calibration_ssm: Estimation for the linear SSM calibration model of Blocker &...
In networkTomography: Tools for network tomography

Description Usage Arguments Value References See Also Examples

Maximum likelihood estimation of the parameters of the calibration model from Blocker & Airoldi (2011) via direct numerical maximization of the marginal log-likelihood. This relies upon efficient Kalman smoothing to evaluate the marginal likelihood, which is provided here by the KFAS package.

calibration_ssm(tme, y, A, Ft, Rt, lambda0, phihat0, tau = 2, w = 11,
  initScale = 1/(1 - diag(Ft)^2), nugget = sqrt(.Machine$double.eps),
  verbose = FALSE, logTrans = TRUE, method = "L-BFGS-B",
  optimArgs = list())

`tme`	integer time at which to center moving window for estimation
`y`	matrix (n x m) of observed link loads from all times (not just the window used for estimation; one observation per row
`A`	routing matrix (m x k) for network; should be full row rank
`Ft`	matrix (k x k) containing fixed autoregressive parameters for state evolution equation; upper-left block of overall matrix for expanded state
`Rt`	covariance matrix for observation equation; typically small and fixed
`lambda0`	matrix (n x k) of initial estimates for lambda (e.g. obtained via IPFP)
`phihat0`	numeric vector (length n) of initial estimates for phi
`tau`	numeric power parameter for mean-variance relationship
`w`	number of observations to use for rolling-window estimation; handles boundary cases cleanly
`initScale`	numeric inflation factor for time-zero state covariance; defaults to steady-state variance setting
`nugget`	small positive value to add to diagonal of state evolution covariance matrix to ensure numerical stability
`verbose`	logical to select verbose output from algorithm
`logTrans`	logical whether to log-transform parameters for optimization. If FALSE, sets method to "L-BFGS-B".
`method`	optimization method to use (in optim calls)
`optimArgs`	list of arguments to append to control argument for optim. Can include all arguments except for fnscale, which is automatically set

list containing lambdahat, a numeric vector (length k) containing the MLE for lambda; phihat, the MLE for phi; xhat, the smoothed estimates of the OD flows for the window used as a k x w matrix; and varhat, a k x w matrix containing the diagonal of the estimated covariance for each OD flow in the window

A.W. Blocker and E.M. Airoldi. Deconvolution of mixing time series on a graph. Proceedings of the Twenty-Seventh Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-11) 51-60, 2011.

Other calibrationModel: llCalibration; mle_filter

data(bell.labs)

lambda0 <- matrix(1, nrow(bell.labs$Y), ncol(bell.labs$A))
lambda0[100,] <- ipfp(y=bell.labs$Y[100,], A=bell.labs$A,
                      x0=rep(1, ncol(bell.labs$A)))
phihat0 <- rep(1, nrow(bell.labs$Y))
Ft <- 0.5 * diag_mat(rep(1, ncol(bell.labs$A)))
Rt <- 0.01 * diag_mat(rep(1, nrow(bell.labs$A)))

# Not run
#fit.calibration <- calibration_ssm(tme=100, y=bell.labs$Y, A=bell.labs$A,
#                                   Ft=Ft, Rt=Rt, lambda0=lambda0,
#                                   phihat0=phihat0, w=23)