Related papers: Multivariate approximation in downward closed poly…
Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not…
Polynomial approximations to boolean functions have led to many positive results in computer science. In particular, polynomial approximations to the sign function underly algorithms for agnostically learning halfspaces, as well as…
In this work we study convergence properties of sparse polynomial approximations for a class of affine parametric saddle point problems. Such problems can be found in many computational science and engineering fields, including the Stokes…
Stochastic computational models in the form of pure jump processes occur frequently in the description of chemical reactive processes, of ion channel dynamics, and of the spread of infections in populations. For spatially extended models,…
We consider an incremental approximation method for solving variational problems in infinite-dimensional Hilbert spaces, where in each step a randomly and independently selected subproblem from an infinite collection of subproblems is…
The inverse of a large matrix can often be accurately approximated by a polynomial of degree significantly lower than the order of the matrix. The iteration polynomial generated by a run of the GMRES algorithm is a good candidate, and its…
We determine the power of the weighted sum scalarization with respect to the computation of approximations for general multiobjective minimization and maximization problems. Additionally, we introduce a new multi-factor notion of…
This article presents an empirical validation of the functional multidimensional scaling model, a novel approach that improves the smoothness of time-varying dissimilarities in a low-dimensional space, embedding a modified Adam stochastic…
We consider the following problem: given a program, find tight asymptotic bounds on the values of some variables at the end of the computation (or at any given program point) in terms of its input values. We focus on the case of…
We study the approximation of functions which are invariant with respect to certain permutations of the input indices using flow maps of dynamical systems. Such invariant functions includes the much studied translation-invariant ones…
It is more and more frequently the case in applications that the data we observe come from one or more random variables taking values in an infinite dimensional space, e.g. curves. The need to have tools adapted to the nature of these data…
We describe a framework in which is possible to develop and implement algorithms for the approximation of invariant measures of dynamical systems with a given bound on the error of the approximation. Our approach is based on a general…
Many combinatorial optimization problems can be formulated as the search for a subgraph that satisfies certain properties and minimizes the total weight. We assume here that the vertices correspond to points in a metric space and can take…
This paper puts forward a new generalized polynomial dimensional decomposition (PDD), referred to as GPDD, comprising hierarchically ordered measure-consistent multivariate orthogonal polynomials in dependent random variables. Unlike the…
For the Poisson equation posed in a domain containing a large number of polygonal perforations, we propose a low-dimensional coarse approximation space based on a coarse polygonal partitioning of the domain. Similarly to other multiscale…
We propose an algorithmic framework, that employs active subspace techniques, for scalable global optimization of functions with low effective dimension (also referred to as low-rank functions). This proposal replaces the original…
Rational approximation appears in many contexts throughout science and engineering, playing a central role in linear systems theory, special function approximation, and many others. There are many existing methods for solving the rational…
In this paper, we first describe a matricial Newton-type algorithm designed to solve the multivariable spectrum approximation problem. We then prove its global convergence. Finally, we apply this approximation procedure to multivariate…
We consider the regression problem of estimating functions on $\mathbb{R}^D$ but supported on a $d$-dimensional manifold $ \mathcal{M} \subset \mathbb{R}^D $ with $ d \ll D $. Drawing ideas from multi-resolution analysis and nonlinear…
Multipoint evaluation is the computational task of evaluating a polynomial given as a list of coefficients at a given set of inputs. And while \emph{nearly linear time} algorithms have been known for the univariate instance of multipoint…