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
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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.
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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
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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
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5
6. Application of HMM - 1
• Input: A dataset of sequences.
• Output: The parameters of HMM: transition
and emission probabilities.
• Algorithm: Baum-Welch algorithm.
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6
7. Application of HMM - 2
• Input: The parameters of HMM.
• Output: The most likely sequence of
hidden statess.
• Algorithm: Viterbi algorithm.
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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.
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