Related papers: AAA interpolation of equispaced data
Rational approximation schemes for reconstructing periodic signals from samples with poorly separated spectral content are described. These methods are automatic and adaptive, requiring no tuning or manual parameter selection. Collectively,…
Function approximation is a generic process in a variety of computational problems, from data interpolation to the solution of differential equations and inverse problems. In this work, a unified approach for such techniques is…
The combination of several socio-economic data bases originating from different administrative sources collected on several different partitions of a geographic zone of interest into administrative units induces the so called areal…
Mixup is a powerful data augmentation method that interpolates between two or more examples in the input or feature space and between the corresponding target labels. Many recent mixup methods focus on cutting and pasting two or more…
We describe a simple method for making inference on a functional of a multivariate distribution. The method is based on a copula representation of the multivariate distribution and it is based on the properties of an Approximate Bayesian…
Both Approximate Bayesian Computation (ABC) and composite likelihood methods are useful for Bayesian and frequentist inference, respectively, when the likelihood function is intractable. We propose to use composite likelihood score…
Matrices resulting from the discretization of a kernel function, e.g., in the context of integral equations or sampling probability distributions, can frequently be approximated by interpolation. In order to improve the efficiency, a…
A stochastic conjugate gradient method for approximation of a function is proposed. The proposed method avoids computing and storing the covariance matrix in the normal equations for the least squares solution. In addition, the method…
System modeling is a classical approach to ensure their reliability since it is suitable both for a formal verification and for software testing techniques. In the context of model-based testing an approach combining random testing and…
Explainable AI (XAI) is an active research area to interpret a neural network's decision by ensuring transparency and trust in the task-specified learned models. Recently, perturbation-based model analysis has shown better interpretation,…
The empirical beta copula is a simple but effective smoother of the empirical copula. Because it is a genuine copula, from which, moreover, it is particularly easy to sample, it is reasonable to expect that resampling procedures based on…
An algorithm for computing an analytic function of a matrix $A$ is described. The algorithm is intended for the case where $A$ has some close eigenvalues, and clusters (subsets) of close eigenvalues are separated from each other. This…
We first consider the problem of approximating a few eigenvalues of a rational matrix-valued function closest to a prescribed target. It is assumed that the proper rational part of the rational matrix-valued function is expressed in the…
Continuous representations are fundamental for modeling sampled data and performing computations and numerical simulations directly on the model or its elements. To effectively and efficiently address the approximation of point clouds we…
This paper develops a comprehensive probabilistic setup to compute approximating functions in active subspaces. Constantine et al. proposed the active subspace method in (Constantine et al., 2014) to reduce the dimension of computational…
Approximate Bayesian computation (ABC) performs statistical inference for otherwise intractable probability models by accepting parameter proposals when corresponding simulated datasets are sufficiently close to the observations. Producing…
Approximate Bayesian Computation (ABC) methods are commonly used to approximate posterior distributions in models with unknown or computationally intractable likelihoods. Classical ABC methods are based on nearest neighbor type algorithms…
Background: When conducting a meta-analysis of a continuous outcome, estimated means and standard deviations from the selected studies are required in order to obtain an overall estimate of the mean effect and its confidence interval. If…
We study constrained nested stochastic optimization problems in which the objective function is a composition of two smooth functions whose exact values and derivatives are not available. We propose a single time-scale stochastic…
Sample average approximation (SAA) is a technique for obtaining approximate solutions to stochastic programs that uses the average from a random sample to approximate the expected value that is being optimized. Since the outcome from…