Algorithms for variable length Markov chain modeling

1. Algorithms for variable length Markov chain modeling Author: Gill Bejerano Presented by Xiangbin Qiu

2. Review of Markov Chain Model • Often used in bioinformatics to capture relatively simple sequence patterns, such as genomic CpG islands.

3. Problem • The low order Markov chains are poor classifiers • Higher order chains are often impractical to implement or train. • The memory and training set size requirements of an order-k Markov chain grow exponentially with k!

4. Variable length Markov Model (VMM) • The models are not restricted to a predefined uniform depth (e.g. order-k). • The model is constructed that fits higher order Markov dependencies where such contexts exist, while using lower order Markov dependencies elsewhere. • The order is determined by examining the training data.

5. Description of Author’s Work • Four main modules are implemented: • Train • Predict • Emit • 2pfa

6. Probabilistic Suffix Tree (PST) • A special tree data structure

7. PST-Definitions • Σ the alphabet, string set: i= 1, 2 ..m • Empirical probability: • Conditional empirical probability:

8. Parameters • Minimum probability: • Smoothing factors: • Memory length: L • Difference measure parameter: r

9. Building the PST

10. Biologically Extended PST- a Variant of PST Model

11. Incremental Model Refinement • ↑ • L ↑ • r → 1

12. Prediction using a PST

13. Results and Discussion • When averaged over all 170 families, the PST detected 90.7% of the true positives. • Much better than a typical BLAST search, and comparable to an HMM trained from a multiple alignment of the input sequences in a global search mode.

14. Results and Discussion (Cont.)

15. Results and Discussion (Cont.)

16. Limitations

17. Why Significant? • While performance comparable to HMM models • Built in a fully automated manner • Without multiple alignment • Without scoring matrices • Less demanding than HMMs in terms of data abundance and quality

18. Future Work • An additional improvement is expected if a larger sample set is used to train the PST. Currently the PST is built from the training set alone. • Obviously, training the PST on all strings of a family should improve its prediction as well.

19. Confused?