binomial.bmm: binomial.bmm: Fits a binomial mixture using a variational...

In genome/bmm: Variational Bayesian approach to fitting mixtures of beta, binomial, or Gaussian distributions

binomial.bmm: Fits a binomial mixture using a variational Bayesian approach

Description

Use a variational Bayesian approach to fit a mixture of binomial distributions to count data, dropping any components/clusters that have small probability/mass.

NB: Clustering is first run to convergence using binomial.bmm.fixed.num.components. If any components have probability less than pi.threshold, they are discarded and the clustering is run to convergence again.

Usage

  binomial.bmm(successes, total.trials, N.c, r, a, b, alpha,
               a0, b0, alpha0, convergence.threshold = 10^-4, 
               max.iterations = 10000, verbose = 0, pi.threshold = 10^-2)

Arguments

successes	an N x D matrix with rows holding the number of successes in each dimension. All entries are assumed to be counts–not proportions.
total.trials	an N x D matrix with rows holding the number of trials in each dimension. All entries are assumed to be counts–not proportions.
N.c	the number of components/clusters to attempt
r	the N x N.c matrix of initial responsibilities, with r[n, nc] giving the probability that item n belongs to component nc
a
b
alpha	a D x N.c matrix holding the _initial_ values of the rate (i.e., inverse scale) parameters for the gamma prior distributions over the u parameters. i.e., mu[d,n] is the rate parameter governing u[d,n]. Introduced in eqn (15). NB: this is the initial value alpha, which is updated upon iteration. It is not (necessarily) the same as the hyperparameter alpha0, which is unchanged by iteration.
a0, b0, alpha0	the hyperparameters corresponding to the above initial values (and with the same respective matrix/vector dimensionality).
convergence.threshold	minimum absolute difference between mixing coefficient (expected) values across consecutive iterations to reach converge.
max.iterations	maximum number of iterations to attempt
verbose	output progress in terms of mixing coefficient (expected) values if 1
pi.threshold

Value

A list with the following entries:

retVal	0 indicates successful convergence; -1 indicates a failure to converge.
a
b
alpha	a D x N.c matrix holding the _converged final_ values of the rate (i.e., inverse scale) parameters for the gamma prior distributions over the u parameters. i.e., mu[d,n] is the rate parameter governing u[d,n]. Introduced in eqn (15).
r	the N x N.c matrix of responsibilities, with r[n, nc] giving the probability that item n belongs to component nc
num.iterations	the number of iterations required to reach convergence.
ln.rho	an N x N.c matrix holding the ln[rho], as defined in eqn (32).
E.lnpi	the D-vector holding the values E[ln pi], defined following eqn (51).
E.pi	the D-vector holding the values E[pi], i.e., the expected values of the mixing coefficients, defined in eqn (53).

genome/bmm documentation built on Aug. 4, 2022, 8:01 a.m.