Efficient Computation of Stochastic Complexity (2003)
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| Venue: | Proceedings of the Ninth International Conference on Artificial Intelligence and Statistics |
| Citations: | 8 - 7 self |
BibTeX
@INPROCEEDINGS{Kontkanen03efficientcomputation,
author = {Petri Kontkanen and Wray Buntine and Petri Myllymäki and Jorma Rissanen and Henry Tirri},
title = {Efficient Computation of Stochastic Complexity},
booktitle = {Proceedings of the Ninth International Conference on Artificial Intelligence and Statistics},
year = {2003},
pages = {233--238}
}
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Abstract
Stochastic 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 clustering. Unfortunately, computing the modern version of stochastic complexity, defined as the Normalized Maximum Likelihood (NML) criterion, requires computing a sum with an exponential number of terms. Therefore, in order to be able to apply the stochastic complexity measure in practice, in most cases it has to be approximated. In this paper, we show that for some interesting and important cases with multinomial data sets, the exponentiality can be removed without loss of accuracy. We also introduce a new computationally efficient approximation scheme based on analytic combinatorics and assess its accuracy, together with earlier approximations, by comparing them to the exact form.
