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Relabel partitions by decreasing \(\lambda\), compute point estimates, and quantify uncertainty via credible balls

Source: R/utils.R
relabel_by_lambda.Rd

Given posterior samples of labels x_samples (S x N) and corresponding cluster-level intensities lambda_samples per iteration, this function: (i) relabels each draw so that cluster 1 has the largest \(\lambda\), cluster 2 the second largest, etc.; (ii) computes posterior similarity matrix (PSM) and partition point estimates (minVI and Binder); and (iii) constructs a VI-credible ball around the minVI partition and returns the extremal partitions on its surface (lower/upper), relabelled by decreasing strength for interpretability. It also returns per-item assignment probabilities and the posterior distribution of the number of clusters.

Usage

relabel_by_lambda(x_samples, lambda_samples)

Arguments

x_samples

Integer matrix (S x N) of sampled partitions; rows index MCMC iterations and columns index items. Cluster labels are arbitrary across iterations.

lambda_samples

Either:

  • a list of length S; element [[s]] is a numeric vector of cluster intensities \(\lambda_\ell\) indexed by the raw label id used at iteration s (NAs allowed for non-occupied ids), or

  • a matrix (S x L) whose row s gives \(\lambda_\ell\) for label \(\ell\) at iteration s (sparse columns with NAs permitted).

Value

A named list with components:

x_samples_relabel

Integer matrix (S x N) of relabelled draws (labels 1..K_s per iteration s, ordered by decreasing \(\lambda\)).

lambda_samples_relabel

Numeric matrix (S x N) assigning each item its cluster's \(\lambda\) after relabelling.

co_clustering

Posterior similarity matrix (N x N).

minVI_partition

Partition estimated by minimizing posterior expected VI using salso.

partition_binder

Partition estimated by Binder's loss using salso.

n_clusters_each_iter

Integer vector (length S) of occupied cluster counts per iteration.

block_count_distribution

Data frame with columns num_blocks, count, prob summarizing the posterior of the number of clusters.

item_cluster_assignment_probs

Data frame (N x Kmax) of per-item marginal assignment probabilities (columns Cluster_1, Cluster_2, ...).

avg_top_block_count

Average size of the top-\(\lambda\) cluster across iterations.

top_block_count_per_iter

Integer vector (length S) with the size of the top-\(\lambda\) cluster per iteration.

top_block_size_distribution

Data frame with columns top_block_size, count, prob summarizing the posterior distribution of the strongest block size.

cluster_lambda_ordered

List of length S; each element is the vector of cluster \(\lambda\) values for that iteration, ordered decreasingly.

Details

Relabelling. For each iteration, occupied labels are compacted to 1..K_s and reordered by decreasing \(\lambda\), producing a canonical “1 = strongest” labelling.

Point estimation. The posterior similarity matrix is computed from relabelled draws; the minVI and Binder partitions are estimated with salso using the generalized variation of information and Binder losses.

Input requirements

  • x_samples must be integer-valued with no missing items per row.

  • lambda_samples may be sparse (NAs for non-occupied labels).

  • salso must be available for the point-estimate summaries.

References

Wade, S., 2023. Bayesian cluster analysis. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 381, 20220149. https://doi.org/10.1098/rsta.2022.0149

See also

salso, VI, binder, comp.psm

Examples

if (FALSE) { # \dontrun{
set.seed(42)
S <- 50; N <- 15
x_samps <- matrix(sample(1:4, S*N, TRUE), S, N)
# Sparse lambda per-iter: labels up to 6, only first 4 occupied typically
lam_list <- replicate(S, { v <- rep(NA_real_, 6); v[1:4] <- rexp(4, 1); v }, simplify = FALSE)
out <- relabel_by_lambda(x_samps, lam_list)
out$minVI_partition[1:10]
out$K_VI_lower; out$K_VI_upper
} # }