1. Hidden Markov Models in Bioinformatics
Example Domains: Gene Finding &
Protein Family Modeling
Colin Cherry

2. My Credentials By day, I do NLP work with Dekang Lin
Worked with HMMs in the 1st term of my 1st year here
Did a review paper with Guohui Lin. Today’s presentation is borrowed from that
Worked on speeding up sequence alignment to profile HMMs with Martin Müller

3. 5 Second Overview
Today’s goal: Introduce HMMs as general tools in bioinformatics
I will use the problem of Gene Finding as an example of an “ideal” HMM problem domain
I will use the problem of Protein Family Modeling as an example of a clever way to fit HMMs to a problem

4. Learning Objectives When I’m done you should know:
When is an HMM a good fit for a problem space?
What materials are needed before work can begin with an HMM?
What are the advantages and disadvantages of using HMMs?

5. Outline HMMs as Statistical Models The example tasks at a glance
Good problems for HMMs
HMM Advantages
HMM Disadvantages
Gene Finding Examples

6. Statistical Models HMMs are just a little more complicated…
Definition:
Any mathematical construct that attempts to parameterize a random process
Example: A normal distribution
Assumptions
Parameters
Estimation
Usage
HMMs are just a little more complicated…

7. HMM Assumptions Observations are ordered
Random process can be represented by a stochastic finite state machine with emitting states.

8. HMM Parameters Using weather example Modeling daily weather for a year
Ra Ra Su Su Su Ra..
Lots of parameters
One for each table entry
Represented in two tables.
One for emissions
One for transitions

9. HMM Estimation Called training, it falls under machine learning
Feed an architecture (given in advance) a set of observation sequences
The training process will iteratively alter its parameters to fit the training set
The trained model will assign the training sequences high probability

10. HMM Usage Two major tasks
Evaluate the probability of an observation sequence given the model (Forward)
Find the most likely path through the model for a given observation sequence (Viterbi)

11. Gene Finding (An Ideal HMM Domain)
Our Objective:
To find the coding and non-coding regions of an unlabeled string of DNA nucleotides
Our Motivation:
Assist in the annotation of genomic data produced by genome sequencing methods
Gain insight into the mechanisms involved in transcription, splicing and other processes

12. Gene Finding Terminology
A string of DNA nucleotides containing a gene will have separate regions (lines):
Introns – non-coding regions within a gene
Exons – coding regions
Separated by functional sites (boxes)
Start and stop codons
Splice sites – acceptors and donors

13. Gene Finding Challenges
Need the correct reading frame
Introns can interrupt an exon in mid-codon
There is no hard and fast rule for identifying donor and acceptor splice sites
Signals are very weak

14. Protein Family Modeling (A clever fit of HMMs)
I have a protein sequence.
What family is it in?
Can you give me a quick alignment to the other members of the family?
These amino acids here, do they match the families consensus positions, or are they inserts?

15. Profile HMM Square: Match (consensus) state
Diamond: Insert state – notice the loops
Circle: Delete state – allows you to “jump” a match

16. What makes a good HMM problem space?
Characteristics:
Classification problems
There are two main types of output from an HMM:
Scoring of sequences
(Protein family modeling)
Labeling of observations within a sequence
(Gene Finding)

17. HMM Problem Characteristics Continued
The observations in a sequence should have a clear, and meaningful order
Unordered observations will not map easily to states
It’s beneficial, but not necessary for the observations follow some sort of grammar
Makes it easier to design an architecture
Gene Finding
Protein Family Modeling
Fortunately, most materials in bioinformatics can be interpreted as sequences with well-defined order, be they gene sequences, structure sequences or nucleotide sequences

18. HMM Requirements So you’ve decided you want to build an HMM,
here’s what you need:
An architecture
Probably the hardest part
Should be biologically sound & easy to interpret
A well-defined success measure
Necessary for any form of machine learning

19. HMM Requirements Continued
Training data
Labeled or unlabeled – it depends
You do not always need a labeled training set to do observation labeling, but it helps
Amount of training data needed is:
Directly proportional to the number of free parameters in the model
Inversely proportional to the size of the training sequences

20. Why HMMs might be a good fit for Gene Finding
Classification: Classifying observations within a sequence
Order: A DNA sequence is a set of ordered observations
Grammar / Architecture: Our grammatical structure (and the beginnings of our architecture) is right here:
Success measure: # of complete exons correctly labeled
Training data: Available from various genome annotation projects

21. Why HMMs can be made to fit Protein Family Modeling
Classification: What model fits a sequence best?
Order: An amino acid sequence is well ordered
Grammar: Any two matches can be separated by a series of inserts and deletes… okay, maybe the word “grammar” is a bit of a stretch
Success Measure: How many sequences can we correctly label after training?

22. HMM Advantages Statistical Grounding
Statisticians are comfortable with the theory behind hidden Markov models
Freedom to manipulate the training and verification processes
Mathematical / theoretical analysis of the results and processes
HMMs are still very powerful modeling tools – far more powerful than many statistical methods

23. HMM Advantages continued
Modularity
HMMs can be combined into larger HMMs
Transparency of the Model
Assuming an architecture with a good design
People can read the model and make sense of it
The model itself can help increase understanding

24. HMM Advantages continued
Incorporation of Prior Knowledge
Incorporate prior knowledge into the architecture
Initialize the model close to something believed to be correct
Use prior knowledge to constrain training process
Start the model close to something that is correct – this takes advantage of model transparency
Use prior knowledge to constrain the training process – takes advantage of statistical grounding

25. How does Gene Finding make use of HMM advantages?
Statistics:
Many systems alter the training process to better suit their success measure
Modularity:
Almost all systems use a combination of models, each individually trained for each gene region
Prior Knowledge:
A fair amount of prior biological knowledge is built into each architecture
Point 1 (statistics): Find a good way to phrase that a state sequence that fits the observations with highest probability is not necessarily the state sequence that assigns the highest probability to complete exons and introns
Point 4 (modularity): Each sub-model’s architecture is constructed to encapsulate biological knowledge about that region of the gene

26. HMM Disadvantages … Markov Chains
States are supposed to be independent
P(y) must be independent of P(x), and vice versa
This usually isn’t true
Can get around it when relationships are local
Not good for RNA folding problems
P(x)
P(y) …

27. HMM Disadvantages continued
…and then there are the standard Machine Learning Problems
Watch out for local maxima
Model may not converge to a truly optimal parameter set for a given training set
Avoid over-fitting
You’re only as good as your training set
More training is not always good

28. HMM Disadvantages continued
Speed!!!
Almost everything one does in an HMM involves: “enumerating all possible paths through the model”
There are efficient ways to do this
Still slow in comparison to other methods

29. HMM Gene Finders: VEIL A straight HMM Gene Finder
Takes advantage of grammatical structure and modular design
Uses many states that can only emit one symbol to get around state independence

30. HMM Gene Finders: HMMGene
Uses an extended HMM called a CHMM
CHMM = HMM with classes
Takes full advantage of being able to modify the statistical algorithms
Uses high-order states
Trains everything at once

31. HMM Gene Finders: Genie
Uses a generalized HMM (GHMM)
Edges in model are complete HMMs
States can be any arbitrary program
States are actually neural networks specially designed for signal finding

32. Conclusions
HMMs have problems where they excel, and problems where they do not
You should consider using one if:
Problem can be phrased as classification
Observations are ordered
The observations follow some sort of grammatical structure (optional)

33. Conclusions Advantages: Disadvantages: Statistics Modularity
Transparency
Prior Knowledge
Disadvantages:
State independence
Over-fitting
Local Maximums
Speed

34. Some final words…
Lots of problems can be phrased as classification problems
Homology search
Build a model of the sequence with a few close homologs, and use the model the search for more distant homologs
Sequence alignment
Align all of these sequences to the model that represents their family

35. Questions
Any Questions?