Related papers: Adaptive Bivariate Quarklet Tree Approximation via…
Let $\{(X_i,Y_i)\}_{i\in \{1,..., n\}}$ be an i.i.d. sample from the random design regression model $Y=f(X)+\epsilon$ with $(X,Y)\in [0,1]\times [-M,M]$. In dealing with such a model, adaptation is naturally to be intended in terms of…
A novel framework for a unifying treatment of quaternion valued adaptive filtering algorithms is introduced. This is achieved based on a rigorous account of quaternion differentiability, the proposed I-gradient, and the use of augmented…
In this work we introduce and study novel Quasi Newton minimization methods based on a Hessian approximation Broyden Class-\textit{type} updating scheme, where a suitable matrix $\tilde{B}_k$ is updated instead of the current Hessian…
This paper summarizes the work on implementing few solutions for the Steiner Tree problem which we undertook in the PAAL project. The main focus of the project is the development of generic implementations of approximation algorithms…
We study the properties of a simple greedy algorithm for the generation of data-adapted anisotropic triangulations. Given a function f, the algorithm produces nested triangulations and corresponding piecewise polynomial approximations of f.…
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…
Tensor network contractions are widely used in statistical physics, quantum computing, and computer science. We introduce a method to efficiently approximate tensor network contractions using low-rank approximations, where each intermediate…
The use of neural networks to approximate partial differential equations (PDEs) has gained significant attention in recent years. However, the approximation of PDEs with localised phenomena, e.g., sharp gradients and singularities, remains…
We consider the problem of approximately solving a standard bi-quadratic programming (StBQP), which is NP-hard. After reformulating the original problem as an equivalent copositive tensor programming, we show how to approximate the optimal…
Quaternion optimization has attracted significant interest due to its broad applications, including color face recognition, video compression, and signal processing. Despite the growing literature on quadratic and matrix quaternion…
We develop fast approximation algorithms for the minimum-cost version of the Bounded-Degree MST problem (BD-MST) and its generalization the Crossing Spanning Tree problem (Crossing-ST). We solve the underlying LP to within a $(1+\epsilon)$…
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…
We present approximation algorithms for the following NP-hard optimization problems related to bottleneck spanning trees in metric spaces. 1. The disjoint bottleneck spanning tree problem: Given $n$ pairs of points in a metric space, find…
The suboptimal performance of wavelets with regard to the approximation of multivariate data gave rise to new representation systems, specifically designed for data with anisotropic features. Some prominent examples of these are given by…
A key problem in approximation theory is the recovery of high-dimensional functions from samples. In many cases, the functions of interest exhibit anisotropic smoothness, and, in many practical settings, the nature of this anisotropy may be…
For adaptive mixed finite element methods (AMFEM), we first introduce the data oscillation to analyze, without the restriction that the inverse of the coefficient matrix of the partial differential equations (PDEs) is a piecewise polynomial…
We introduce an adaptive scattered data fitting scheme as extension of local least squares approximations to hierarchical spline spaces. To efficiently deal with non-trivial data configurations, the local solutions are described in terms of…
We propose an inexact variable-metric proximal point algorithm to accelerate gradient-based optimization algorithms. The proposed scheme, called QNing can be notably applied to incremental first-order methods such as the stochastic…
Recently, shearlet systems were introduced as a means to derive efficient encoding methodologies for anisotropic features in 2-dimensional data with a unified treatment of the continuum and digital setting. However, only very few…
We provide the first stochastic convergence rates for a family of adaptive quadrature rules used to normalize the posterior distribution in Bayesian models. Our results apply to the uniform relative error in the approximate posterior…