Gridge Approximation and Radon Compass

Gridge Approximation and Radon Compass

Gridge approximation compiles greedy algorithms and ridge approximation. It is a class of algorithmic constructions of ridge functions - finite linear combinations of planar waves. The goal is to approximate a given target which is a multivariate function. On each step, a new planar wave is added to...

Ausführliche Beschreibung

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Bibliographische Detailangaben
Hauptverfasser: Maiorov, V E, Oskolkov, K I, Temlyakov, V N
Format: Report
Sprache:eng
Schlagworte:
ALGORITHMS
COMPASSES
CONSTRUCTION
FUNCTIONS
HILBERT SPACE
MULTIVARIATE ANALYSIS
Numerical Mathematics
PLANAR STRUCTURES
PROFILES
PURSUIT COURSES
RADON
REGRESSION ANALYSIS
RIDGES
STATISTICS
TARGETS
WAVES
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Beschreibung
Zusammenfassung:Gridge approximation compiles greedy algorithms and ridge approximation. It is a class of algorithmic constructions of ridge functions - finite linear combinations of planar waves. The goal is to approximate a given target which is a multivariate function. On each step, a new planar wave is added to the preceeding linear combination. This wave is selected greedily, i.e. optimally with regard to both the direction of propagation and the profile. In Mathematical Statistics, gridge approximation is known as projection pursuit regression. We consider gridge approximation in weighted Hilbert functional spaces on d-dimensional Euclidean space. Supported in part by N00014-91-J-1343 and N00014-97-1-0806 and NSF-DMS-9970326.