Nonlinear approximation is widely used in signal processing. Real-life signals can be modeled as functions of bounded variation. Thus the variable knot of approximating function could be selfadaptively chosen by balancing the total variation of the target function. In this paper, we adopt continuous piecewise linear approximation instead of the existing piecewise constants approximation. The re...

We propose semi-random features for nonlinear function approximation. The flexibility of semirandom feature lies between the fully adjustable units in deep learning and the random features used in kernel methods. For one hidden layer models with semi-random features, we prove with no unrealistic assumptions that the model classes contain an arbitrarily good function as the width increases (univ...

Since the single input rule modules connected fuzzy inference model (SIRMs model) is proposed by Yubazaki, Yi et al., many researches on the extension of the SIRMs model have been reported. Moreover, the fuzzy functional SIRMs inference model, in which the consequent parts of the functional-type SIRMs model are generalized to fuzzy function, has proposed as one of various extension SIRMs models...

It is well understood that the limitations of hydrological measurement techniques warrants for modeling of hydrological processes in a basin. However, most hydrologic systems are extremely complex and modeling them with the available limited measurements is a difficult task. The basic purpose of a model is to simulate and predict the operation of the system that is unduly complex, and also to p...

Multi-step methods are important in reinforcement learning (RL). Eligibility traces, the usual way of handling them, works well with linear function approximators. Recently, van Seijen (2016) had introduced a delayed learning approach, without eligibility traces, for handling the multi-step λ-return with nonlinear function approximators. However, this was limited to action-value methods. In thi...

We describe a method for discrete representation of continuous functions and show how this may be used for typical computations in nonlinear control design. The method involves representing functions by their values and nitely many derivatives at discrete set of points on the domain. We propose a grid structure based on a hierarchy of rectangular boxes that provides exibility in placing grid po...

A technique for approximating a continuous function of n variables with a radial basis function (RBF) neural network is presented. The method uses an n-dimensional raised-cosine type of RBF that is smooth, yet has compact support. The RBF network coefficients are low-order polynomial functions of the input. A simple computational procedure is presented which significantly reduces the network tr...

This work considers the infinite-time discounted optimal control problem for continuous time input-affine polynomial dynamical systems subject to polynomial state and box input constraints. We propose a sequence of sum-of-squares (SOS) approximations of this problem obtained by first lifting the original problem into the space of measures with continuous densities and then restricting these den...

This is a survey of nonlinear approximation, especially that part of the subject which is important in numerical computation. Nonlinear approximation means that the approximants do not come from linear spaces but rather from nonlinear manifolds. The central question to be studied is what, if any, are the advantages of nonlinear approximation over the simpler, more established, linear methods. T...

We have analyzed the far-field approximation of the Green’s function representation for seismic interferometry. By writing each of the Green’s functions involved in the correlation process as a superposition of a direct wave and a scattered wave, the Green’s function representation is rewritten as a superposition of four terms. When the scattered waves are modeled with the Born approximation, i...