1. Hidden Markov Model (HMM)
Mahfuzul Haque
www.monash.edu.au

2. An HMM System
Transition Probability
0.7
0.6
Hidden States
0.3
Rainy
0.6
0.1
0.4
Sunny
0.4
0.4
0.5
0.6
0.3
State Probability
0.1
Emission Probability
Walk
Shop
Clean
Visible States
www.monash.edu.au
2

3. Limitations of a Markov Process
• In some cases the patterns that we wish to find
are not described sufficiently by a Markov
process.
• We may not have access to some observations,
which are closely linked with observable states.
• In this case we have two sets of states, the
observable states and the hidden states.
• There are algorithms to forecast hidden states
from the observable states without actually ever
seeing the hidden observations.
www.monash.edu.au
3

4. HMM
• A hidden Markov model (HMM) is a
statistical model
• The system being modelled is assumed
to be a Markov process with unknown
parameters
• The challenge is to determine the hidden
parameters from the observable
parameters
www.monash.edu.au
4

5. An HMM System
Transition Probability
0.7
0.6
Hidden States
0.3
Rainy
0.6
0.1
0.4
Sunny
0.4
0.4
0.5
0.6
0.3
State Probability
0.1
Emission Probability
Walk
Shop
Clean
Visible States
www.monash.edu.au
5

6. Application of HMM - 1
• Input: A dataset of sequences.
• Output: The parameters of HMM: transition
and emission probabilities.
• Algorithm: Baum-Welch algorithm.
www.monash.edu.au
6

7. Application of HMM - 2
• Input: The parameters of HMM.
• Output: The most likely sequence of
hidden statess.
• Algorithm: Viterbi algorithm.
www.monash.edu.au
7

8. Application of HMM - 3
• Input: The parameters of HMM. A output
sequence.
• Output: The probability of that output
sequence and the hidden state values.
• Algorithm: Forward-backward algorithm.
www.monash.edu.au
8