Question

What is the result of applying the Viterbi algorithm to a Hidden Markov Model given an observed sequence and a model structure?

Accepted Answer

The result of applying the Viterbi algorithm to a Hidden Markov Model is the single most likely sequence of hidden states that explains a given sequence of observations. A Hidden Markov Model represents a system where you observe outputs but cannot directly see the underlying processes, called hidden states, that generate them. The algorithm identifies the optimal path through these hidden states by calculating the maximum probability for reaching every state at every time step. It works through dynamic programming, which is a method of breaking a complex problem into simpler subproblems and storing their results to avoid redundant calculations. At each step, the algorithm records the highest probability path to arrive at the current state, known as the Viterbi path. By keeping track of the previous states that led to these maximum probabilities using a backpointer, the algorithm can trace back from the final step to the beginning once the entire observation sequence is processed. This process reconstructs the entire sequence of states that possesses the highest joint probability given the model parameters and the observations. For example, if you observe the weather indicators of dry grass and wet ground over several days, the Viterbi algorithm identifies the most probable underlying sequence of actual weather states, such as sunny or rainy, that could have caused those observations.

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What is the result of applying the Viterbi algorithm to a Hidden Markov Model given an observed sequence and a model structure?