Hidden Markov Model

Definition

A Hidden Markov Model (HMM) is a statistical model that represents systems which are assumed to follow a Markov process with unobserved, or 'hidden,' states. In this framework, the system transitions between hidden states based on defined probabilities, while the observed outcomes depend probabilistically on these hidden states. HMMs are widely used in various fields such as speech recognition, bioinformatics, and finance due to their ability to model temporal sequences effectively.

5 Must Know Facts For Your Next Test

1. HMMs are characterized by their two main components: the hidden states and the observable outputs, where the former cannot be directly observed.
2. The training of an HMM typically involves algorithms like the Baum-Welch algorithm, which optimizes model parameters based on observed data.
3. The Viterbi algorithm is commonly used with HMMs to find the most probable sequence of hidden states that lead to a sequence of observed events.
4. HMMs can be visualized as directed graphs where nodes represent states and edges represent transition probabilities between those states.
5. Applications of HMMs include natural language processing for tasks like part-of-speech tagging and time series analysis in finance.

Review Questions

• How does a Hidden Markov Model differ from a standard Markov chain?
  • A Hidden Markov Model differs from a standard Markov chain in that it incorporates hidden states that cannot be directly observed, while standard Markov chains only deal with observable states. In an HMM, the system transitions between these hidden states according to certain probabilities, and observable outputs depend on which hidden state is currently active. This added layer of complexity allows HMMs to model real-world processes more effectively where direct observation is not possible.
• What roles do emission probabilities and state transition probabilities play in the functionality of a Hidden Markov Model?
  • Emission probabilities determine how likely an observable output is given a specific hidden state, while state transition probabilities define how likely it is to move from one hidden state to another. Together, these probabilities form the core mechanism of an HMM, allowing it to represent complex systems and generate sequences of observations that correspond to underlying hidden processes. Understanding both types of probabilities is crucial for analyzing and interpreting the behavior modeled by HMMs.
• Evaluate the significance of algorithms like Baum-Welch and Viterbi in working with Hidden Markov Models, particularly in practical applications.
  • Algorithms like Baum-Welch and Viterbi are essential for training and decoding in Hidden Markov Models. The Baum-Welch algorithm is used to estimate the parameters of an HMM from observed data by maximizing the likelihood of the observations under the model. On the other hand, the Viterbi algorithm helps in determining the most likely sequence of hidden states given a set of observations. These algorithms make HMMs powerful tools for practical applications such as speech recognition and bioinformatics by enabling efficient parameter estimation and prediction based on sequential data.

Related terms

Markov Chain: A Markov Chain is a stochastic model describing a sequence of possible events where the probability of each event depends only on the state attained in the previous event.

Emission Probability: Emission probability refers to the likelihood of observing a specific output given the current hidden state in a Hidden Markov Model.

State Transition Probability: State transition probability defines the likelihood of moving from one hidden state to another in a Markov process.