Related papers: The EM Algorithm in Genetics, Genomics and Public …
Bayesian networks (BN) are used in a big range of applications but they have one issue concerning parameter learning. In real application, training data are always incomplete or some nodes are hidden. To deal with this problem many learning…
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…
Random graphs, where the connections between nodes are considered random variables, have wide applicability in the social sciences. Exponential-family Random Graph Models (ERGM) have shown themselves to be a useful class of models for…
We develop a general framework for proving rigorous guarantees on the performance of the EM algorithm and a variant known as gradient EM. Our analysis is divided into two parts: a treatment of these algorithms at the population level (in…
We propose a general formulation of a univariate estimation-of-distribution algorithm (EDA). It naturally incorporates the three classic univariate EDAs \emph{compact genetic algorithm}, \emph{univariate marginal distribution algorithm} and…
The Expectation-Maximization (EM) algorithm is a widely used method for maximum likelihood estimation in models with latent variables. For estimating mixtures of Gaussians, its iteration can be viewed as a soft version of the k-means…
Nan McKenzie Laird is the Harvey V. Fineberg Professor of Biostatistics at the Harvard T. H. Chan School of Public Health. She has made fundamental contributions to statistical methods for longitudinal data analysis, missing data and…
Maximum likelihood estimators are proposed for the parameters and the densities in a semiparametric density ratio model in which the nonparametric baseline density is approximated by the Bernstein polynomial model. The EM algorithm is used…
Expectation maximisation (EM) is an unsupervised learning method for estimating the parameters of a finite mixture distribution. It works by introducing "hidden" or "latent" variables via Baum's auxiliary function $Q$ that allow the joint…
Many optimization problems in engineering and industrial design applications can be formulated as optimization problems with highly nonlinear objectives, subject to multiple complex constraints. Solving such optimization problems requires…
In an earlier work, the statistical physics associated with finite--temperature decoding of code ensembles, along with the relation to their random coding error exponents, were explored in a framework that is analogous to Derrida's random…
Gaussian mixture models (GMMs) are fundamental statistical tools for modeling heterogeneous data. Due to the nonconcavity of the likelihood function, the Expectation-Maximization (EM) algorithm is widely used for parameter estimation of…
Recently Asimit et. al used an EM algorithm to estimate Marshall-Olkin bivariate Pareto distribution. The distribution has seven parameters. We describe few alternative approaches of EM algorithm. A numerical simulation is performed to…
General Effect Modelling (GEM) is an umbrella over different methods that utilise effects in the analyses of data with multiple design variables and multivariate responses. To demonstrate the methodology, we here use GEM in gene expression…
Finite mixture models are among the most popular statistical models used in different data science disciplines. Despite their broad applicability, inference under these models typically leads to computationally challenging non-convex…
The Mixture Transition Distribution (MTD) model was introduced by Raftery to face the need for parsimony in the modeling of high-order Markov chains in discrete time. The particularity of this model comes from the fact that the effect of…
Recently, a general method for analyzing the statistical accuracy of the EM algorithm has been developed and applied to some simple latent variable models [Balakrishnan et al. 2016]. In that method, the basin of attraction for valid…
They run our lives, if you believe the hype in the news, but there is no precise definition of "algorithms" which is generally accepted by the mathematicians, logicians and computer scientists who create and study them. My main aims here…
We present a quantum version of the classical probabilistic algorithms $\grave{a}$ la Rabin. The quantum algorithm is based on the essential use of Grover's operator for the quantum search of a database and of Shor's Fourier transform for…
Cryptography and data science research grew exponential with the internet boom. Legacy encryption techniques force users to make a trade-off between usability, convenience, and security. Encryption makes valuable data inaccessible, as it…