Hidden Markov Models (HMM) and Viterbi Algorithm Hidden Markov models (HMMs) are a powerful tool in machine learning for analyzing and processing sequences o...
Hidden Markov models (HMMs) are a powerful tool in machine learning for analyzing and processing sequences of data. These models consist of two main components: hidden states and transition probabilities.
Hidden States:
Hidden states represent the underlying, unobservable underlying events or processes that generate the observed sequence. Imagine hidden states like the state of a coin toss (heads or tails) or the internal conditions of a machine.
Transition Probabilities:
Transition probabilities describe the probability of the hidden state transitioning to another state in a given time step. These probabilities are crucial for understanding how the system evolves over time. For example, in a language model, transition probabilities would represent the probability of a word being emitted based on the previous word.
Viterbi Algorithm:
The Viterbi algorithm is a dynamic programming technique used to find the most likely sequence of hidden states for an HMM. It iteratively updates the probability of each state in the sequence, starting from the initial state and moving backward in time. The algorithm employs a technique called smoothing to account for the uncertainty in the transition probabilities.
Think of the Viterbi algorithm as a detective investigating a mystery scene. Starting with the initial clues, the algorithm explores different possibilities and updates the probability of each state based on the observed sequence. By following the most likely paths and accounting for uncertainties, the Viterbi algorithm can uncover the hidden sequence that generated the observed sequence.
In simpler terms:
An HMM is a model that describes a sequence of events where the state of the system changes between hidden states over time.
Hidden states are the internal conditions of the system that we cannot directly observe.
Transition probabilities describe how likely it is for the system to transition between different states.
The Viterbi algorithm is a computational technique used to find the most likely sequence of hidden states for an HMM.
It iteratively updates the probability of each state in the sequence, considering both the transition probabilities and the observed sequence