init.bmm.parameters: init.bmm.parameters: Initialize bmm parameters

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

init.bmm.parameters: Initialize bmm parameters

Description

Initialize the bmm parameters (to be passed to bmm or bmm.fixed.num.components

Initialize parameters such that expected proportions have the values determined by an initial k-means clustering.

NB: This provides what should be a generally reasonable initialization of hyperparameters. However, better results may be obtained by tuning these in an application-specific manner.

Usage

   init.bmm.parameters(X, N.c, mu0, alpha0, nu0, beta0, c0, verbose=0)

Arguments

X	an N x D matrix with rows being the items to cluster. All entries are assumed to be proportions (i.e., between 0 and 1). Notice that there are no summation restrictions–i.e., proportions do not sum to unity across an item's dimensions.
N.c	the number of components/clusters to attempt
mu0	a D x N.c matrix holding the hyperparameter values of the shape parameters for the gamma prior distributions over the u parameters. i.e., mu[d,n] is the shape parameter governing u[d,n]. Introduced in eqn (15).
alpha0	a D x N.c matrix holding the hyperparameter 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).
nu0	a D x N.c matrix holding the hyperparameter values of the shape parameters for the gamma prior distributions over the v parameters. i.e., nu[d,n] is the shape parameter governing v[d,n]. Introduced in eqn (16).
beta0	a D x N.c matrix holding the hyperparameter values of the rate (i.e., inverse scale) parameters for the gamma prior distributions over the v parameters. i.e., beta[d,n] is the rate parameter governing v[d,n]. Introduced in eqn (16).
c0	a vector with D components holding the hyperparameter values of the parameters of the Dirichlet distribution over the mixing coefficients pi. Introduced in eqn (19).
verbose	output progress in terms of mixing coefficient (expected) values if 1.

Value

A list with the following entries:

mu	a D x N.c matrix holding the _initial_ values of the shape parameters for the gamma prior distributions over the u parameters. i.e., mu[d,n] is the shape parameter governing u[d,n]. NB: this is the initial value mu, which is updated upon iteration. It is not (necessarily) the same as the hyperparameter mu0, which is unchanged by iteration. Introduced in eqn (15).
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.
nu	a D x N.c matrix holding the _initial_ values of the shape parameters for the gamma prior distributions over the v parameters. i.e., nu[d,n] is the shape parameter governing v[d,n]. Introduced in eqn (16). NB: this is the initial value nu, which is updated upon iteration. It is not (necessarily) the same as the hyperparameter nu0, which is unchanged by iteration.
beta	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 v parameters. i.e., beta[d,n] is the rate parameter governing v[d,n]. Introduced in eqn (16). NB: this is the initial value beta, which is updated upon iteration. It is not (necessarily) the same as the hyperparameter beta0, which is unchanged by iteration.
c	a vector with D components holding the _initial_ values of the parameters of the Dirichlet distribution over the mixing coefficients pi. Introduced in eqn (19). NB: this is the initial value c, which is updated upon iteration. It is not (necessarily) the same as the hyperparameter c0, which is unchanged by iteration.
r	the N x N.c matrix of initial responsibilities, with r[n, nc] giving the probability that item n belongs to component nc
kmeans.clusters	an N-vector giving the assignment of each of the N items to a cluster, as determined by kmeans.
kmeans.centers	an N.c x D matrix holding the centers of the N.c clusters/components determined by kmeans

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