Compute per-coordinate contributions to the collapsed objective C for csmooth_em

Returns a length-d vector C_j such that C_total = sum_j C_j + entropy(Gamma) + sum_k Nk * log(pi_k), where C_total corresponds to the collapsed objective recorded as ml_trace (up to constants consistent with include_constant).

compute_C_by_coord_csmooth(
  X,
  Gamma,
  params,
  Q_K,
  lambda_vec,
  modelName,
  relative_lambda,
  eigen_tol = NULL,
  rw_q = 0L,
  include_constant = TRUE
)

Arguments

X

n-by-d data matrix

Gamma

n-by-K responsibilities

params

list(pi, mu, sigma2)

Q_K

base RW precision (K x K)

lambda_vec

length-d vector

modelName

"homoskedastic" or "heteroskedastic"

relative_lambda

logical

eigen_tol

numeric; passed to generalized_logdet

rw_q

integer; rank deficiency of RW precision

include_constant

logical; include +(K/2)log(2pi) per coordinate if TRUE

Value

a list with - C_coord: length-d vector of per-coordinate collapsed contributions - global_logpi: scalar sum_k Nk log(pi_k) - global_entropy: scalar entropy term -sum Gamma log Gamma - logdetH_coord: length-d vector log|A_j| (for diagnostics)