Related papers: A novel for prediction and approximation of functi…
An approach is presented for making predictions about functional time series. The method is applied to data coming from periodically correlated processes and electricity demand, obtaining accurate point forecasts and narrow prediction bands…
We introduce a novel arithmetic function $w(n)$, a generalization of the Liouville function $\lambda(n)$, as the coefficients of a Dirichlet series. By spatially encoding information in a natural way about the distribution of prime factors…
The paper presents new and known results on estimates of important linear and nonlinear approximation characteristics of generalized Wiener classes of functions of several variables in different metrics.
There is proposed a method for improving the convergence of Fourier series by function systems, orthogonal at the segment, the application of which allows for smooth functions to receive uniformly convergent series. There is also proposed…
This article introduces an effective generalization of the polar flavor of the Fourier Theorem based on a new method of analysis. Under the premises of the new theory an ample class of functions become viable as bases, with the further…
We investigate analytic properties of the double Fourier sphere (DFS) method, which transforms a function defined on the two-dimensional sphere to a function defined on the two-dimensional torus. Then the resulting function can be written…
Dealing with massive data is a challenging task for machine learning. An important aspect of machine learning is function approximation. In the context of massive data, some of the commonly used tools for this purpose are sparsity,…
It has long been agreed by academics that the inversion method is the method of choice for generating random variates, given the availability of the quantile function. However for several probability distributions arising in practice a…
This is a textbook on Fourier Series, suitable for both undergraduate and graduate courses. The textbook is endowed with exercises, and full solutions are provided at the end of the book.
In this paper we show that there is a link between approximate Bayesian methods and prior robustness. We show that what is typically recognized as an approximation to the likelihood, either due to the simulated data as in the Approximate…
Fourier series with power series coefficients for the normal and distance to a point from an ellipse are derived. These expressions are the first of their kind and opens up a range of analysis and computational possibilities.
In our recent publication [1] we presented an exponential series approximation suitable for highly accurate computation of the complex error function in a rapid algorithm. In this Short Communication we describe how a simplified…
The proposed system of integer functions is logically fully independent from the traditional mathematical analysis of the real functions, but there is a well-defined mutual correspondence between the two disciplines. The system of integer…
A neural network computes a function. A central property of neural networks is that they are "universal approximators:" for a given continuous function, there exists a neural network that can approximate it arbitrarily well, given enough…
In this paper, we propose a generic framework for devising an adaptive approximation scheme for value function approximation in reinforcement learning, which introduces multiscale approximation. The two basic ingredients are multiresolution…
There have been a number of papers written on semi-parametric estimation methods of the long-memory exponent of a time series, some applied, others theoretical. Some using Fourier methods, others using a wavelet-based technique. In this…
We survey key techniques and results from approximation theory in the context of uniform approximations to real functions such as e^{-x}, 1/x, and x^k. We then present a selection of results demonstrating how such approximations can be used…
The focus of this article is the approximation of functions which are analytic on a compact interval except at the endpoints. Typical numerical methods for approximating such functions depend upon the use of particular conformal maps from…
Recent years have witnessed a hot wave of deep neural networks in various domains; however, it is not yet well understood theoretically. A theoretical characterization of deep neural networks should point out their approximation ability and…
A general framework with a series of different methods is proposed to improve the estimate of convex function (or functional) values when only noisy observations of the true input are available. Technically, our methods catch the bias…