2,012 research outputs found
mixtools: An R Package for Analyzing Mixture Models
The mixtools package for R provides a set of functions for analyzing a variety of finite mixture models. These functions include both traditional methods, such as EM algorithms for univariate and multivariate normal mixtures, and newer methods that reflect some recent research in finite mixture models. In the latter category, mixtools provides algorithms for estimating parameters in a wide range of different mixture-of-regression contexts, in multinomial mixtures such as those arising from discretizing continuous multivariate data, in nonparametric situations where the multivariate component densities are completely unspecified, and in semiparametric situations such as a univariate location mixture of symmetric but otherwise unspecified densities. Many of the algorithms of the mixtools package are EM algorithms or are based on EM-like ideas, so this article includes an overview of EM algorithms for finite mixture models.
On nonparametric estimation of a mixing density via the predictive recursion algorithm
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
algorithm. After introducing the algorithm and giving a few examples, I
summarize the available asymptotic convergence theory, describe an important
semiparametric extension, and highlight two interesting applications. I
conclude with a discussion of several recent developments in this area and some
open problems.Comment: 22 pages, 5 figures. Comments welcome at
https://www.researchers.one/article/2018-12-
A semiparametric extension of the stochastic block model for longitudinal networks
To model recurrent interaction events in continuous time, an extension of the
stochastic block model is proposed where every individual belongs to a latent
group and interactions between two individuals follow a conditional
inhomogeneous Poisson process with intensity driven by the individuals' latent
groups. The model is shown to be identifiable and its estimation is based on a
semiparametric variational expectation-maximization algorithm. Two versions of
the method are developed, using either a nonparametric histogram approach (with
an adaptive choice of the partition size) or kernel intensity estimators. The
number of latent groups can be selected by an integrated classification
likelihood criterion. Finally, we demonstrate the performance of our procedure
on synthetic experiments, analyse two datasets to illustrate the utility of our
approach and comment on competing methods
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