Open-simplex start for ILR solvers

The convolution log-likelihood is not globally concave, so the start can change which basin the solver enters. Draw several independent Dirichlet starts (different RNG streams or multistart_decovart()) rather than a single draw when probing multimodality.

Usage

starting_simplex(
  n_celltypes,
  initial_p = NULL,
  nms = NULL,
  y = NULL,
  mean_signature_matrix = NULL,
  dirichlet_alpha = 1
)

Arguments

n_celltypes

Integer \(J\).

initial_p

One of:

• NULL or "barycentre": equi-balanced \((1/J,\ldots,1/J)\);

• a numeric vector of length \(J\): used as-is after repair_simplex();

• "dirichlet": one Dirichlet\((\alpha,\ldots,\alpha)\) draw (see dirichlet_alpha);

• "qp" (aliases "deconrnaseq", "lsei"): mean-only simplex QP from deconvolute_ratios_deconrnaseq() (y and mean_signature_matrix required).

nms

Optional names (cell-type colnames).

y, mean_signature_matrix

Bulk and signature, required for a QP start.

dirichlet_alpha

Positive concentration, recycled to length \(J\). The default 1 is uniform on the simplex. \(\alpha>1\) concentrates mass near the barycentre; \(\alpha<1\) puts extra mass near faces (boundary-biased restarts).

Value

A length-\(J\) open-simplex vector.

See also

multistart_decovart(), deconvolute_ratios_deconrnaseq()

Examples

starting_simplex(3L)
#> [1] 0.3333333 0.3333333 0.3333333
set.seed(1)
starting_simplex(3L, "dirichlet")
#>        ct1        ct2        ct3 
#> 0.04037978 0.48994649 0.46967373