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I read through a tutorial on MATLAB website on HMM. It is not easy to digest so I had to look for other sources and found a good explanation on Wikipedia (HMM). Everything is more understandable but there are still a couple of things I find unclear.

Please correct me if I ma wrong, in the example:

  • the states are X = {1, 2} (red, green)
  • probability that: system stays in red = 0.9, moves from red to green = 0.1, stays in green = 0.95, moves from green to red = 0.05. I understand rows and columns of TRANS correspond to state before and after transition
  • because of two states, transition matrix T is 2x2
  • Y = {1,2,3,4,5,6} - observations
  • emission in the example is categorical
  • probability distribution is determined in EMIS matrix
  • the matrix EMIS is 2x6 due to 2 states and 6 different observations per state; probability of emission depends on a state and can be different in each state: in red, probability of each observation Y = {1,2,3, ..., 6} is equal; in green probability is weighted towards 1.

Wikipedia also explains that probability that we observe a particular output doesn't have to be categorical. In the example on MATLAB website I understand that emission is categorical. How can I chnage it to apply continuous probability distribution so that I would have similar outputs? I am thinking of Guassian distr. or Guassian Mixture distr. to increase probability of Y = 1.

Thanks

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    $\begingroup$ I mean that observed variable and its emission is discrete with possible categories $\endgroup$ – Celdor Aug 30 '16 at 14:12
  • $\begingroup$ Observe answer by MathWorks Support Team here. apparently "The ability to do hidden Markov model estimation for continuous-valued emissions is not available in the Statistics Toolbox 7.1 (R2009a)." $\endgroup$ – havakok Aug 30 '16 at 14:26
  • $\begingroup$ They do suggest this toolbox instead. $\endgroup$ – havakok Aug 30 '16 at 14:27
  • $\begingroup$ @havakok Thanks for the answer and link to another toolbox. I guess they have not changed much since 2012. We currently use MATLAB 2015 SP1 with Statistics and Machine Learning Toolbox Version 10.0 (R2015aSP1). $\endgroup$ – Celdor Aug 31 '16 at 8:34
  • $\begingroup$ I am sorry I could not help any further. I could not find any other reference to any other toolkit. Maybe the correct procedure is posting to whoever is releasing this toolbox? $\endgroup$ – havakok Aug 31 '16 at 15:18

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