Editing Hidden Markov Models (section)

== Introduction ==

A '''Hidden Markov Model (HMM)''' is a temporal probabilistic model characterized by a sequence of hidden states, which are concealed from direct observation but influence observable variables generated by these states. <ref>Russell, S. J. (2010). ''Artificial intelligence a modern approach''. Pearson Education, Inc..</ref> These hidden states adhere to the Markov property, signifying that the future state depends solely on the current state. Given the unavailability of direct access to the underlying states in a specific model, the learning process involves aligning the HMM with observable states.<ref>Eddy, S. R. (1996). Hidden markov models. ''Current opinion in structural biology'', ''6''(3), 361-365.</ref><ref name=":0">Rabiner, L. R. (1989). A tutorial on hidden Markov models and selected applications in speech recognition. ''Proceedings of the IEEE'', ''77''(2), 257-286.</ref> 

In many real-world scenarios, concealed variables are only discernible through their emitted outcomes. For example, in speech recognition, we often observe the speech signal of a word rather than the specific phoneme states that constitute the hidden states. To decipher the sequence of phonemes leading to a particular word, HMMs facilitate the modeling of the relationship between observable and unobservable variables.<ref>Juang, B. H., & Rabiner, L. R. (1991). Hidden Markov models for speech recognition. ''Technometrics'', ''33''(3), 251-272.</ref> 

Furthermore, the application of HMMs has exhibited connections with [[Dynamic Time Warping]], offering insights into their utility across diverse domains.<ref>Juang, B. H. (1984). On the hidden Markov model and dynamic time warping for speech recognition—A unified view. ''AT&T Bell Laboratories Technical Journal'', ''63''(7), 1213-1243.</ref><ref>Fang, C. (2009). From dynamic time warping (DTW) to hidden markov model (HMM). ''University of Cincinnati'', ''3'', 19.</ref>