AntMAN: Anthology of Mixture ANalysis tools AntMan is an R package fitting Finite Bayesian Mixture models with a random number of components. The MCMC algorithm behind AntMAN is based on point processes and offers a more computationally efficient alternative to the Reversible Jump. Different mixture kernels can be specified: univariate Gaussian, multivariate Gaussian, univariate Poisson, and multivariate Bernoulli (Latent Class Analysis). For the parameters characterising the mixture kernel, we specify conjugate priors, with possibly user specified hyper-parameters. We allow for different choices on the prior on the number of components: Shifted Poisson, Negative Binomial, and Point Masses (i.e. mixtures with fixed number of components).
The main function of the AntMAN package is
AM_mcmc_fit. AntMAN performs a Gibbs sampling in order to fit,
in a Bayesian framework, a mixture model of a predefined type
mix_kernel_hyperparams given a sample
Additionally AntMAN allows the user to specify a prior on the number of components
mix_components_prior and on the weights
mix_weight_prior of the mixture.
mcmc_parameters need to be given as argument for the Gibbs sampler (number of interations, burn-in, ...).
Initial values for the number of clusters (
init_K) or a specific clustering allocation (
init_clustering) can also be user-specified.
Otherwise, by default, we initialise each element of the sample
y to a different cluster allocation. This choice can be computationally inefficient.
For example, in order to identify clusters over a population of patients given a set of medical assumptions:
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mcmc = AM_mcmc_parameters(niter=20000) mix = AM_mix_hyperparams_multiber () fit = AM_mcmc_fit (mix, mcmc) summary (fit)
In this example
AM_mix_hyperparams_multiber is one of the possible mixtures to use.
AntMAN currently support four different mixtures :
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Additionally, three types of kernels on the prior number of components are available:
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For example, in the context of image segmentation, if we know that there are 10 colours present, a prior dirac can be used :
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