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Computing the regret table for multinomial data
Petri Kontkanen and Petri Myllymäki
(2005)
Technical Report.
HIIT, Helsinki, Finland.
AbstractStochastic complexity of a data set is defined as the
shortest possible code length for the data obtainable
by using some fixed set of models. This measure is
of great theoretical and practical importance as a
tool for tasks such as model selection or data clus-
tering. In the case of multinomial data, comput-
ing the modern version of stochastic complexity,
defined as the Normalized Maximum Likelihood
(NML) criterion, requires computing a sum with
an exponential number of terms. Furthermore, in
order to apply NML in practice, one often needs to
compute a whole table of these exponential sums.
In our previous work, we were able to compute this
table by a recursive algorithm. The purpose of this
paper is to significantly improve the time complex-
ity of this algorithm. The techniques used here are
based on the discrete Fourier transform and the con-
volution theorem.
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