Section:
New Results
Soft level splitting for rare event
estimation
Participants :
Frédéric Cérou, Arnaud Guyader.
See
3.3
and
4.2 .
This is a collaboration with Nicolas Hengartner (Los Alamos).
It is well established now that one can use adaptive splitting levels
to compute the conditional probabilities of nested sets. To get an
efficient algorithm, the probability of a set given the previous one
should be always the same, which is approximately achieved adaptively
by using the empirical cdf (cumulative distribution function) of the scores.
The way to proceed is to fix
a probability of success , and then choose the quantile of the
current scores. Here we investigate whether, by using the whole cdf,
and not only one quantile, we can design an algorithm with better
performance. The main trick is a transformation to have a sample of
exponential variables. This would require the knowledge of the cdf of
the cost, which is obviously unvailable, but we can replace it by the
empirical cdf of the sample at the previous level.
The complete theoretical study of this algorithm is still to be done,
but we have illustrated by some examples that it can lead to
significantly better results than the standard splitting procedure
with the same number of intermediate levels.
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