# HMM and non categorical values of emmision (MATLAB)

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

• I mean that observed variable and its emission is discrete with possible categories – Celdor Aug 30 '16 at 14:12
• 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)." – havakok Aug 30 '16 at 14:26
• They do suggest this toolbox instead. – havakok Aug 30 '16 at 14:27
• @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). – Celdor Aug 31 '16 at 8:34
• 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? – havakok Aug 31 '16 at 15:18