MATLAB: Does the “SEQ” output from the HMMGENERATE function from the Statistics Toolbox not return emission probabilty

docemissionhmmgenerateStatistics and Machine Learning Toolboxsymbols

According to the documentation for HMMGENERATE:

 [seq, states] = hmmgenerate(len,TRANS,EMIS) generates a random sequence of emissions, seq, and 
 a random sequence of states, states, from a Markov model specified by transition probability 
 matrix TRANS and emission probability matrix EMIS. TRANS(i,j) is the probability of transition
from state i to state j. EMIS(k,l) is the probability that symbol l is emitted from state k.

It seems the matrix "SEQ" should be a matrix of probabilties and not symbols.

Best Answer

This bug has been fixed for Release 14 (R14). For previous releases, documentation on the HMMGENERATE function is missing from the Statistics Toolbox.

The output "SEQ" from the HMMGENERATE function should return a random sequence of emission symbols. The documentation should mention "random sequence of emission symbols".

Related Solutions

MATLAB: What are the formats of the “seq” and “states” vectors used by the HMMESTIMATE function in the Statistics Toolbox 4.0 (R13)

To explain the format of the "seq" and "states" parameters of the HMMESTIMATE function, a hidden Markov model will be used.

First, take a non-fair coin, with a probability "p" of coming up heads. The two states shall be defined as "heads" and "tails", and the transition from one state to the next is defined by the next flip of the coin. Therefore, the transition matrix would be:

 TM = [p 1-p; ...
 p 1-p];

Assume that whenever the coin is in state 1, the value of the model is 2, and whenever the coin is in state 2, the value of the model is 1 or 3, with equal probability. Therefore, the emission matrix will be:

 E = [0 1 0; ...
 1/2 0 1/2];

If you simulate the hidden Markov model states using the TM matrix (choosing a state at random each simulation step based on the probabilities given in TM), and record the state of the model at each simulation step, the "states" parameter for HMMESTIMATE is obtained. Likewise, if you take that "states" parameter and generate a random value for the model at each simulation step (using the probabilities from the E matrix), the vector of sequence values "seq" is obtained.

To clarify, if the coin is twice as likely to come up heads as tails, you would expect "states" to have twice as many 1's as 2's. You would also expect that the "seq" vector will be one-fourth 1, one-half 2, and one-fourth 3:

p = 2/3; % (1-p) = tails probability = 1/3 = p/2 = half the heads probability
TM = [p 1-p; ...
p 1-p];
E = [0 1 0; ...
1/2 0 1/2];
[SEQ, STATES] = hmmgenerate(1000, TM, E); % Generate 1000 simulation steps
[TM_est, E_est] = hmmestimate(SEQ, STATES) % TM_est should be roughly TM and E_est should be roughly E

MATLAB: Am I unable to reproduce the random numbers generated by the GAMRND function in the Statistics Toolbox

This change has been incorporated into the documentation in Release 14 Service Pack 3 (R14SP3). For previous releases, read below for any additional information:

We have verified that the documentation for reproducing outputs of random number generator functions in the Statistics Toolbox is incomplete.

To reproduce the output of GAMRND, you need to set the state of both RAND and RANDN. Below is an example to illustrate this:

state = 0
rand('state', state);
randn('state', state);
n1 = gamrnd(1,1)

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Related Solutions

MATLAB: What are the formats of the “seq” and “states” vectors used by the HMMESTIMATE function in the Statistics Toolbox 4.0 (R13)

MATLAB: Am I unable to reproduce the random numbers generated by the GAMRND function in the Statistics Toolbox

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