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]