Benchmark bivariate Gaussian convolutions

Wrapper reproducing the bivariate (\(G=2\), \(J=2\)) toy study of the article: for each scenario it builds \(\boldsymbol{\mu}\) and \((\boldsymbol{\Sigma}_j)_{j}\), simulates \(\boldsymbol{Y}\) via simulate_bulk_mixture(), and deconvolves with the supplied algorithms. Performance is summarised against entropy of \(\boldsymbol{p}\) and overlap of the Gaussian mixture.

Usage

benchmark_bivariate_gaussian_convolutions(
  proportions = list(balanced = c(0.5, 0.5), `small unbalanced` = c(0.6, 0.4),
    `highly unbalanced` = c(0.05, 0.95)),
  signature_matrices = list(`small OVL` = matrix(c(20, 40, 40, 20), nrow = 2)),
  corr_sequence = seq(-0.8, 0.8, 0.2),
  diagonal_terms = list(homoscedastic = c(1, 1), heteroscedastic = c(1, 2)),
  deconvolution_functions = list(lsfit = list(FUN = deconvolute_ratios_lsfit,
    additional_parameters = NULL)),
  n = 200,
  scaled = FALSE,
  cores = ifelse(.Platform$OS.type == "unix", getOption("mc.cores",
    parallel::detectCores()), 1)
)

Arguments

proportions

List of simplex vectors \(\boldsymbol{p}\).

signature_matrices

List of mean matrices \(\boldsymbol{\mu}\in\mathcal{M}_{2\times 2}^{+}\).

corr_sequence, diagonal_terms

Correlation sequence and diagonal variance templates used to assemble \(\boldsymbol{\Sigma}_j= \mathrm{D}_{j}^{1/2}\mathbf{R}_j\mathrm{D}_{j}^{1/2}\).

deconvolution_functions

Named list of deconvolution callables (each with FUN and optional additional_parameters).

n

Number of bulk replicates \(N\) per scenario.

scaled

Logical; whether to log-scale inputs before estimation.

cores

Parallel workers for deconvolute_ratios().

Value

A list with config (design + entropy/overlap) and simulations (estimation tibble).

Details

Designed for two cell types and two genes. Larger \((G,J)\) with only bivariate observations is prone to non-identifiability.

Scenarios are enumerated with tidyr::expand_grid() and tagged with a unique ID via dplyr::row_number(), so no side-effect mutation is needed while looping over the design.

See also

simulate_bulk_mixture(), deconvolute_ratios()

Examples

set.seed(1)
out <- benchmark_bivariate_gaussian_convolutions(
  proportions = list("balanced" = c(0.5, 0.5)),
  signature_matrices = list("small" = matrix(c(20, 22, 22, 20), 2)),
  corr_sequence = 0,
  diagonal_terms = list("homoscedastic" = c(1, 1)),
  deconvolution_functions = list(
    "nnls" = list(FUN = deconvolute_ratios_nnls)
  ),
  n = 2,
  cores = 1
)
#> Scenario B1_Ho: balanced, corr=(0, 0), centroids=small, variance=homoscedastic.
nrow(out$simulations)
#> [1] 2