qpIPF {qpgraph}R Documentation

Iterative proportional fitting algorithm

Description

Performs maximum likelihood estimation of a sample covariance matrix given the independence constraints from in input list of (maximal) cliques.

Usage

qpIPF(vv, clqlst, tol = 0.001, verbose = FALSE, R.code.only = FALSE)

Arguments

vv input matrix, in the context of this package, the sample covariance matrix.
clqlst list of maximal cliques obtained from an undirected graph by using the function qpGetCliques.
tol tolerance under which the iterative algorithm stops.
verbose show progress on calculations.
R.code.only logical; if FALSE then the faster C implementation is used (default); if TRUE then only R code is executed.

Details

The Iterative proportional fitting algorithm (see, Whittaker, 1990, pp. 182-185) adjusts the input matrix to the independence constraints in the undirected graph from where the input list of cliques belongs to, by going through each of the cliques fitting the marginal distribution over the clique for the fixed conditional distribution of the clique. It stops when the adjusted matrix at the current iteration differs from the matrix at the previous iteration in less or equal than a given tolerance value.

Value

The input matrix adjusted to the constraints imposed by the list of cliques, i.e., a maximum likelihood estimate of the sample covariance matrix that includes the independence constraints encoded in the undirected graph formed by the given list of cliques.

Author(s)

R. Castelo and A. Roverato

References

Castelo, R. and Roverato, A. A robust procedure for Gaussian graphical model search from microarray data with p larger than n. J. Mach. Learn. Res., 7:2621-2650, 2006.

Whittaker, J. Graphical models in applied multivariate statistics. Wiley, 1990.

See Also

qpGetCliques qpPAC

Examples

nVar <- 50 # number of variables
maxCon <- 5  # maximum connectivity per variable
nObs <- 10 # number of observations to simulate

I <- qpRndGraph(n.vtx=nVar, n.bd=maxCon)
K <- qpI2K(I)
Sigma <- qpDscale(solve(K)) # true covariance matrix

X <- qpSampleMvnorm(K, nObs)

# scaled sample covariance matrix
S <- qpDscale(cov(X))

# more efficient scaled sample covariance matrix
clqs <- qpGetCliques(I, verbose=FALSE)
S2 <- qpIPF(S, clqs)
S2 <- qpDscale(S2)

# mean squared error of S
mean((abs(Sigma-S)^2)[upper.tri(Sigma)])

# mean squared error of S2
mean((abs(Sigma-S2)^2)[upper.tri(Sigma)])


[Package qpgraph version 1.0.0 Index]