Hidden Markov Model

Definition

A Hidden Markov Model (HMM) is a statistical model that represents systems that are assumed to be a Markov process with unobservable (hidden) states. HMMs are widely used in various fields such as speech recognition, natural language processing, and bioinformatics, as they provide a way to model temporal sequences where the states of the system are not directly visible but can be inferred through observed data.

5 Must Know Facts For Your Next Test

1. HMMs consist of two main components: hidden states and observed outputs, where the states are not directly observable.
2. The model relies on two key assumptions: the Markov property and the assumption of conditional independence of observations given the hidden state.
3. HMMs use transition probabilities to describe the likelihood of moving from one hidden state to another, which is crucial for modeling sequences over time.
4. Training an HMM involves estimating its parameters, typically using algorithms like the Baum-Welch algorithm, which applies expectation-maximization techniques.
5. The Viterbi Algorithm plays a vital role in decoding HMMs by determining the most likely sequence of hidden states based on observed data.

Review Questions

• How do Hidden Markov Models utilize the concept of hidden states to infer information from observable data?
  • Hidden Markov Models leverage hidden states to represent underlying processes that generate observable outputs. The model operates on the premise that while the hidden states themselves are not directly visible, they influence the observed data through defined emission probabilities. By analyzing these observations and using transition probabilities between hidden states, HMMs can infer the most likely sequence of hidden states, thus providing insights into complex processes.
• Compare and contrast Hidden Markov Models and traditional Markov Chains in terms of their structure and application.
  • Hidden Markov Models differ from traditional Markov Chains primarily in that they include unobservable states influencing observable outputs. While Markov Chains assume complete visibility of states and transitions based solely on those states, HMMs account for scenarios where states are hidden, making them more suitable for applications such as speech recognition and biological sequence analysis. This added complexity allows HMMs to model more intricate systems where direct observation is not feasible.
• Evaluate the impact of using the Viterbi Algorithm in conjunction with Hidden Markov Models for applications like speech recognition.
  • The Viterbi Algorithm significantly enhances the utility of Hidden Markov Models in applications like speech recognition by efficiently determining the most probable sequence of hidden states that produced a given set of observations. This algorithm addresses computational challenges associated with direct enumeration of all possible state sequences, providing a feasible solution to real-time processing needs. Its integration with HMMs leads to improved accuracy and performance in recognizing spoken language patterns, demonstrating its critical role in advancing technology in this domain.

Related terms

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

Emission Probability: Emission probability in HMMs refers to the likelihood of observing a particular output from a given hidden state.

Viterbi Algorithm:

The Viterbi Algorithm is an efficient dynamic programming algorithm used to find the most probable sequence of hidden states in an HMM given a sequence of observed events.