# Hidden Markov Model

(Redirected from Hidden Markov Models)

Markov chains are named for Russian mathematician Andrei Markov (1856-1922), and they are defined as observed sequences. A Markov model is a system that produces a Markov chain, and a hidden Markov model is one where the rules for producing the chain are unknown or "hidden." The rules include two probabilities: (i) that there will be a certain observation and (ii) that there will be a certain state transition, given the state of the model at a certain time.

The Hidden Markov Model (HMM) method is a mathematical approach to solving certain types of problems: (i) given the model, find the probability of the observations; (ii) given the model and the observations, find the most likely state transition trajectory; and (iii) maximize either i or ii by adjusting the model's parameters. For each of these problems, algorithms have been developed: (i) Forward-Backward, (ii) Viterbi, and (iii) Baum-Welch (and the Segmental K-means alternative).

The HMM method has been traditionally used in signal processing, speech recognition, and, more recently, bioinformatics. It may generally be used in pattern recognition problems, anywhere there may be a model producing a sequence of observations. In bioinformatics, it has been used in sequence alignment, in silico gene detection, structure prediction, data-mining literature, and so on.

Here is a simple example of the use of the HMM method in in silico gene detection:

• Codons (or DNA triplets) are the observations.
• 64 codons equals a probability of 1/64.
• The DNA sequence is the Markov chain (set of observations).
• Switches from one genomic region to another are the state transitions.
• 5'UTR to CDS
• CDS to intron
• intron to CDS
• CDS to 3'UTR
• 4 state transitions equals a probability of ¼.

Difficulties with the HMM method include the need for accurate, applicable, and sufficiently sized training sets of data. As for the example of gene detection, in order to accurately predict genes in the human genome, many genes in the genome must be accurately known.

## Software

• HMMER - Profile hidden Markov models for biological sequence analysis
• SAM - Sequence Alignment and Modeling System, a collection of flexible software tools for creating, refining, and using linear hidden Markov models for biological sequence analysis
• VEIL - A hidden Markov model for finding genes in vertebrate DNA
• UGENE - A free multi-platform graphical interface for algortihms based on HMMER2 and HMMER3 packages