BGL_DC: Basis Graphical Lasso Difference of Convex Algorithm
In mlkrock/BasisGraphicalLasso: Basis Graphical Lasso

Description Usage Arguments Details Value Examples

View source: R/BGL_DC.R

Estimates the precision matrix from the basis graphical lasso model.

BGL_DC(
  lambda,
  Phi_Dinv_Phi,
  Phi_Dinv_S_Dinv_Phi,
  guess,
  outer_tol = NULL,
  MAX_ITER = NULL,
  MAX_RUNTIME_SECONDS = NULL,
  verbose = TRUE
)

`lambda`	Penalty be either a nonnegative real, or a matrix of nonnegative reals whose dimension is the same as the number of graph nodes.
`Phi_Dinv_Phi`	Inner product of basis matrices, Φ'D^{-1}Φ. Typically obtained from using `BGLBasisSetup` with D = τ^2 I.
`Phi_Dinv_S_Dinv_Phi`	Inner product of the basis matrices and data, Φ'D^{-1}SD^{-1}Φ. Typically obtained from using `BGLBasisSetup` with D = τ^2 I. This is where the data directly enters the algorithm. Note: do not compute sample covariance S explicitly. With `dat` as the n by m matrix with columns corresponding to realizations of the mean zero spatial field, we have S=XX'/m. So, setting D = I for simplicity, we can compute as Φ'SΦ as `tcrossprod(crossprod(Phi, dat))/m`.
`guess`	Initial guess for the precision matrix.
`outer_tol`	Tolerance. Default: NULL.
`MAX_ITER`	Maximum number of iterations. Default: NULL.
`MAX_RUNTIME_SECONDS`	Maximum runtime in seconds. Default: NULL.
`verbose`	Print algorithm details after each iteration. Default: TRUE.

This is the DC algorithm suggested in the paper and is the workhorse of the package. It uses the QUIC algorithm to solve the inner graphical lasso problem which arises after linearizing all concave functions w.r.t Q in the negative log likelihood. D is the covariance matrix of the additive error term epsilon in the model formulation; in the paper D = τ^2 I. The package does not estimate non-identity multiple of D but we include the more general version for possible future research.

Precision matrix of the random coefficients in the weighted sum of basis functions.

basis.setup <- BGLBasisSetup(y=tmin$data,locs=tmin$lon.lat.proj,basis="LatticeKrig", 
     crossvalidation=FALSE,NC=20,nlevel=1)
Phi_Phi <- basis.setup$Phi_Phi
Phi_S_Phi <- basis.setup$Phi_S_Phi
tau_sq <- 2
lambda <- matrix(10,nrow=dim(Phi_Phi)[1],ncol=dim(Phi_Phi)[1])
diag(lambda) <- 0
BGLguess <- BGL_DC(lambda=lambda,Phi_Dinv_Phi=Phi_Phi/tau_sq,
     Phi_Dinv_S_Dinv_Phi=Phi_S_Phi/(tau_sq^2), guess=diag(dim(Phi_Phi)[1]),
     outer_tol=0.05,MAX_ITER=50,MAX_RUNTIME_SECONDS=86400)