Hidden Markov model: Difference between revisions

Revision as of 19:01, 22 March 2023

Revision as of 21:01, 22 March 2023

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== Extensions ==

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In the hidden Markov models considered above, the state space of the hidden variables is discrete, while the observations themselves can either be discrete (typically generated from a [[categorical distribution]]) or continuous (typically from a [[Gaussian distribution]]). Hidden Markov models can also be generalized to allow continuous state spaces. Examples of such models are those where the Markov process over hidden variables is a [[linear dynamical system]], with a linear relationship among related variables and where all hidden and observed variables follow a [[Gaussian distribution]]. In simple cases, such as the linear dynamical system just mentioned, exact inference is tractable (in this case, using the [[Kalman filter]]); however, in general, exact inference in HMMs with continuous latent variables is infeasible, and approximate methods must be used, such as the [[extended Kalman filter]] or the [[particle filter]].