Hidden Markov model

A probabilistic model of sequences in which each observation is generated by an unobserved state, and state transitions follow a Markov process.

Markov chain: A stochastic process whose next state depends only on its current state. The hidden state sequence follows this memoryless transition structure.
Conditional probability: The probability of an event given that another event has occurred. State transitions and observation emissions are expressed as conditional probabilities.
Speech recognition: The computational task of converting spoken language into written words. Hidden states can represent phonetic units underlying acoustic observations.
Conditional random field: A discriminative probabilistic model that predicts structured labels conditioned on observed data. Unlike a hidden Markov model, it models label probabilities directly given the full observation sequence.
Transition matrix: A matrix whose entries give probabilities of moving between states in a stochastic process. Its entries specify the probabilities of each hidden-state change.
Latent variable: A variable in a statistical model that is not directly observed. The hidden states are latent variables inferred from observed sequences.
Part-of-speech tagging: The assignment of grammatical categories, such as noun or verb, to words in a text. Words serve as observations while grammatical tags form the hidden sequence.
Hidden semi-Markov model: A sequence model that explicitly represents the duration of each hidden state. It relaxes the ordinary model's implied geometric state-duration distribution.
Emission probability: The probability of an observation given the state that produced it. These probabilities connect unobserved states to measured sequence elements.
Bayes' theorem: A rule for updating probabilities of hypotheses using observed evidence. Inference uses observed data to revise probabilities over hidden states.

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