric Analysis and Learning Theory

Objective

In a typical learning problem one tries to approximate an unknown function by a function from a given class using random data, sampled according to an unknown measure. In this project we will be interested in parameters that govern the complexity of a learning problem. It turns out that this complexity is determined by the geometry of certain sets in high dimension that are connected to the given class (random coordinate projections of the class). Thus, one has to understand the structure of these sets as a function of the dimension - which is given by the cardinality of the random sample. The resulting analysis leads to many theoretical questions in Asymptotic Geometric Analysis, Probability (most notably, Empirical Processes Theory) and Combinatorics, which are of independent interest beyond the application to Learning Theory. Our main goal is to describe the role of various complexity parameters involved in a learning problem, to analyze the connections between them and to investigate the way they determine the geometry of the relevant high dimensional sets. Some of the questions we intend to tackle are well known open problems and making progress towards their solution will have a significant theoretical impact. Moreover, this project should lead to a more complete theory of learning and is likely to have some practical impact, for example, in the design of more efficient learning algorithms.

Field of science

  • /natural sciences/mathematics/pure mathematics/geometry

Call for proposal

ERC-2007-StG
See other projects for this call

Funding Scheme

ERC-SG - ERC Starting Grant

Host institution

TECHNION - ISRAEL INSTITUTE OF TECHNOLOGY
Address
Senate Building Technion City
32000 Haifa
Israel
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 750 000
Principal investigator
Shahar Mendelson (Prof.)
Administrative Contact
Mark Davison (Mr.)

Beneficiaries (1)

TECHNION - ISRAEL INSTITUTE OF TECHNOLOGY
Israel
EU contribution
€ 750 000
Address
Senate Building Technion City
32000 Haifa
Activity type
Higher or Secondary Education Establishments
Principal investigator
Shahar Mendelson (Prof.)
Administrative Contact
Mark Davison (Mr.)