locally_iid_EM: Run EM algorithm to obtain MLE for locally IID model of Cao et al. (2000)

Description

Runs EM algorithm to compute MLE for the locally IID model of Cao et al. (2000). Uses numerical optimization of Q-function for each M-step with analytic computation of its gradient.

Usage

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locally_iid_EM(Y, A, lambda0, phi0 = NULL, c = 2, maxiter = 1000,
  tol = 1e-06, epsilon = 0.01, method = "L-BFGS-B", checkActive = FALSE)

Arguments

Y

matrix (h x k) of observations in local window; columns correspond to OD flows, and rows are individual observations

A

routing matrix (m x k) for network being analyzed

lambda0

initial vector of values (length k) for lambda; ipfp is a good way to obtain this

phi0

initial value for covariance scale phi; initializes automatically using phi_init if NULL, but you can likely do better

c

power parameter in model of Cao et al. (2000)

maxiter

maximum number of EM iterations to run

tol

tolerance (in relative change in Q function value) for stopping EM iterations

epsilon

numeric nugget to add to diagonal of covariance for numerical stability

method

optimization method to use (in optim calls)

checkActive

logical check for deterministically known OD flows

Value

list with 3 elements: lambda, the estimated value of lambda; phi, the estimated value of phi; and iter, the number of iterations run

References

J. Cao, D. Davis, S. Van Der Viel, and B. Yu. Time-varying network tomography: router link data. Journal of the American Statistical Association, 95:1063-75, 2000.

See Also

Other CaoEtAl: Q_iid; Q_smoothed; R_estep; grad_iid; grad_smoothed; m_estep; phi_init; smoothed_EM


Questions? Problems? Suggestions? or email at ian@mutexlabs.com.

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