Re: Expectation Maximization Initialization

In article <44b233c4$1@xxxxxxxxxxxxxx>, David Jones <dajxxx@xxxxxxxxx>
writes
dbmining@xxxxxxxxx wrote:
How is the expectation maximization algorithm initialized? How are
the initial values estimated.


In principle this should not matter too much, so you would need to
judge how much to worry about being sophisticated. However convergence
can be slow.

You can try setting missing values temporarily to a mean value,
although this will lead to an initially underestimated variance. You
could use a second stage to this where missing values are replaced by
random values generated from a first stage (poor) fitted model.

You might find it beneficial to start from several different initial
parameter sets in order to help you judge whether to stop iterating.

David Jones


Does this advice stem from an assumption about the presence (or rather
absence) of multiple local minima? I have seen Expectation Maximization
considered in situations where the presence of multiple local minima was
obvious (for example, to fit mixture models where the presence of a
minimum at e.g. A=1, B=2 implied the existence of one at A=2, B=1). In
this case you might try multiple starts from random initial parameters
in the hope that at least one of your random starts would lead you to
converge to a local minimum which was also a global minimum. I am not
sure what you could deduce about convergence from the different local
minima found.
--
A.G.McDowell
.

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