EM_templateICA: EM Algorithms for Template ICA Models

Description

EM Algorithms for Template ICA Models

Usage

EM_templateICA.spatial(
  template_mean,
  template_var,
  meshes,
  BOLD,
  theta0,
  C_diag,
  H,
  Hinv,
  maxiter = 100,
  usePar = FALSE,
  epsilon = 0.001,
  reduce_dim = TRUE,
  verbose = FALSE
)
EM_templateICA.independent(
  template_mean,
  template_var,
  BOLD,
  theta0,
  C_diag,
  H,
  Hinv,
  maxiter = 100,
  epsilon = 0.001,
  reduce_dim = FALSE,
  usePar = FALSE,
  verbose
)

Value

A list: theta (list of final parameter estimates), subICmean (estimates of subject-level ICs), subICvar (variance of subject-level ICs, for non-spatial model) or subjICcov (covariance matrix of subject-level ICs, for spatial model -- note that only diagonal and values for neighbors are computed), and success (flag indicating convergence (TRUE) or not (FALSE))

Arguments

template_mean: (\(V \times Q\) matrix) mean maps for each IC in template, where \(Q\) is the number of ICs, \(V=nvox\) is the number of data locations.
template_var: (\(V \times Q\) matrix) between-subject variance maps for each IC in template
meshes: NULL for spatial independence model, otherwise a list of objects of class "templateICA_mesh" containing the triangular mesh (see make_mesh) for each brain structure.
BOLD: (\(V \times Q\) matrix) dimension-reduced fMRI data
theta0: (list) initial guess at parameter values: A (\(QxQ\) mixing matrix), nu0_sq (residual variance from first level) and (for spatial model only) kappa (SPDE smoothness parameter for each IC map)
C_diag: (\(Qx1\)) diagonal elements of matrix proportional to residual variance.
H, Hinv: For dimension reduction of the spatial template ICA model, which assumes that all IC's have the same smoothness parameter, \(\kappa\)
maxiter: Maximum number of EM iterations. Default: 100.
usePar: Parallelize the computation? Default: FALSE. Can be the number of cores to use or TRUE, which will use the number available minus two. Not yet implemented for spatial template ICA.
epsilon: Smallest proportion change between iterations. Default: 0.001.
reduce_dim: Reduce the temporal dimension of the data using PCA? Default: TRUE for the spatial EM algorithm, and FALSE for the independent EM algorithm.
verbose: If TRUE, display progress of algorithm. Default: FALSE.

Details

EM_templateICA.spatial implements the expectation-maximization (EM) algorithm described in Mejia et al. (2019+) for estimating the subject-level ICs and unknown parameters in the template ICA model with spatial priors on subject effects.

In both models, if original fMRI timeseries has covariance \(\sigma^2 I_T\), the prewhitened timeseries achieved by premultiplying by (\(QxT\)) matrix \(H\) from PCA has diagonal covariance \(\sigma^2HH'\), so C_diag is \(diag(HH')\).