Related papers: Tackling the infinite likelihood problem when fitt…
A mixture of shifted asymmetric Laplace distributions is introduced and used for clustering and classification. A variant of the EM algorithm is developed for parameter estimation by exploiting the relationship with the general inverse…
Mixtures of multivariate contaminated shifted asymmetric Laplace distributions are developed for handling asymmetric clusters in the presence of outliers (also referred to as bad points herein). In addition to the parameters of the related…
A family of parsimonious shifted asymmetric Laplace mixture models is introduced. We extend the mixture of factor analyzers model to the shifted asymmetric Laplace distribution. Imposing constraints on the constitute parts of the resulting…
In this paper we introduce five different algorithms based on method of moments, maximum likelihood and full Bayesian estimation for learning the parameters of the Inverse Gamma distribution. We also provide an expression for the KL…
Mixture models whose components have skewed hypercube contours are developed via a generalization of the multivariate shifted asymmetric Laplace density. Specifically, we develop mixtures of multiple scaled shifted asymmetric Laplace…
In this paper, we propose finite mixtures of multivariate skew Laplace distributions to model both skewness and heavy-tailedness in the heterogeneous data sets. The maximum likelihood estimators for the parameters of interest are obtained…
In this study, we address the problem of clustering string data in an unsupervised manner by developing a theory of a mixture model and an EM algorithm for string data based on probability theory on a topological monoid of strings developed…
Popular deterministic approximations of posterior distributions from, e.g. the Laplace method, variational Bayes and expectation-propagation, generally rely on symmetric approximating families, often taken to be Gaussian. This choice…
This paper considers an extension of the multivariate symmetric Laplace distribution to matrix variate case. The symmetric Laplace distribution is a scale mixture of normal distribution. The maximum likelihood estimators (MLE) of the…
In this paper we introduce two Bayesian estimators for learning the parameters of the Gamma distribution. The first algorithm uses a well known unnormalized conjugate prior for the Gamma shape and the second one uses a non-linear…
In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a…
Probabilistic mixture models have been widely used for different machine learning and pattern recognition tasks such as clustering, dimensionality reduction, and classification. In this paper, we focus on trying to solve the most common…
Using observation data to estimate unknown parameters in computational models is broadly important. This task is often challenging because solutions are non-unique due to the complexity of the model and limited observation data. However,…
This paper introduces constrained mixtures for continuous distributions, characterized by a mixture of distributions where each distribution has a shape similar to the base distribution and disjoint domains. This new concept is used to…
A novel data-driven methodology is presented for the joint selection of prior parameters for both fixed and random effects in Linear Mixed Models (LMMs). This approach facilitates the estimation of complex random-effects structures, as well…
The Laplace approximation is sometimes not sufficiently accurate for smoothing parameter estimation in generalized additive mixed models. A novel estimation strategy is proposed that solves this problem and leads to estimates exhibiting the…
Skew normal mixture models provide a more flexible framework than the popular normal mixtures for modelling heterogeneous data with asymmetric behaviors. Due to the unboundedness of likelihood function and the divergency of shape…
A method for sequential inference of the fixed parameters of a dynamic latent Gaussian models is proposed and evaluated that is based on the iterated Laplace approximation. The method provides a useful trade-off between computational…
This paper tackles the challenge of parameter calibration in stochastic models, particularly in scenarios where the likelihood function is unavailable in an analytical form. We introduce a gradient-based simulated parameter estimation…
The systematic collection of longitudinal data is very common in practice, making mixed models widely used. Most developments around these models focus on modeling the mean trajectory of repeated measurements, typically under the assumption…