Related papers: Multivariate approximation in downward closed poly…
This article describes a multivariate polynomial regression method where the uncertainty of the input parameters are approximated with Gaussian distributions, derived from the central limit theorem for large weighted sums, directly from the…
We survey the main results of approximation theory for adaptive piecewise polynomial functions. In such methods, the partition on which the piecewise polynomial approximation is defined is not fixed in advance, but adapted to the given…
This paper introduces a novel algorithmic solution for the approximation of a given multivariate function by a nomographic function that is composed of a one-dimensional continuous and monotone outer function and a sum of univariate…
We consider the problem of approximating an unknown function from point evaluations. This problem is a crucial subproblem in many modern (nonlinear) approximation schemes. When obtaining these point evaluations is costly, minimising the…
Learning approximations to smooth target functions of many variables from finite sets of pointwise samples is an important task in scientific computing and its many applications in computational science and engineering. Despite well over…
Motivated by the need to better understand the properties of sparse cutting-planes used in mixed integer programming solvers, the paper [2] studied the idealized problem of how well a polytope is approximated by the use of sparse valid…
High-dimensional classification has become an increasingly important problem. In this paper we propose a "Multivariate Adaptive Stochastic Search" (MASS) approach which first reduces the dimension of the data space and then applies a…
Infinite-dimensional, holomorphic functions have been studied in detail over the last several decades, due to their relevance to parametric differential equations and computational uncertainty quantification. The approximation of such…
In this work, we discuss the problem of approximating a multivariate function by discrete least squares projection onto a polynomial space using a specially designed deterministic point set. The independent variables of the function are…
The problem of multivariate exponential analysis or sparse interpolation has received a lot of attention, especially with respect to the number of samples required to solve it unambiguously. In this paper we show how to bring the number of…
The dynamics of anisotropic particles are dictated by forces and torques that can be challenging to mathematically represent in computer simulations. Several data-driven approaches have been developed to approximate these interactions, but…
This work concerns the minimization of the pseudospectral abscissa of a matrix-valued function dependent on parameters analytically. The problem is motivated by robust stability and transient behavior considerations for a linear control…
Functions with discontinuities appear in many applications such as image reconstruction, signal processing, optimal control problems, interface problems, engineering applications and so on. Accurate approximation and interpolation of these…
Computational difficulty of quadratic matching and the Gromov-Wasserstein distance has led to various approximation and relaxation schemes. One of such methods, relying on the notion of distance profiles, has been widely used in practice,…
We consider the problem of approximating a function from $L^2$ by an element of a given $m$-dimensional space $V_m$, associated with some feature map $\boldsymbol{\varphi}$, using evaluations of the function at random points $x_1,…
The works presented in this habilitation concern the algorithmics of polynomials. This is a central topic in computer algebra, with numerous applications both within and outside the field - cryptography, error-correcting codes, etc. For…
Bilevel optimization problems are receiving increasing attention in machine learning as they provide a natural framework for hyperparameter optimization and meta-learning. A key step to tackle these problems is the efficient computation of…
This paper is devoted to developing and applications of a generalized differential theory of variational analysis that allows us to work in incomplete normed spaces, without employing conventional variational techniques based on…
Finding a \emph{single} best solution is the most common objective in combinatorial optimization problems. However, such a single solution may not be applicable to real-world problems as objective functions and constraints are only…
We discuss the notion of optimal polynomial approximants in multivariable reproducing kernel Hilbert spaces. In particular, we analyze difficulties that arise in the multivariable case which are not present in one variable, for example, a…