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Strict Minimum Message Length (SMML) inference (Wallace & Boulton 1975)
constructs a mapping from the data space to the set of models (parameters)
so as to minimise the expected length of a two-part message:
`model; (data|model)'.
Note that the mapping defines a partition of the data space,
each part being the data values that
map to a particular model (parameter value).
SMML is invariant and consistent, and handles
model selection, parameter estimation and hypothesis testing.
Unfortunately SMML inference is NP-hard for most problems,
although a polynomial-time algorithm exists for
the Binomial distribution (Farr & Wallace 1997, 2002).
Fortunately, MML
(Wallace & Boulton 1968, Wallace & Freeman 1987)
is a feasible approximation to SMML.
- G. E. Farr & C. S. Wallace.
The Complexity of Strict Minimum Message Length Inference.
The Computer Journal 45(3), pp285-292, 2002.
Also TR 97/321, Department of Computer Science,
Monash University (Clayton), Victoria 3168, Australia.
11 August 1997.
(Also see Binomial.)
- C. S. Wallace,
False Oracles and SMML Estimators,
Proc. Int. Conf. on Information, Statistics and Induction in Science (ISIS),
pp.304-316, 1996.
- C. S. Wallace & D. M. Boulton.
An information measure for classification.
Computer Journal, 11(2), pp185-194, 1968.
- C. S. Wallace & D. M. Boulton.
An invariant Bayes method for point estimation.
Classification Soc. Bulletin. 3, pp11-34, 1975.
- C. S. Wallace & P. R. Freeman.
Estimation and inference by compact coding.
J. Royal Stat. Soc. B 49(3), pp230-265, 1987.
- Bibliography
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