CRF and HMM probabilistiv models

A conditional random field (CRF) is a type of discriminative probabilistic model most often used for the labeling or parsing of sequential data, such as natural language text or biological sequences. Specifically, CRFs find applications in shallow parsing, named entity recognition and gene finding, among other tasks, being an alternative to the related hidden Markov models.

http://en.wikipedia.org/wiki/Conditional_random_field


A hidden Markov model (HMM) is a statistical Markov model in which the system being modeled is assumed to be a Markov process with unobserved state. A HMM can be considered as the simplest dynamic Bayesian network.

In a regular Markov model, the state is directly visible to the observer, and therefore the state transition probabilities are the only parameters. In a hidden Markov model, the state is not directly visible, but output, dependent on the state, is visible. Each state has a probability distribution over the possible output tokens. Therefore the sequence of tokens generated by an HMM gives some information about the sequence of states. Note that the adjective 'hidden' refers to the state sequence through which the model passes, not to the parameters of the model; even if the model parameters are known exactly, the model is still 'hidden'.

Hidden Markov models are especially known for their application in temporal pattern recognition such as speech, handwriting, gesture recognition, part-of-speech tagging, musical score following, partial discharges and bioinformatics.

http://en.wikipedia.org/wiki/Hidden_Markov_model

Consider two friends, Alice and Bob, who live far apart from each other and who talk together daily over the telephone about what they did that day. Bob is only interested in three activities: walking in the park, shopping, and cleaning his apartment. The choice of what to do is determined exclusively by the weather on a given day. Alice has no definite information about the weather where Bob lives, but she knows general trends. Based on what Bob tells her he did each day, Alice tries to guess what the weather must have been like.

A Markov chain is a random process with the property that the next state depends only on the current state.

A finite state machine can be used as a representation of a Markov chain