Related papers: Evidential-EM Algorithm Applied to Progressively C…

The Expectation--Maximization Maximum Likelihood (EMML) algorithm belongs to the Expectation--Maximization family and is widely used for image reconstruction problems under Poisson noise.In this paper, we reinterpret EMML as a mirror…

We provide a general theory of the expectation-maximization (EM) algorithm for inferring high dimensional latent variable models. In particular, we make two contributions: (i) For parameter estimation, we propose a novel high dimensional EM…

Deep directed generative models have attracted much attention recently due to their expressive representation power and the ability of ancestral sampling. One major difficulty of learning directed models with many latent variables is the…

The Expectation-Maximization (EM) algorithm is routinely used for the maximum likelihood estimation in the latent class analysis. However, the EM algorithm comes with no guarantees of reaching the global optimum. We study the geometry of…

Model error covariances play a central role in the performance of data assimilation methods applied to nonlinear state-space models. However, these covariances are largely unknown in most of the applications. A misspecification of the model…

Robust quantification of predictive uncertainty is critical for understanding factors that drive weather and climate outcomes. Ensembles provide predictive uncertainty estimates and can be decomposed physically, but both physics and machine…

This article explores the estimation of unknown parameters and reliability characteristics under the assumption that the lifetimes of the testing units follow an Inverted Exponentiated Pareto (IEP) distribution. Here, both point and…

Evidential Deep Learning (EDL) has emerged as an efficient, sampling-free strategy for uncertainty estimation. A series of EDL variants have been proposed to address specific limitations of the original framework, achieving notable success.…

Popular approaches for quantifying predictive uncertainty in deep neural networks often involve distributions over weights or multiple models, for instance via Markov Chain sampling, ensembling, or Monte Carlo dropout. These techniques…

Estimators derived from a divergence criterion such as $\varphi-$divergences are generally more robust than the maximum likelihood ones. We are interested in particular in the so-called MD$\varphi$DE, an estimator built using a dual…

In this article, we consider the estimation of unknown parameters of Weibull distribution when the lifetime data are observed in the presence of progressively type-I hybrid censoring scheme. The Newton-Raphson algorithm,…

We investigate the convergence properties of the EM algorithm when applied to overspecified Gaussian mixture models -- that is, when the number of components in the fitted model exceeds that of the true underlying distribution. Focusing on…

Nowadays, the confidentiality of data and information is of great importance for many companies and organizations. For this reason, they may prefer not to release exact data, but instead to grant researchers access to approximate data. For…

We propose a method called EDML for learning MAP parameters in binary Bayesian networks under incomplete data. The method assumes Beta priors and can be used to learn maximum likelihood parameters when the priors are uninformative. EDML…

Evidential deep learning (EDL) has shown remarkable success in uncertainty estimation. However, there is still room for improvement, particularly in out-of-distribution (OOD) detection and classification tasks. The limited OOD detection…

Improved EM strategies, based on the idea of efficient data augmentation (Meng and van Dyk 1997, 1998), are presented for ML estimation of mixture proportions. The resulting algorithms inherit the simplicity, ease of implementation, and…

Mixture models of Plackett-Luce (PL) -- one of the most fundamental ranking models -- are an active research area of both theoretical and practical significance. Most previously proposed parameter estimation algorithms instantiate the EM…

We present a computational motivation for restricted maximum likelihood (REML) estimation in linear mixed models using an expectation--maximization (EM) algorithm. At each iteration, maximum likelihood (ML) and REML solve the same…

This note aims to demonstrate that performing maximum-likelihood estimation for a mixture model is equivalent to minimizing over the parameters an optimal transport problem with entropic regularization. The objective is pedagogical: we seek…

Modelling highly multi-modal data is a challenging problem in machine learning. Most algorithms are based on maximizing the likelihood, which corresponds to the M(oment)-projection of the data distribution to the model distribution. The…