An MML Approach for Discovering Structure in Discrete One-Dimensional Data

A.C. Bickerstaffe and P.E. Tischer (Australia)

Keywords

Periodicity, MML, Markov, discrete, onedimensional

Abstract

We propose a preliminary approach for determining the optimal order, lag, and state transition probabilities for a Markov model given a sequence of discrete data symbols. Our approach uses Minimum Message Length (MML) en coding to trade-off model complexity against goodness of fit to the data. The encoding scheme does not make the assumption of data being waveform in nature we assume no correlation between symbol labels and thus, our method is invariant to linear transformations of symbol labels. Ex periments using synthetic data indicate that our approach to Markov modelling is capable of inferring appropriately simple models which capture periodicity and sub-structure present in the data. The proposed scheme of Markov mod elling compares well against elementary correlation coeffi cient tests and a more complex periodicity transform (PT) approach.

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