SCFCpath: Fit the model parameters along a path of tuning parameters
In IxavierHiggins/siGGMrepo: siGGM Package

Description Usage Arguments Details Value References Examples

View source: R/SCFCpath.R

Estimates sparse inverse covariance matrices along a grid of regularization parameters, where edge-specific shrinkage parameters are informed by the anatomical connectivity information.

SCFCpath(y, P, siglam = 10, sigmu = 5, maxits = 500, method = "glasso",
  etaInd = 1, mu_init = NULL, a0_init = 30, b0_init = 5,
  nulist = 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.
`nulist`	Vector of non-negative regularization parameters. The values should increase from smallest to largest. If the nulist is NULL, then 10 values are chosen based on the minimum and maximum of the elements in the empirical covariance matrix.
`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 along a path of regularization parameters. 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 matrices, a list of length length(nulist).
`Covariance`	Estimated covariance matrices, a list of length length(nulist).
`lambda`	Estimated anatomically informed shrinkage factor at each edge, a list of length length(nulist).
`Eta`	A list of length length(nulist) containing scalar valued estimates of the average effect of structural connectivity on functional connectivity.
`Method`	Method to estimate the inverse covariance matrix.
`iters`	A list of length length(nulist) containing the number of iterations until convergence criteria reached.
`Mu`	A list of length length(nulist) containing estimates of the non-anatomical source of variation in functional connectivity at each edge.
`LogLike`	A list of length length(nulist) containing the value of the objective function at convergence.
`del`	A list of length length(nulist) containing the change in the objective function at covergence.
`BIC`	A list of length length(nulist) containing 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.

# Generate data and structural connectivity information
  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<-SCFCpath(y,SC,method="QUIC",etaInd=1,nulist=NULL,siglam=10,sigmu=5,maxits=500,mu_init=0,a0_init=30,b0_init=6,outerits = 100);