Related papers: A Component-wise EM Algorithm for Mixtures
We consider h-adaptive algorithms in the context of the finite element method (FEM) and the boundary element method (BEM). Under quite general assumptions on the building blocks SOLVE, ESTIMATE, MARK, and REFINE of such algorithms, we prove…
We introduce an adaptive superconvergent finite element method for a class of mixed formulations to solve partial differential equations involving a diffusion term. It combines a superconvergent postprocessing technique for the primal…
Surveillance system (SS) development requires hi-tech support to prevail over the shortcomings related to the massive quantity of visual information from SSs. Anything but reduced human monitoring became impossible by means of its physical…
We consider finite element approximations of ill-posed elliptic problems with conditional stability. The notion of {\emph{optimal error estimates}} is defined including both convergence with respect to mesh parameter and perturbations in…
In the modal approach to clustering, clusters are defined as the local maxima of the underlying probability density function, where the latter can be estimated either non-parametrically or using finite mixture models. Thus, clusters are…
This paper studies the problem of estimation from relative measurements in a graph, in which a vector indexed over the nodes has to be reconstructed from pairwise measurements of differences between its components associated to nodes…
We propose an ensemble algorithm, which provides a new approach for evaluating and summing up a set of function samples. The proposed algorithm is not a quantum algorithm, insofar it does not involve quantum entanglement. The query…
The rigorous convergence analysis of adaptive finite element methods for regularized variational models of quasi-static brittle fracture in strain-limiting elastic solids is presented. This work introduces two novel adaptive mesh refinement…
Maximum likelihood estimation of mixture proportions has a long history, and continues to play an important role in modern statistics, including in development of nonparametric empirical Bayes methods. Maximum likelihood of mixture…
We study optimization for losses that admit a variance-mean scale-mixture representation. Under this representation, each EM iteration is a weighted least squares update in which latent variables determine observation and parameter weights;…
The scaled boundary finite element method (SBFEM) is a relatively recent boundary element method that allows the approximation of solutions to PDEs without the need of a fundamental solution. A theoretical framework for the convergence…
The Expectation-Maximization (EM) algorithm is one of the most popular methods used to solve the problem of parametric distribution-based clustering in unsupervised learning. In this paper, we propose to analyze a generalized EM (GEM)…
A reduced-rank mixed effects model is developed for robust modeling of sparsely observed paired functional data. In this model, the curves for each functional variable are summarized using a few functional principal components, and the…
Inference networks of traditional Variational Autoencoders (VAEs) are typically amortized, resulting in relatively inaccurate posterior approximation compared to instance-wise variational optimization. Recent semi-amortized approaches were…
The state-of-the art proof of a global inf-sup condition on mixed finite element schemes does not allow for an analysis of truly indefinite, second-order linear elliptic PDEs. This paper, therefore, first analyses a nonconforming finite…
Mixture of Experts (MoE) are successful models for modeling heterogeneous data in many statistical learning problems including regression, clustering and classification. Generally fitted by maximum likelihood estimation via the well-known…
Latent class model (LCM), which is a finite mixture of different categorical distributions, is one of the most widely used models in statistics and machine learning fields. Because of its non-continuous nature and the flexibility in shape,…
In this paper, we present a finite element method (FEM) framework enhanced by an operator-adapted wavelet decomposition algorithm designed for the efficient analysis of multiscale electromagnetic problems. Usual adaptive FEM approaches,…
We design an adaptive finite element method to approximate the solutions of quasi-linear elliptic problems. The algorithm is based on a Ka\v{c}anov iteration and a mesh adaptation step is performed after each linear solve. The method is…
Mixture-of-Experts (MoE) is a widely popular model for ensemble learning and is a basic building block of highly successful modern neural networks as well as a component in Gated Recurrent Units (GRU) and Attention networks. However,…