2. HIDDEN MARKOV
MODEL
A Hidden Markov Model (HMM) is a statistical model that
represents a system containing hidden states where the
system evolves over time. It is "hidden" because the state
of the system is not directly visible to the observer; instead,
the observer can only see some output that depends on the
state. Markov models are characterized by the Markov
property, which states that the future state of a process only
depends on its current state, not on the sequence of events
that preceded it.
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3. COMPONENTS OF A
HIDDEN MARKOV
MODEL
A Hidden Markov Model consists of the
following components:
4. States:
Observations:
These are the visible outputs that are
probabilistically dependent on the hidden states.
These represent the different possible conditions
of the system which are not directly visible.
Transition probabilities:
These are the probabilities of transitioning from
one state to another.
5. Emission probabilities:
Also known as observation probabilities, these
are the probabilities of an observation being
generated from a state.
Initial state probabilities:
These indicate the likelihood of the system starting in
a particular state.
The model is defined by the matrix of transition probabilities, the
emission probability distribution for each state, and the initial
state distribution. The power of HMMs lies in their ability to
model sequences where the state transitions are not directly
observable.
6. HOW HIDDEN MARKOV
MODELS WORK
The operation of a Hidden Markov Model can
be broken down into three fundamental
problems:
7. Evaluation:
Given the model parameters and an observed sequence of
data, the evaluation problem is to compute the probability of
the observed sequence. This is typically solved using the
Forward-Backward algorithm.
Decoding:
Given the model parameters and an observed
sequence of data, the decoding problem is to
determine the most likely sequence of hidden states.
The Viterbi algorithm is commonly used for this
purpose.
Learning:
Given an observed sequence of data and the number of
states in the model, the learning problem is to estimate
the model parameters (transition and emission
probabilities). The Baum-Welch algorithm, a special case
of the Expectation-Maximization algorithm, is often used
to solve this problem.
8. APPLICATIONS OF
HIDDEN MARKOV
MODELS
Hidden Markov Models have been applied in
various fields due to their versatility in handling
temporal data. Some notable applications include:
9. Speech Recognition:
HMMs can model the sequence of sounds in speech and
are used to recognize spoken words or phrases.
Bioinformatics:
In bioinformatics, HMMs are used for gene prediction,
modeling protein sequences, and aligning biological
sequences.
Natural Language Processing:
HMMs are used for part-of-speech tagging, where the
goal is to assign the correct part of speech to each
word in a sentence based on the context.
Finance:
In finance, HMMs can be used to model the hidden factors
that influence market conditions and to predict stock prices
or market regimes.
11. •The Markov property assumes that future states
depend only on the current state, which may not
always be a realistic assumption for complex systems.
•HMMs can become computationally expensive as the
number of states increases.
•The model may not perform well if the true underlying
process does not conform to the assumptions of the
HMM.
Despite these limitations, Hidden Markov Models
remain a fundamental tool in the analysis of sequential
data and continue to be used in research and industry
applications where temporal dynamics play a crucial
role.
12. CONCLUSION
Hidden Markov Models provide a framework for
modeling systems with hidden states and have
been instrumental in advancing various fields that
involve sequence analysis. Their ability to capture
the temporal dynamics in data makes them an
invaluable tool in many applications, despite their
inherent assumptions and limitations. As with any
model, the key to successful application lies in
understanding the underlying system and ensuring
that the assumptions of the HMM are reasonably
met.
