Related papers: Approximation of the Gompertz function with a mult…
In statistics and machine learning, logistic regression is a widely-used supervised learning technique primarily employed for binary classification tasks. When the number of observations greatly exceeds the number of predictor variables, we…
In this paper we consider the approximation of a function by its interpolating multilinear spline and the approximation of its derivatives by the derivatives of the corresponding spline. We derive formulas for the uniform approximation…
This paper addresses the problem of providing robust estimators under a functional logistic regression model. Logistic regression is a popular tool in classification problems with two populations. As in functional linear regression,…
Submodular functions are a fundamental object of study in combinatorial optimization, economics, machine learning, etc. and exhibit a rich combinatorial structure. Many subclasses of submodular functions have also been well studied and…
Logistic regression is the most commonly used method for constructing predictive models for binary responses. One significant drawback to this approach, however, is that the asymptotes of the logistic response function are fixed at 0 and 1,…
In this paper, we estimate the simultaneous approximation exponents of the values of certain Mahler functions. For this we construct Hermite-Pad\'{e} approximations of the functions under consideration, then apply the functional equations…
Having a function $f$ and a set of functionals $\{\mathcal{C}_{n}\}$, $c_n^f \equiv \mathcal{C}_n \left(f\right)$, one can interpret function approximation very generally as a construction of some function $\mathcal{A}_{N}^{f}$ such that…
We introduce certain linear positive operators and study some approximation properties of these operators in the space of functions, continuous on a compact set, of two variables. We also find the order of this approximation by using…
We give an explicit sequence of polarizations such that for every measurable function, the sequence of iterated polarizations converge to the symmetric rearrangement of the initial function.
We study the possibility of using multilevel algorithms for the computation of correlation functions of gradient flow observables. For each point in the correlation function an approximate flow is defined which depends only on links in a…
In this work, we consider the approximate reconstruction of high-dimensional periodic functions based on sampling values. As sampling schemes, we utilize so-called reconstructing multiple rank-1 lattices, which combine several preferable…
In the article the necessary and sufficient conditions for a representation of Lipschitz function of two variables as a difference of two convex functions are formulated. An algorithm of this representation is given. The outcome of this…
Motivated by applications for simulating quantum many body functions, we propose a new universal ansatz for approximating anti-symmetric functions. The main advantage of this ansatz over previous alternatives is that it is bi-Lipschitz with…
We present two approaches for computing rational approximations to multivariate functions, motivated by their effectiveness as surrogate models for high-energy physics (HEP) applications. Our first approach builds on the Stieltjes process…
In this paper, we discuss the problem of minimizing the sum of two convex functions: a smooth function plus a non-smooth function. Further, the smooth part can be expressed by the average of a large number of smooth component functions, and…
The paper deals with the problem of approximating the functions of several variables by branched continued fractions, in particular, multidimensional A- and J-fractions with independent variables. A generalization of Gragg's algorithm is…
We exploit the properties of a sequence of functions that approximate the divisor functions and combine them with an analytical formula of a delta-like sequence to give a new proof of a theorem of Gronwall on the asymptotic of the divisor…
Algorithms for numerical computation of symmetric elliptic integrals of all three kinds are improved in several ways and extended to complex values of the variables (with some restrictions in the case of the integral of the third kind).…
We combine the method of exchangeable pairs with Stein's method for functional approximation. As a result, we give a general linearity condition under which an abstract Gaussian approximation theorem for stochastic processes holds. We apply…
We provide a comprehensive study of interrelations between different measures of smoothness of functions on various domains and smoothness properties of approximation processes. Two general approaches to this problem have been developed:…