This article was published online on [31 October 2013]. The images of figures 1 and 3 were subsequently changed. This notice is included in the online and print versions to indicate that both have been corrected [27 December 2013].
Sparse Markov Chains for Sequence Data†
Article first published online: 31 OCT 2013
© 2013 Board of the Foundation of the Scandinavian Journal of Statistics.
Scandinavian Journal of Statistics
Volume 41, Issue 3, pages 639–655, September 2014
How to Cite
2014), Sparse Markov Chains for Sequence Data, Scandinavian Journal of Statistics, 41, pages 639–655, doi: 10.1111/sjos.12053, , and (
- Issue published online: 11 AUG 2014
- Article first published online: 31 OCT 2013
- Manuscript Accepted: 3 SEP 2013
- Manuscript Revised: 21 JUN 2013
- Manuscript Received: 2 AUG 2012
- Bayesian learning;
- data compression;
- predictive inference;
- Markov chains;
- variable order Markov models
Finite memory sources and variable-length Markov chains have recently gained popularity in data compression and mining, in particular, for applications in bioinformatics and language modelling. Here, we consider denser data compression and prediction with a family of sparse Bayesian predictive models for Markov chains in finite state spaces. Our approach lumps transition probabilities into classes composed of invariant probabilities, such that the resulting models need not have a hierarchical structure as in context tree-based approaches. This can lead to a substantially higher rate of data compression, and such non-hierarchical sparse models can be motivated for instance by data dependence structures existing in the bioinformatics context. We describe a Bayesian inference algorithm for learning sparse Markov models through clustering of transition probabilities. Experiments with DNA sequence and protein data show that our approach is competitive in both prediction and classification when compared with several alternative methods on the basis of variable memory length.