Hidden Markov model
Statistical Markov model / From Wikipedia, the free encyclopedia
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A hidden Markov model (HMM) is a Markov model in which the observations are dependent on a latent (or "hidden") Markov process (referred to as ). An HMM requires that there be an observable process
whose outcomes depend on the outcomes of
in a known way. Since
cannot be observed directly, the goal is to learn about state of
by observing
By definition of being a Markov model, an HMM has an additional requirement that the outcome of
at time
must be "influenced" exclusively by the outcome of
at
and that the outcomes of
and
at
must be conditionally independent of
at
given
at time
Estimation of the parameters in an HMM can be performed using maximum likelihood. For linear chain HMMs, the Baum–Welch algorithm can be used to estimate the parameters.
Hidden Markov models are known for their applications to thermodynamics, statistical mechanics, physics, chemistry, economics, finance, signal processing, information theory, pattern recognition—such as speech,[1] handwriting, gesture recognition,[2] part-of-speech tagging, musical score following,[3] partial discharges[4] and bioinformatics.[5][6]