Compute Mixtures of Mallows Models

Convenience function for computing Mallows models with varying numbers of mixtures. This is useful for deciding the number of mixtures to use in the final model.

Usage

compute_mallows_mixtures(
  n_clusters,
  data,
  model_options = set_model_options(),
  compute_options = set_compute_options(),
  priors = set_priors(),
  initial_values = set_initial_values(),
  pfun_estimate = NULL,
  progress_report = set_progress_report(),
  cl = NULL
)

Arguments

n_clusters: Integer vector specifying the number of clusters to use.
data: An object of class "BayesMallowsData" returned from setup_rank_data().
model_options: An object of class "BayesMallowsModelOptions" returned from set_model_options().
compute_options: An object of class "BayesMallowsComputeOptions" returned from set_compute_options().
priors: An object of class "BayesMallowsPriors" returned from set_priors().
initial_values: An object of class "BayesMallowsInitialValues" returned from set_initial_values().
pfun_estimate: Object returned from estimate_partition_function(). Defaults to NULL, and will only be used for footrule, Spearman, or Ulam distances when the cardinalities are not available, cf. get_cardinalities().
progress_report: An object of class "BayesMallowsProgressReported" returned from set_progress_report().
cl: Optional cluster returned from parallel::makeCluster(). If provided, chains will be run in parallel, one on each node of cl.

Value

A list of Mallows models of class BayesMallowsMixtures, with one element for each number of mixtures that was computed. This object can be studied with plot_elbow().

Details

The n_clusters argument to set_model_options() is ignored when calling compute_mallows_mixtures.

Examples

# SIMULATED CLUSTER DATA
set.seed(1)
n_clusters <- seq(from = 1, to = 5)
models <- compute_mallows_mixtures(
  n_clusters = n_clusters, data = setup_rank_data(cluster_data),
  compute_options = set_compute_options(nmc = 2000, include_wcd = TRUE))

# There is good convergence for 1, 2, and 3 cluster, but not for 5.
# Also note that there seems to be label switching around the 7000th iteration
# for the 2-cluster solution.
assess_convergence(models)

# We can create an elbow plot, suggesting that there are three clusters, exactly
# as simulated.
burnin(models) <- 1000
plot_elbow(models)


# We now fit a model with three clusters
mixture_model <- compute_mallows(
  data = setup_rank_data(cluster_data),
  model_options = set_model_options(n_clusters = 3),
  compute_options = set_compute_options(nmc = 2000))

# The trace plot for this model looks good. It seems to converge quickly.
assess_convergence(mixture_model)

# We set the burnin to 500
burnin(mixture_model) <- 500

# We can now look at posterior quantities
# Posterior of scale parameter alpha
plot(mixture_model)

plot(mixture_model, parameter = "rho", items = 4:5)

# There is around 33 % probability of being in each cluster, in agreemeent
# with the data simulating mechanism
plot(mixture_model, parameter = "cluster_probs")

# We can also look at a cluster assignment plot
plot(mixture_model, parameter = "cluster_assignment")


# DETERMINING THE NUMBER OF CLUSTERS IN THE SUSHI EXAMPLE DATA
if (FALSE) {
  # Let us look at any number of clusters from 1 to 10
  # We use the convenience function compute_mallows_mixtures
  n_clusters <- seq(from = 1, to = 10)
  models <- compute_mallows_mixtures(
    n_clusters = n_clusters, data = setup_rank_data(sushi_rankings),
    compute_options = set_compute_options(include_wcd = TRUE))
  # models is a list in which each element is an object of class BayesMallows,
  # returned from compute_mallows
  # We can create an elbow plot
  burnin(models) <- 1000
  plot_elbow(models)
  # We then select the number of cluster at a point where this plot has
  # an "elbow", e.g., n_clusters = 5.

  # Having chosen the number of clusters, we can now study the final model
  # Rerun with 5 clusters
  mixture_model <- compute_mallows(
    rankings = sushi_rankings,
    model_options = set_model_options(n_clusters = 5),
    compute_options = set_compute_options(include_wcd = TRUE))
  # Delete the models object to free some memory
  rm(models)
  # Set the burnin
  burnin(mixture_model) <- 1000
  # Plot the posterior distributions of alpha per cluster
  plot(mixture_model)
  # Compute the posterior interval of alpha per cluster
  compute_posterior_intervals(mixture_model, parameter = "alpha")
  # Plot the posterior distributions of cluster probabilities
  plot(mixture_model, parameter = "cluster_probs")
  # Plot the posterior probability of cluster assignment
  plot(mixture_model, parameter = "cluster_assignment")
  # Plot the posterior distribution of "tuna roll" in each cluster
  plot(mixture_model, parameter = "rho", items = "tuna roll")
  # Compute the cluster-wise CP consensus, and show one column per cluster
  cp <- compute_consensus(mixture_model, type = "CP")
  cp$cumprob <- NULL
  stats::reshape(cp, direction = "wide", idvar = "ranking",
                 timevar = "cluster", varying = list(as.character(unique(cp$cluster))))

  # Compute the MAP consensus, and show one column per cluster
  map <- compute_consensus(mixture_model, type = "MAP")
  map$probability <- NULL
  stats::reshape(map, direction = "wide", idvar = "map_ranking",
                 timevar = "cluster", varying = list(as.character(unique(map$cluster))))

  # RUNNING IN PARALLEL
  # Computing Mallows models with different number of mixtures in parallel leads to
  # considerably speedup
  library(parallel)
  cl <- makeCluster(detectCores() - 1)
  n_clusters <- seq(from = 1, to = 10)
  models <- compute_mallows_mixtures(
    n_clusters = n_clusters,
    rankings = sushi_rankings,
    compute_options = set_compute_options(include_wcd = TRUE),
    cl = cl)
  stopCluster(cl)
}

Usage

Arguments

Value

Details

See also

Examples