Permuting CM Steps Within the ECM Algorithm
David A. van Dyk and Xiao-Li Meng
Department of Statistics, The University of Chicago,
Chicago, IL 60637, U.S.A.
The ECM Algorithm (Meng and Rubin, 1993), is a
generalization of the EM
algorithm in which the maximization (M) step is replaced by several
conditional
maximization (CM) steps. The order that the CM steps are performed
is completely arbitrary, trivial to change, and generally effects how
fast ECM converges.
Moreover, the same order of CM steps need not be used at each ECM
iteration. In this paper, we
use the contingency table problem to illustrate the effect of
changing the order of CM steps on the actual number of ECM iterations
required for convergence.
Our examples both show that the effect can be substantial and illustrate
that the problem of
finding efficient orderings is generally quite difficult because both
theory and common sense can be misleading.
Key Words: Contingency Table;
Convergence Rate; Gibbs Sampler; EM Algorithm;
Incomplete Data; IPF; Missing Data
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