

Colloquium of the Steklov Mathematical Institute of Russian Academy of Sciences
December 5, 2019 16:00, Moscow, Steklov Mathematical Institute of RAS, Conference Hall (8 Gubkina)






Statistical Problems of Manifold Learning for Predictive Modeling
E. V. Burnaev^{} ^{} Skolkovo Institute of Science and Technology

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Abstract:
Predictive Modeling tasks deal with highdimensional data, and curse of
dimensionality is an obstacle to the use of many methods for their
solutions. In many applications, realworld data occupy only a very
small part of highdimensional observation space whose intrinsic
dimension is essentially lower than dimension of the space. Popular
model for such data is a Manifold one in accordance with which data lie
on or near an unknown lowdimensional Data manifold (DM) embedded in an
ambient highdimensional space. Predictive Modeling tasks studied under
this assumption are referred to as the manifold learning ones whose
general goal is discovering a lowdimensional structure of
highdimensional manifold valued data from a given dataset. If dataset
points are sampled according to an unknown probability measure on the
DM, we face with statistical problems about manifold valued data. In the
talk we will provide a short review of statistical problems regarding
highdimensional manifold valued data and their solutions.

