Identifying linear combinations of ridge functions

DOI10.1006/aama.1998.0623zbMath0931.41011OpenAlexW1983767920MaRDI QIDQ1277211

Martin D. Buhmann, Allan Pinkus

Publication date: 21 February 2000

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/aama.1998.0623

zbMATH Keywords

inverse problemridge function

Mathematics Subject Classification ID

Approximation by other special function classes (41A30) Representation and superposition of functions (26B40)

Related Items (20)

Linear/ridge expansions: enhancing linear approximations by ridge functions ⋮ Approximation by ridge function fields over compact sets ⋮ Robust recovery of stream of pulses using convex optimization ⋮ Characterization of an extremal sum of ridge functions ⋮ On the representation by linear superpositions ⋮ On a smoothness problem in ridge function representation ⋮ Approximation by sums of ridge functions with fixed directions ⋮ The ridge function representation of polynomials and an application to neural networks ⋮ On some properties of smooth sums of ridge functions ⋮ The recovery of ridge functions on the hypercube suffers from the curse of dimensionality ⋮ Some problems in the theory of ridge functions ⋮ A note on continuous sums of ridge functions ⋮ Smoothness and uniqueness in ridge function representation ⋮ Entropy and sampling numbers of classes of ridge functions ⋮ On the representation by bivariate ridge functions ⋮ A representation problem for smooth sums of ridge functions ⋮ On some aspects of approximation of ridge functions ⋮ Stable recovery of entangled weights: towards robust identification of deep neural networks from minimal samples ⋮ Recovery of regular ridge functions on the ball ⋮ On best approximation of classes by radial functions

Cites Work

• Projection-based approximation and a duality with kernel methods
• Optimal reconstruction of a function from its projections
• Fundamentality of ridge functions
• Reconstructing a neural net from its output
• On Nonlinear Functions of Linear Combinations
• Generalised functions and their convolution
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