hmmFitEm fails in simple case

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What steps will reproduce the problem?
1. Running MATLAB 2012A on win7.
2. call model = hmmFitEm(X, 25, 'gauss'); where X = 1x8,000 vector of values 
between -3 and +3 on a grid with 0.25 spacing.
3. Following output seen:

Error using chol
Matrix must be positive definite.

Error in gaussLogprob (line 52)
    R    = chol(Sigma);

Error in mixGaussInferLatent (line 17)
  logPz(:, k) = logMix(k) + gaussLogprob(mu(:, k), Sigma(:, :, k), X);

Error in mixGaussFit>estep (line 52)
[weights, ll] = mixGaussInferLatent(model, data);

Error in emAlgo (line 62)
    [ess, ll] = estep(model, data);

Error in mixGaussFit (line 25)
[model, loglikHist] = emAlgo(model, data, initFn, @estep, @mstep , ...

Error in hmmFitEm>initWithMixModel (line 244)
    mixModel    = mixGaussFit(stackedData, nstates,  'verbose', false, 'maxIter', 10);

Error in hmmFitEm>initGauss (line 146)
        model = initWithMixModel(model, data);

Error in hmmFitEm>@(m,X,r)initFn(m,X,r,emissionPrior) (line 45)
initFn = @(m, X, r)initFn(m, X, r, emissionPrior);

Error in emAlgo (line 56)
model = init(model, data, restartNum);

Error in hmmFitEm (line 46)
[model, loglikHist] = emAlgo(model, data, initFn, @estep, @mstep, EMargs{:});


model = hmmFitEm(X, config.K, 'gauss');

Original issue reported on code.google.com by hughchri...@gmail.com on 14 Nov 2012 at 1:23

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I have this working now, but something funny is going on...

More general example than provided in hmmGaussTest.m is below:

nDays = 252;
nObsPerDay = 855;
z = 1;                  %z = 1 is univariate, z> 1 is multivariate
thisPdf = @rand;
data = repmat({thisPdf(z, nObsPerDay)}, [nDays 1]);
kStates = 25;
model = hmmFitEm(data, kStates, 'gauss');

Original comment by hughchri...@gmail.com on 21 Nov 2012 at 2:34

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Having said that when I try with "real data" i get the same error as above for 
chol(Sigma) with Sigma = 0, even though the synthetic data (with thisPdf = 
@randn) works fine.

any suggestions? thanks

Original comment by hughchri...@gmail.com on 21 Nov 2012 at 2:54

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[deleted comment]

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The problem seems to be related to specifying too large a number of states for 
a given data set.

When Mu and Sigma can not be assigned correctly (ie are set to NaN or zero or 
-inf etc), they cause the code to fail in odd ways...

It would be nicer if at the point of assigning unsuitable parameters, the code 
gave a sensible error message saying that the data will not support this number 
of states.

The largest value for kStates I can get to run is 4, which does not seem very 
many. Zoubin G's code allows much larger values (~500) to run, but without 
really digging down into the code, I dont know why this is.

Original comment by hughchri...@gmail.com on 21 Nov 2012 at 3:20

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Moved to GitHub: https://github.com/probml/pmtk3/issues/49

Original comment by irosen on 4 Jan 2014 at 2:37