Algorithms for variable length Markov chain modeling

Author: Gill Bejerano

Presented by Xiangbin Qiu

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

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 requirement

s of an order-k Markov chain grow exponentially with k!

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.

Description of Author’s Work

Four main modules are implemented:TrainPredictEmit2pfa

Probabilistic Suffix Tree (PST)

A special tree data structure

PST-Definitions

Σ the alphabet, string set: i= 1, 2 ..m

Empirical probability:

Conditional empirical probability:

Parameters

Minimum probability:

Smoothing factors:

Memory length: L

Difference measure parameter: r

Building the PST

Biologically Extended PST- a Variant of PST Model

Incremental Model Refinement

↑ L ↑ r → 1

Prediction using a PST

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.

Results and Discussion (Cont.)

Results and Discussion (Cont.)

Limitations

Why Significant?

While performance comparable to HMM models

Built in a fully automated mannerWithout multiple alignmentWithout scoring matrices

Less demanding than HMMs in terms of data abundance and quality

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.

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