## 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

##
**Three fundamental
problems of HMM**

**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*)*, 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.*O = o*_{1}, o_{2}, …, o_{T}

**Question answered by Evaluation problem:***W**hat is the probability that a particular sequence of symbols is produced by a particular model?*

**Decoding problem**: Given an HMM*λ = (A, B,**π*and an observation sequence*)*, how do we choose the corresponding optimal hidden state sequence (most likely sequence)*O = o*_{1}, o_{2}, …, o_{T}that can best explain the observations.*Q = q*_{1}, q_{2}, …, q_{T}**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.*

**Learning problem**: Given a sequence of observation, estimate the transition and emission probabilities that are most likely to give*O = o*_{1}, o_{2}, …, o_{T}. that is, using the observation sequence and HMM general structure, determine the HMM model*O**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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