ivar iable Functional Interpolation and Adaptive N etworks
نویسندگان
چکیده
A b st r act . The relationship between "learning" in ad aptive layered networks and the fit ting of data wit h high dimensional surfaces is discussed . T his leads natu rally to a picture of "generalization" in terms of interp olation between known data points and suggests a rat ional approach to th e theory of such networks. A class of adaptive networks is identified which makes the inte rpo lation scheme explicit. This class has the property t ha t learning is equivalent to the solution of a set of linear equations. T hese netwo rks t hus represent nonlinear relati onships while ha ving a guaranteed learning rule.
منابع مشابه
ult ivar iable Functional Interpolation and Adaptive N etworks
A b st r act . The relationship between "learning" in ad aptive layered networks and the fit ting of data wit h high dimensional surfaces is discussed . T his leads natu rally to a picture of "generalization" in terms of interp olation between known data points and suggests a rat ional approach to th e theory of such networks. A class of adaptive networks is identified which makes the inte rpo ...
متن کاملMercer Kernels and Integrated Variance Experimental Design: Connections Between Gaussian Process Regression and Polynomial Approximation | SIAM/ASA Journal on Uncertainty Quantification | Vol. 4, No. 1 | Society for Industrial and Applied Mathematics
This paper examines experimental design procedures used to develop surrogates of computational models, exploring the interplay between experimental designs and approximation algorithms. We focus on two widely used approximation approaches, Gaussian process (GP) regression and nonintrusive polynomial approximation. First, we introduce algorithms for minimizing a posterior integrated variance (IV...
متن کاملMercer kernels and integrated variance experimental design: connections between Gaussian process regression and polynomial approximation
Abstract. This paper examines experimental design procedures used to develop surrogates of computational models, exploring the interplay between experimental designs and approximation algorithms. We focus on two widely used approximation approaches, Gaussian process (GP) regression and nonintrusive polynomial approximation. First, we introduce algorithms for minimizing a posterior integrated va...
متن کاملNew adaptive interpolation schemes for efficient meshbased motion estimation
Motion estimation and compensation is an essential part of existing video coding systems. The mesh-based motion estimation (MME) produces smoother motion field, better subjective quality (free from blocking artifacts), and higher peak signal-to-noise ratio (PSNR) in many cases, especially at low bitrate video communications, compared to the conventional block matching algorithm (BMA). Howev...
متن کاملNumerical solution of functional integral equations by using B-splines
This paper describes an approximating solution, based on Lagrange interpolation and spline functions, to treat functional integral equations of Fredholm type and Volterra type. This method can be extended to functional differential and integro-differential equations. For showing efficiency of the method we give some numerical examples.
متن کامل