Three fundamental problems of HMM

Three fundamental problems of HMM that are to be solved, Evaluation, Decoding and Learning problems of HMM, How these HMM fundamental problems are related to NLP applications

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Three fundamental problems of HMM

For the HMM to be useful in real-world applications in solving problems like sequence labeling, following three fundamental problems to be solved;

• Evaluation problem: Given an HMM λ = (A, B, π) and an observation sequence O = o₁, o₂, …, o_T, how do we compute the probability that the observed sequence was produced by the model. In other words, it is about determining the likelihood of the observation sequence.

• Question answered by Evaluation problem: What is the probability that a particular sequence of symbols is produced by a particular model?

• What is it? – More details here

• Decoding problem: Given an HMM λ = (A, B, π) and an observation sequence O = o₁, o₂, …, o_T, how do we choose the corresponding optimal hidden state sequence (most likely sequence) Q = q₁, q₂, …, q_T that can best explain the observations.
• Question answered by Decoding problem: Given a sequence of symbols (your observations) and a model, what is the most likely sequence of states that produced the sequence. 

• What is it? - More details here

• Learning problem: Given a sequence of observation O = o₁, o₂, …, o_T, estimate the transition and emission probabilities that are most likely to give O. that is, using the observation sequence and HMM general structure, determine the HMM model λ = (A, B, π) that best fit training data.
• Question answered by Learning problem: Given a model structure and a set of sequences, find the model that best fits the data.  

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