Foundations and Algorithms for Statistics and Learning for Data in Metric Spaces
Abstract
The well-known curse of dimensionality makes many estimation problems in high-dimensional spaces exponentially hard in D, and several approaches towards defeating, or bypass, such a curse have been proposed, which necessarily entail imposing assumptions on the data. It is classical in statistics to construct models for such high-dimensional data sets, typically parameterized by a small number of parameters and, in a somewhat related fashion, in machine learning one often observes that real-world data sets may concentrate near manifolds, see for example, and more general and realistic models have been proposed. In both cases, the effective or intrinsic dimensionality of the data is much lower, and independent, of the dimensionality of the ambient space, and such low intrinsic dimension is exploited to circumvent the curse of dimensionality.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jul 28, 2017
- Source ID
- FA95501710280
Entities
People
- Mauro Maggioni
Organizations
- Air Force Office of Scientific Research
- Johns Hopkins University
- United States Air Force