Hidden Markov model: Difference between revisions

Revision as of 14:45, 12 November 2004

Revision as of 14:05, 14 November 2004

Line 1:

A '''hidden Markov model''' ('''HMM''') is a [[statistical model]] where the system being modelled is assumed to be a [[Markov process]] with unknown parameters, and the challenge is to determine the hidden parameters, from the [[observable]] parameters, based on this assumption. The extracted model parameters can then be used to perform further analysis, for example for [[pattern recognition]] applications.

The notions of observable and hidden are similar to [[Plato]]'s notions of shadows and forms in the [[Plato's allegory of the cave|allegory of the cave]]. The allegory claims that perceived reality is but the shadow thrown into the world of experience of a true reality which is inaccessible to direct sensory experience. `Forms' in the true reality contain the essence of a class of object which can be experienced only incompletely in perceived reality. This analogy is particularly strong when modelling parts of speech and sentences, and other entities which have a strongly defined semantic meaning independent of the myriad of possible representations in the observable sequence.

In a regular Markov model, the state is directly visible to the observer, and therefore the state transition probabilities are the only parameters. A '''hidden Markov model''' adds outputs: each state has a probability distribution over the possible output tokens. Therefore, looking at a sequence of tokens generated by an '''HMM''' does not directly indicate the sequence of states.

== A concrete example ==

Assume you have a friend who lives far away and who you call daily to talk about what each of you did that day. Your friend has only three things he's interested in: 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. You have no definite information about the weather where your friend lives, but you know general trends. Based on what he tells you he did each day, you try to guess what the weather must have been like.

You believe that the weather operates as a discrete [[Markov chain]]. There are two states, "Rainy" and "Sunny", but you cannot observe them directly, that is, they are ''hidden'' from you. On each day, there is a certain chance that your friend will perform one of the following activities, depending on the weather: "walk", "shop", or "clean". Since your friend tells you about his activities, those are the ''observations''. The entire system is that of a hidden Markov model (HMM).

''This examaple is further elaborated in [[Viterbi algorithm]] page''

==State transitions in a hidden Markov model==