batchSemiSupervisedMixtureModel {batchmix}

Batch semisupervised mixture model

Description

A Bayesian mixture model with batch effects.

Usage

batchSemiSupervisedMixtureModel(
  X,
  R,
  thin,
  initial_labels,
  fixed,
  batch_vec,
  type,
  K_max = length(unique(initial_labels)),
  alpha = NULL,
  concentration = NULL,
  mu_proposal_window = 0.5^2,
  cov_proposal_window = 0.002,
  m_proposal_window = 0.3^2,
  S_proposal_window = 0.01,
  t_df_proposal_window = 0.015,
  m_scale = NULL,
  rho = 3,
  theta = 1,
  initial_class_means = NULL,
  initial_class_covariance = NULL,
  initial_batch_shift = NULL,
  initial_batch_scale = NULL,
  initial_class_df = NULL,
  verbose = TRUE
)

Arguments

X

Data to cluster as a matrix with the items to cluster held in rows.

R

The number of iterations in the sampler.

thin

The factor by which the samples generated are thinned, e.g. if “thin=50“ only every 50th sample is kept.

initial_labels

Initial clustering.

fixed

Which items are fixed in their initial label.

batch_vec

Labels identifying which batch each item being clustered is from.

type

Character indicating density type to use. One of 'MVN' (multivariate normal distribution) or 'MVT' (multivariate t distribution).

K_max

The number of components to include (the upper bound on the number of clusters in each sample). Defaults to the number of unique labels in “initial_labels“.

alpha

The concentration parameter for the stick-breaking prior and the weights in the model.

concentration

Initial concentration vector for component weights.

mu_proposal_window

The proposal window for the cluster mean proposal kernel. The proposal density is a Gaussian distribution, the window is the variance.

cov_proposal_window

The proposal window for the cluster covariance proposal kernel. The proposal density is a Wishart distribution, this argument is the reciprocal of the degree of freedom.

m_proposal_window

The proposal window for the batch mean proposal kernel. The proposal density is a Gaussian distribution, the window is the variance.

S_proposal_window

The proposal window for the batch standard deviation proposal kernel. The proposal density is a Gamma distribution, this argument is the reciprocal of the rate.

t_df_proposal_window

The proposal window for the degrees of freedom for the multivariate t distribution (not used if type is not 'MVT'). The proposal density is a Gamma distribution, this argument is the reciprocal of the rate.

m_scale

The scale hyperparameter for the batch shift prior distribution. This defines the scale of the batch effect upon the mean and should be in (0, 1].

rho

The shape of the prior distribution for the batch scale.

theta

The scale of the prior distribution for the batch scale.

initial_class_means

A $P x K$ matrix of initial values for the class means. Defaults to draws from the prior distribution.

initial_class_covariance

A $P x P x K$ array of initial values for the class covariance matrices. Defaults to draws from the prior distribution.

initial_batch_shift

A $P x B$ matrix of initial values for the batch shift effect Defaults to draws from the prior distribution.

initial_batch_scale

A $P x B$ matrix of initial values for the batch scales Defaults to draws from the prior distribution.

initial_class_df

A $K$ vector of initial values for the class degrees of freedom. Defaults to draws from the prior distribution.

verbose

Logiccal indicating if warning about proposal windows should be printed.

Value

A named list containing the sampled partitions, cluster and batch parameters, model fit measures and some details on the model call.

Examples

# Data in a matrix format
X <- matrix(c(rnorm(100, 0, 1), rnorm(100, 3, 1)), ncol = 2, byrow = TRUE)

# Initial labelling
labels <- c(
  rep(1, 10),
  sample(c(1, 2), size = 40, replace = TRUE),
  rep(2, 10),
  sample(c(1, 2), size = 40, replace = TRUE)
)

fixed <- c(rep(1, 10), rep(0, 40), rep(1, 10), rep(0, 40))

# Batch
batch_vec <- sample(seq(1, 5), replace = TRUE, size = 100)

# Density choice
type <- "MVN"

# Sampling parameters
R <- 1000
thin <- 50

# MCMC samples and BIC vector
samples <- batchSemiSupervisedMixtureModel(
  X,
  R,
  thin,
  labels,
  fixed,
  batch_vec,
  type
)

# Given an initial value for the parameters
initial_class_means <- matrix(c(1, 1, 3, 4), nrow = 2)
initial_class_covariance <- array(c(1, 0, 0, 1, 1, 0, 0, 1),
  dim = c(2, 2, 2)
)

# We can use values from a previous chain
initial_batch_shift <- samples$batch_shift[, , R / thin]
initial_batch_scale <- matrix(
  c(1.2, 1.3, 1.7, 1.1, 1.4, 1.3, 1.2, 1.2, 1.1, 2.0),
  nrow = 2
)

samples <- batchSemiSupervisedMixtureModel(X,
  R,
  thin,
  labels,
  fixed,
  batch_vec,
  type,
  initial_class_means = initial_class_means,
  initial_class_covariance = initial_class_covariance,
  initial_batch_shift = initial_batch_shift,
  initial_batch_scale = initial_batch_scale
)