HIDDEN MARKOV MODEL(HMM)
Real-world has structures and processes which have
– Usually sequential .
– Cannot see the event producing the output.
Problem: how to construct a model of the structure or
process given only observations.
HISTORY OF HMM
• Basic theory developed and published in 1960s and 70s
• No widespread understanding and application until late
– Theory published in mathematic journals which were
not widely read.
– Insufficient tutorial material for readers to understand
and apply concepts.
Andrei Andreyevich Markov
Andrey Andreyevich Markov was a Russian
He is best known for his work on stochastic
A primary subject of his research later became
known as Markov chains and Markov processes .
HIDDEN MARKOV MODEL
• A Hidden Markov Model (HMM) is a statical model in
which the system is being modeled is assumed to be
a Markov process with hidden states.
• Markov chain property: probability of each
subsequent state depends only on what was the
EXAMPLE OF HMM
• Coin toss:
– Heads, tails sequence with 2 coins
– You are in a room, with a wall
– Person behind wall flips coin, tells result
– Coin selection and toss is hidden
– Cannot observe events, only output (heads, tails) from events
– Problem is then to build a model to explain observed
sequence of heads and tails.
EXAMPLE OF HMM
– Once each day weather is observed
– State 1: rain
– State 2: cloudy
– State 3: sunny
– What is the probability the weather for the next 7 days will be:
– sun, sun, rain, rain, sun, cloudy, sun
– Each state corresponds to a physical observable event
• A set of states (x’s)
• A set of possible output symbols (y’s)
• A state transition matrix (a’s)
– probability of making transition from one state to the
• Output emission matrix (b’s)
– probability of a emitting/observing a symbol at a
• Initial probability vector
– probability of starting at a particular state
– Not shown, sometimes assumed to be 1
EXAMPLE OF HMM
• Two states : ‘Rain’ and ‘Dry’.
• Transition probabilities: P(‘Rain’|‘Rain’)=0.3 ,
P(‘Dry’|‘Rain’)=0.7 , P(‘Ra’)=0.6 .
• in’|‘Dry’)=0.2, P(‘Dry’|‘Dry’)=0.8
• Initial probabilities: say P(‘Rain’)=0.4 , P(‘Dry
COMMON HMM TYPES
• Ergodic (fully connected):
– Every state of model can be reached in a single step from
every other state of the model.
• Bakis (left-right):
– As time increases, states proceed from left to right
HMM IN BIOINFORMATICS
• Hidden Markov Models (HMMs) are a
probabilistic model for modeling and
representing biological sequences.
• They allow us to do things like find genes, do
sequence alignments and find regulatory
elements such as promoters in a principled
PROBLEMS OF HMM
• Three problems must be solved for HMMs to be
useful in real-world applications
EVOLUTION OF PROBLEM
Given a set of HMMs, which is the one most
likely to have produced the observation sequence?
• DNA Sequence analysis
• Protein family profiling
• Splicing signals prediction
• Prediction of genes
• Horizontal gene transfer
• Radiation hybrid mapping, linkage analysis
• Prediction of DNA functional sites.
• CpG island
• Speech Recognition
• Vehicle Trajectory Projection
• Gesture Learning for Human-Robot Interface
• Positron Emission Tomography (PET)
• Optical Signal Detection
• Digital Communications
• Music Analysis
• Rabiner, L. R. (1989). A Tutorial on Hidden Markov
Models and Selected Applications in Speech
Recognition. Proceedings of the IEEE, 77(2), 257-285.
• Essential bioinformatics, Jin Xion