[Ml-stat-talks] Yuri Ingster's talk today at 4:30 (Sherrerd 101)
rigollet at Princeton.EDU
Mon Jan 23 10:45:30 EST 2012
Dear ml-stats list members,
Ingster talk is today. See below.
Yuri Ingster from St. Petersburg Electrotechnical University is rarely in the US and we're fortunate to have him give a talk at the ORFE Colloquium this month.
He is THE expert on nonparametric hypothesis testing since the early eighties. His work on detection boundaries for sparse signals has been under the spotlight for the last few years.
His current research focuses on the phase transition that arises when data becomes to scarce compared to the intensity of the signal to be estimated or detected.
It should be enlightening to anyone interested in high-dimensional statistics.
See below for the details.
Monday, January 23, 2012 at 4:30 PM
Sherrerd Hall 101
Speaker: Yuri Ingster, St. Petersburg Electrotechnical University (LETI), Russia
Title: Estimation and Detection of High-variable Functions: The Curse of Dimensionality and How To Fight It
Abstract: We give a survey of resent results in the minimax estimation and detection of a multivariate function under the white Gaussian noise model. We study the "curse of dimensionality" phenomenon for a function from the balls in various functional spaces: Sobolev spaces, tensor product Sobolev spaces, and spaces of analytic functions. Typically, the rates of quadratic risk in estimation problem and separation rates in detection problem become catastrophically bad when the number of variables is larger than log(εˉ1), where ε is the noise intensity.
We show that the curse of dimensionality is "lifted" for the balls in anisotropic Sobolev spaces and in weighted tensor product spaces. The spaces of the last type were introduced by Sloan and Woznjakovski (1998) in the context of numerical integration problem.
The methods of the study are based on known results in estimation and detection problems for ellipsoids corresponding to the balls in functional spaces, and on some new probabilistic tools for studying approximation characteristics of ellipsoids under consideration. These methods seem to be of independent interest. In particular these give some new results in high dimensional lattice problems.
All needed statistical and analytical definitions will be given at the talk.
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