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Bayesian graphical models are a useful tool for understanding dependence relationships among many variables, particularly in situations with external prior information. In high-dimensional settings, the space of possible graphs becomes…
The Expectation-Maximization (EM) algorithm is a fundamental tool in unsupervised machine learning. It is often used as an efficient way to solve Maximum Likelihood (ML) estimation problems, especially for models with latent variables. It…
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 a versatile tool for model parameter estimation in latent data models. When processing large data sets or data stream however, EM becomes intractable since it requires the whole data set to be…
Binary regression models represent a popular model-based approach for binary classification. In the Bayesian framework, computational challenges in the form of the posterior distribution motivate still-ongoing fruitful research. Here, we…
Expectation-Maximization (EM) algorithm is a widely used iterative algorithm for computing maximum likelihood estimate when dealing with Gaussian Mixture Model (GMM). When the sample size is smaller than the data dimension, this could lead…
The multinomial probit model is a popular tool for analyzing choice behaviour as it allows for correlation between choice alternatives. Because current model specifications employ a full covariance matrix of the latent utilities for the…
Online (also called "recursive" or "adaptive") estimation of fixed model parameters in hidden Markov models is a topic of much interest in times series modelling. In this work, we propose an online parameter estimation algorithm that…
Multivariate probit models (MPM) have the appealing feature of capturing some of the dependence structure between the components of multidimensional binary responses. The key for the dependence modelling is the covariance matrix of an…
Bayesian binary regression is a prosperous area of research due to the computational challenges encountered by currently available methods either for high-dimensional settings or large datasets, or both. In the present work, we focus on the…
Ordinal categorical data are routinely encountered in many practical applications. When the primary goal is to construct a regression model for ordinal outcomes, cumulative link models represent one of the most popular choices to link the…
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…
We study a class of weakly identifiable location-scale mixture models for which the maximum likelihood estimates based on $n$ i.i.d. samples are known to have lower accuracy than the classical $n^{- \frac{1}{2}}$ error. We investigate…
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…
The smoothing distribution of dynamic probit models with Gaussian state dynamics was recently proved to belong to the unified skew-normal family. Although this is computationally tractable in small-to-moderate settings, it may become…
The Expectation Maximisation (EM) algorithm is widely used to optimise non-convex likelihood functions with latent variables. Many authors modified its simple design to fit more specific situations. For instance, the Expectation (E) step…
The family of Expectation-Maximization (EM) algorithms provides a general approach to fitting flexible models for large and complex data. The expectation (E) step of EM-type algorithms is time-consuming in massive data applications because…
We study the expectation-maximization (EM) algorithm for general latent-variable models under (i) distributional misspecification and (ii) nonidentifiability induced by a group action. We formulate EM on the quotient parameter space and…
Mixed Probit models are widely applied in many fields where prediction of a binary response is of interest. Typically, the random effects are assumed to be independent but this is seldom the case for many real applications. In the credit…
In this contribution, we propose a generic online (also sometimes called adaptive or recursive) version of the Expectation-Maximisation (EM) algorithm applicable to latent variable models of independent observations. Compared to the…