SCFC: Fit the model parameters
In IxavierHiggins/siGGMrepo: siGGM Package

Description Usage Arguments Details Value References Examples

View source: R/SCFC.R

Estimates a sparse inverse covariance matrix where edge-specific shrinkage parameters are informed by the anatomical connectivity information

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SCFC(y, P, siglam = 10, sigmu = 5, maxits = 500, method = "glasso",
  etaInd = 1, mu_init = NULL, a0_init = 30, b0_init = 5, c0 = NULL,
  cov_init = NULL, alpha_init = NULL, outerits, eps = 1e-04)

`y`	T (timepoints) by p (regions of interest) matrix-valued timecourse data.
`P`	p by p matrix of structural connectivity weights
`siglam`	Variance parameter for shrinkage parameters.
`sigmu`	Variance parameter for prior on non-anatomical source of variation in functional connectivity
`maxits`	Maximum number of iterations.
`method`	Method for updating the inverse covariance matrix. The two options are 'glasso', which implements the graphical lasso of Friedman et al (2007), or 'QUIC' which implements the QUIC
`etaInd`	Argument to indicate the inclusion (etaInd=1) or exclusion (etaInd=0) of the structural connectivity information in the estimation procedure.
`mu_init`	Mean of the prior distribution on non-anatomical source of variation in functional connectivity
`a0_init`	Scale parameter of the gamma prior prior parameter for eta parameter. Ensure a0_init>1
`b0_init`	Shape parameter of the gamma prior prior parameter for eta parameter.
`c0`	Tuning parameter controlling overall network sparsity
`cov_init`	If an initial p by p covariance matrix is known, specify it here. The default is NULL.
`alpha_init`	If edge-specific shrinkage values are known, please specify here. This object must be a p by p matrix but is not required for the function to produce estimates.
`outerits`	The number of outer iterations allowed for each update of the inverse covariance matrix. Value is ignored if method='glasso'
`eps`	Convergence criteria. Default is 1e-4

Estimates the anatomically-informed functional brain network via an edge-specific lasso penalty. The inverse covariance matrix is estimated via the graphical lasso (Friedman et al., 2007) or a quadratic approximation to the multivariate normal likelihood plus penalty (Hsieh et al., 2011) The algorithm also estimates the functional network when the anatomical information is ignored.

A list with components

`Omega`	Estimated inverse covariance matrix (p by p matrix)
`Covariance`	Estimated covariance matrix (p by p matrix)
`lambda`	Estimates of the anatomically informed shrinkage factor at each edge (p by p matrix)
`Eta`	Scalar valued estimate of the average effect of structural connectivity on functional connectivity
`Method`	Method to estimate the inverse covariance matrix
`iters`	Number of iterations until convergence criteria reached
`Mu`	Estimate of the non-anatomical source of variation in functional connectivity at each edge
`LogLike`	Penalized Log-likelihood at convergence
`del`	The change in the objective function at covergence.
`BIC`	The Bayesian Information Criterion.

Higgins, Ixavier A., Suprateek Kundu, and Ying Guo. Integrative Bayesian Analysis of Brain Functional Networks Incorporating Anatomical Knowledge. arXiv preprint arXiv:1803.00513 (2018).

Jerome Friedman, Trevor Hastie and Robert Tibshirani (2007). Sparse inverse covariance estimation with the lasso. Biostatistics 2007. http://www-stat.stanford.edu/~tibs/ftp/graph.pdf

Cho-Jui Hsieh, Matyas A. Sustik, Inderjit S. Dhillon, Pradeep Ravikumar. Sparse Inverse Covariance Matrix Estimation Using Quadratic Approximation. Advances in Neural Information Processing Systems, vol. 24, 2011, p. 2330<e2><80><93>2338.

  fit<-SmallWorld(10,.15,100)
  y=as.matrix(fit$Data)
  covdat=cov(y)
  omegdat=solve(covdat)
  locs=which(abs(omegdat)>quantile(omegdat,probs=.8))
  temp=matrix(runif(100,0,1),10,10)
  SC=matrix(0,10,10)
  SC[locs]=temp[locs]
  diag(SC)=0
# Model fit
  fit<-SCFC(y,SC,method="QUIC",etaInd=1,siglam=10,sigmu=5,maxits=500,mu_init=0,a0_init=30,b0_init=6,c0=.5,outerits = 100);