Related papers: A Component-wise EM Algorithm for Mixtures
We show how the expectation-maximization (EM) algorithm can be applied exactly for the fitting of mixtures of general multivariate skew t (MST) distributions, eliminating the need for computationally expensive Monte Carlo estimation. Finite…
This paper is concerned with learning of mixture regression models for individuals that are measured repeatedly. The adjective "unsupervised" implies that the number of mixing components is unknown and has to be determined, ideally by data…
Estimation of the number of components (or order) of a finite mixture model is a long standing and challenging problem in statistics. We propose the Group-Sort-Fuse (GSF) procedure -- a new penalized likelihood approach for simultaneous…
We study the gradient Expectation-Maximization (EM) algorithm for Gaussian Mixture Models (GMM) in the over-parameterized setting, where a general GMM with $n>1$ components learns from data that are generated by a single ground truth…
An important and yet difficult problem in fitting multivariate mixture models is determining the mixture complexity. We develop theory and a unified framework for finding the nonparametric maximum likelihood estimator of a multivariate…
A general framework for solving image inverse problems is introduced in this paper. The approach is based on Gaussian mixture models, estimated via a computationally efficient MAP-EM algorithm. A dual mathematical interpretation of the…
Estimating the model evidence - or mariginal likelihood of the data - is a notoriously difficult task for finite and infinite mixture models and we reexamine here different Monte Carlo techniques advocated in the recent literature, as well…
Zhu and Melnykov (2018) develop a model to fit mixture models when the components are derived from the Manly transformation. Their EM algorithm utilizes Nelder-Mead optimization in the M-step to update the skew parameter,…
Estimating probabilistic deformable template models is a new approach in the fields of computer vision and probabilistic atlases in computational anatomy. A first coherent statistical framework modelling the variability as a hidden random…
This EM review article focuses on parameter expansion, a simple technique introduced in the PX-EM algorithm to make EM converge faster while maintaining its simplicity and stability. The primary objective concerns the connection between…
Mixture models serve as one fundamental tool with versatile applications. However, their training techniques, like the popular Expectation Maximization (EM) algorithm, are notoriously sensitive to parameter initialization and often suffer…
Nonparametric estimation of a mixing density based on observations from the corresponding mixture is a challenging statistical problem. This paper surveys the literature on a fast, recursive estimator based on the predictive recursion…
The convergence and optimality of adaptive mixed finite element methods for the Poisson equation are established in this paper. The main difficulty for mixed finite element methods is the lack of minimization principle and thus the failure…
The expectation-maximization (EM) algorithm is an iterative method for finding maximum likelihood estimates when data are incomplete or are treated as being incomplete. The EM algorithm and its variants are commonly used for parameter…
This work introduces a new method for selecting the number of components in finite mixture models (FMMs) using variational Bayes, inspired by the large-sample properties of the Evidence Lower Bound (ELBO) derived from mean-field (MF)…
ProbLog is a state-of-art combination of logic programming and probabilities; in particular ProbLog offers parameter learning through a variant of the EM algorithm. However, the resulting learning algorithm is rather slow, even when the…
In this paper, we propose a new approach -- the Tempered Finite Element Method (TFEM) -- that extends the Finite Element Method (FEM) to classes of meshes that include zero-measure or nearly degenerate elements for which standard FEM…
Predictive recursion is an accurate and computationally efficient algorithm for nonparametric estimation of mixing densities in mixture models. In semiparametric mixture models, however, the algorithm fails to account for any uncertainty in…
Modern data-driven and distributed learning frameworks deal with diverse massive data generated by clients spread across heterogeneous environments. Indeed, data heterogeneity is a major bottleneck in scaling up many distributed learning…
Many practitioners who use the EM algorithm complain that it is sometimes slow. When does this happen, and what can be done about it? In this paper, we study the general class of bound optimization algorithms - including…