1. An INTRODUCTION TO HIDDEN MARKOV MODEL
By:
Pejman Golshan
Shu Yu

2. HIDDEN MARKOV MODEL(HMM)
Real-world has structures and processes which have observable outputs.
– Usually sequential .
– Cannot see the event producing the output.
Problem: how to construct a model of the structure or
process given only observations ?

3. HISTORY OF HMM • Basic theory developed and published in 1960s and 70s
• No widespread understanding and application until late
80s
• Why?
– Theory published in mathematic journals which were
not widely read.
– Insufficient tutorial material for readers to understand
and apply concepts.

4. Andrei Andreyevich Markov 1856-1922
Andrey Andreyevich Markov was a Russian
mathematician.
He is best known for his work on stochastic
processes.
A primary subject of his research later became
known as Markov chains and Markov processes .

5. 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
previous state.

6. HMM COMPONENTS • 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
next
• Output emission matrix (b’s)
– probability of a emitting/observing a symbol at a
particular state
• Initial probability vector
– probability of starting at a particular state
– Not shown, sometimes assumed to be 1

7. The Example we had in the class
Two states : ‘Rain’ and ‘Dry’.
Transition probabilities: P(‘Rain’|‘Rain’)=0.3 ,
P(‘Dry’|‘Rain’)=0.7 , P(‘Rain’)=0.6 .
P (‘rain’|‘Dry’)=0.2, P(‘Dry’|‘Dry’)=0.8
Initial probabilities: say P(‘Rain’)=0.4 , P(‘Dry’)=0.6

8. CALCULATION OF HMM
By Markov chain property, probability of the state sequence can be found by:
Suppose we want to calculate a probability of a sequence of states in the example, {Dry,Dry, Rain,Rain}

9. PROBLEMS OF HMM
• Three problems must be solved for HMMs to be useful in real-world applications
Evaluation: • Problem - Compute Probability of observation sequence given a model
• Solution - Forward Algorithm and Viterbi Algorithm
Decoding: • Problem - Find state sequence which maximizes probability of
Observation sequence
• Solution - Viterbi Algorithm
Training: • Problem - Adjust model parameters to maximize probability of
observed sequences
• Solution - Forward-Backward Algorithm

10. EVOLUTION OF PROBLEM Given a set of HMMs, which is the one most
likely to have produced the observation sequence?

11. DECODING PROBLEM

12. Applications • It is able to handle new data robustly
Benefit of Hidden Markov Model
• It is able to handle new data robustly
• Computationally efficient to develop and evaluate (due to the existence of established training algorithms).
• It is able to predict similar patterns efficiently

13. Applications
Stock prediction

14. Applications Stock prediction
Stock behavior of past is similar to behavior of current day
The next day’s stock price should follow about the same past pattern
Using trained HMM
likelihood value P for current day’s dataset can be calculated.
from the past dataset we can locate those instances that would produce the nearest P likelihood value.

15. Applications Speech recognition Observation: speech waveform
phone model
(phonetic symbols)
word model

16. Applications Face Expression Characterization – Using HMM framework
The hidden state of HMMs is the hidden emotional state of the individual.
The observable symbols of HMMs is the feature vectors extracted from face videos
The State Transition matrix and Observation probability matrix of HMMs is Dynamical information extracted from videos accompanied by observation symbols extracted using VQ(vector Quantization)

17. Applications Computational finance Alignment of bio-sequences
Single Molecule Kinetic analysis
Time Series Analysis
Cryptanalysis
Activity recognition
Speech recognition
Protein folding
Speech synthesis
Metamorphic Virus Detection
Part-of-speech tagging
DNA Motif Discovery
Document Separation in scanning solutions
Machine translation
Partial discharge
Gene prediction
Handwriting Recognition

18. References
Nguyen, N and Nguyen, D; Hidden Markov Model for Stock Selection, Journal of
Risks in special issue: Recent Advances in Mathematical Modeling of the Financial
Markets, Risks 2015, 3(4), ; doi: /risks
Cs.cmu.edu. (n.d.). Cite a Website - Cite This For Me. [online] Available at: .
wordspotting, H. (n.d.). HMMs in Speech recognition and wordspotting. [online] Kapelnick.blogspot.ca. Available at:
University of Illinois, C. (n.d.). Microsoft power point Face recognition. [online] Slideshare.net. Available at:

19. Thank you!