Related papers: Local Legendre Frame Approximation from Equispaced…
We introduce numerical optimization of multi-site support functions in the linear-scaling DFT code CONQUEST. Multi-site support functions, which are linear combinations of pseudo-atomic orbitals on a target atom and those neighbours within…
We study the problem of recovering a globally consistent Euclidean embedding of data, given only a local distance graph and propose a method that optimally represents these distances. The method operates solely on a neighborhood graph…
We design Local LMO - a new projection-free gradient-type method for constrained optimization. The key algorithmic idea is to replace the global linear minimization oracle over the constraint set used by Frank-Wolfe (FW) with a local linear…
Recently a deterministic method, frequent directions (FD) is proposed to solve the high dimensional low rank approximation problem. It works well in practice, but experiences high computational cost. In this paper, we establish a fast…
Statistical properties of a local fluctuational fluxes measured at the plasma edge are investigated in the work. It's shown that the amplitudes increments of the local fluctuational fluxes decrease by power law. For approximation of…
Limited-angle computerized tomography stands for one of the most difficult challenges in imaging. Although it opens the way to faster data acquisition in industry and less dangerous scans in medicine, standard approaches, such as the…
In this note, we show that the Local Molecular Field theory of Weeks et. al. can be re-derived as an extremum problem for an approximate Helmholtz free energy. Using the resulting free energy as a classical, fluid density functional yields…
We investigate the statistical properties of Temporal Difference (TD) learning with Polyak-Ruppert averaging, arguably one of the most widely used algorithms in reinforcement learning, for the task of estimating the parameters of the…
Polynomial reproduction plays a relevant role in deriving error estimates for various approximation schemes. Local reproduction in a quasi-uniform setting is a significant factor in the estimation of error and the assessment of stability…
Local Fr'echet Regression (LFR) is a nonparametric regression method for settings in which the explanatory variable lies in a Euclidean space and the response variable lies in a metric space. It is used to estimate smooth trajectories in…
Weighted average sampling is more practical and numerically more stable than sampling at single points as in the classical Shannon sampling framework. Using the frame theory, one can completely reconstruct a bandlimited function from its…
We propose a novel error analysis framework for scaled generalized Laguerre and generalized Hermite approximations.This framework can be regarded as an analogue of the Nyquist-Shannon sampling theorem: It characterizes the spatial and…
We consider the problem of estimating a regularization parameter, or a shrinkage coefficient $\alpha \in (0,1)$ for Regularized Tyler's M-estimator (RTME). In particular, we propose to estimate an optimal shrinkage coefficient by setting…
In this paper we present a new perspective on error analysis of Legendre approximations for differentiable functions. We start by introducing a sequence of Legendre-Gauss-Lobatto polynomials and prove their theoretical properties, such as…
We introduce the DNNLikelihood, a novel framework to easily encode, through Deep Neural Networks (DNN), the full experimental information contained in complicated likelihood functions (LFs). We show how to efficiently parametrise the LF,…
In this paper, we consider an approximation method, and a novel general analysis, for second-order elliptic differential equations with heterogeneous multiscale coefficients. We obtain convergence of the Generalized Multi-scale Finite…
We consider the problem of approximate Bayesian inference in log-supermodular models. These models encompass regular pairwise MRFs with binary variables, but allow to capture high-order interactions, which are intractable for existing…
The common methods of spectral analysis for multivariate ($n$-dimensional) time series, like discrete Frourier transform (FT) or Wavelet transform, are based on Fourier series to decompose discrete data into a set of trigonometric model…
Linear approximation approaches suffer from Gibbs oscillations when approximating functions with singularities. ENO-SR resolution is a local approach avoiding oscillations and with a full order of accuracy, but a loss of regularity of the…
A fast algorithm for the approximation of a low rank LU decomposition is presented. In order to achieve a low complexity, the algorithm uses sparse random projections combined with FFT-based random projections. The asymptotic approximation…