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Discrete Markov chains are frequently used to analyse transition behaviour in sequential data. Here, the transition probabilities can be estimated using varying order Markov chains, where order  k  specifies the length of the sequence history that is used to model these probabilities. Generally, such a model is fitted to the entire dataset, but in practice it is likely that some heterogeneity in the data exists and that some sequences would be better modelled with alternative parameter values, or with a Markov chain of a different order. We use the framework of Exceptional Model Mining (EMM) to discover these exceptionally behaving sequences. In particular, we propose an EMM model class that allows for discovering subgroups with transition behaviour of varying order. To that end, we propose three new quality measures based on information-theoretic scoring functions. Our findings from controlled experiments show that all three quality measures find exceptional transition behaviour of varying order and are reasonably sensitive. The quality measure based on Akaike’s Information Criterion is most robust for the number of observations. We furthermore add to existing work by seeking for subgroups of sequences, as opposite to subgroups of transitions. Since we use sequence-level descriptive attributes, we form subgroups of entire sequences, which is practically relevant in situations where you want to identify the originators of exceptional sequences, such as patients. We show this relevance by analysing sequences of blood glucose values of adult persons with diabetes type 2. In the experiments, we find subgroups of patients based on age and glycated haemoglobin (HbA1c), a measure known to correlate with average blood glucose values. Clinicians and domain experts confirmed the transition behaviour as estimated by the fitted Markov chain models.

Mining sequences with exceptional transition behaviour of varying order using quality measures based on information-theoretic scoring functions