Run collapsed-ML csmoothEM iterations (homoskedastic only)

Iteration order (collapsed-ML): 1) E-step: update responsibilities using current (MAP) \(\mu\). 2) Hyper-step: update \(\pi\), \(\lambda\), and optionally \(\sigma^2\). 3) M-step: update MAP \(\mu\) given current responsibilities and hyperparameters. 4) Record: penalized observed objective (loglik_trace), penalized ELBO (elbo_trace), collapsed objective \(\mathcal{C}\) (ml_trace), and logdetH_trace.

do_csmoothEM_ml_collapsed(
  object,
  data = NULL,
  iter = 1,
  record = TRUE,
  lambda_min = NULL,
  lambda_max = NULL,
  sigma_update = c("mstep", "ml"),
  sigma_min = 1e-10,
  sigma_max = 1e+10,
  verbose = FALSE
)

Arguments

object

A csmooth_em object.

data

Optional n-by-d data matrix. If NULL, uses object$data.

iter

Integer >= 1 number of iterations.

record

Logical; if TRUE, record traces.

lambda_min, lambda_max

Bounds for lambda optimization.

sigma_update

Either "mstep" (standard M-step update) or "ml" (optimize collapsed objective).

sigma_min, sigma_max

Bounds for sigma2 when sigma_update="ml".

verbose

Logical.

Value

Updated csmooth_em object.

Details

The recorded ml_trace is the collapsed objective $$\mathcal{C} \;=\; \text{penELBO} \;+\; \frac{dK}{2}\log(2\pi) \;-\; \frac12 \log|H|,$$ where \(H\) is the Hessian/precision w.r.t. \(\mu\) (block-diagonal over coordinates).