Algorithms for variable length Markov chain modeling

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Algorithms for variable length Markov chain
modeling

• Author Gill Bejerano
• Presented by Xiangbin Qiu

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Review of Markov Chain Model

• Often used in bioinformatics to capture
  relatively simple sequence patterns, such as
  genomic CpG islands.

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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!

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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.

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Description of Authors Work

• Four main modules are implemented
• Train
• Predict
• Emit
• 2pfa

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Probabilistic Suffix Tree (PST)

• A special tree data structure

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PST-Definitions

• S the alphabet, string set i 1, 2 ..m
• Empirical probability
• Conditional empirical probability

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Parameters

• Minimum probability
• Smoothing factors
• Memory length L
• Difference measure parameter r

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Building the PST
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Biologically Extended PST- a Variant of PST Model
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Incremental Model Refinement

• ?
• L ?
• r ? 1

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Prediction using a PST
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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.

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Results and Discussion (Cont.)
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Results and Discussion (Cont.)
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Limitations
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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

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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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Confused?