How can I use continuous sequence values with HMMESTIMATE in the Statistics Toolbox 7.1 (R2009a)?

I am not able to run HMMESTIMATE with a sequence array containing floating values, e.g. in the following code:

trans = [0.95,0.05; 0.10,0.90];

emis = [1/6 1/6 1/6 1/6 1/6 1/6;
1/10 1/10 1/10 1/10 1/10 1/2];
[seq, states] = hmmgenerate(1000, trans, emis);

seq=seq*0.618;

[t_est, e_est] = hmmestimate(seq, states);

I receive the following error:

ERROR: ??? Attempted to access E(1,2.472); index must be a positive integer or logical.

Error in ==> hmmestimate at 170
E(states(count),seq(count)) = E(states(count),seq(count)) + 1;

Answer 1

[MathWorks Support Team]

The ability to do hidden Markov model estimation for continuous-valued emissions is not available in the Statistics Toolbox 7.1 (R2009a).

As a workaround, you can use the following function to see the probability density function estimates of the state's emission values. The function uses quantization to collect values into different bins, and indexes the bins. These indexed bin values are used to create a new sequence array, and HMMESTIMATE is run as usual.

For probability density function estimation, a histogram is obtained and smoothed.

Inputs to the function: Sequence array, States array, and the number of bins to quantize with.

Outputs of the function: Transition matrix, Emission matrix, bin centre array, smoothed estimated PDF matrix.

function [transition_mat, emission_mat, bins, em_pdf] = run_hmm(s_seq, s_mat, x)

% check if number of bins is an integer
if abs(x-round(x))~=0
    disp('Argument must be an integer! Stopping.');
    return;
end


nBins = x;

% obtain histogram for the sequence array
[freq, bins] = hist(s_seq, nBins);

% obtain the bin distance
bin_dist = (bins(2)-bins(1));
fprintf('Bin width: %f\n', bin_dist);

quant_error = 0;

% indexing each float value to the nearest bin
for i = 1:length(s_seq)
    for j = 1:nBins
        dist = abs(bins - s_seq(i));
        [minval, indx] = min(dist);
        quant_error = quant_error + (s_seq(i) - bins(indx));
        s_seq_ind(i) = indx;
    end
end

% total quantization error in indexing
fprintf('Total quantization error in indexing: %f\n', (quant_error));

% obtain HMMESTIMATE
[transition_mat, emission_mat] = hmmestimate(s_seq_ind, s_mat);


% smoothing filter coeffs. to obtain PDF plot
B = (0.3905/4)*[1 2 1];
A = [1 -0.9428 .3333];

% shifting bins to account for filtering delay
bins = bins+(1.1*bin_dist);

% smoothing the histogram
em_pdf = (filter(B, A, emission_mat'))';

figure;
hold on;
legend_str = {};
for i = 1:size(emission_mat,1)
    %normalizing to PDF
    em_pdf(i, :) = em_pdf(i, :)/(bin_dist*sum(em_pdf(i, :)));

    % to get changing color for each State's PDF
    color = (i-1)/size(emission_mat,1);

    % plotting each State's PDF
    plot(bins, em_pdf(i, :), 'Color', [sqrt(color), color, (color)^2]);

    % concatenating to the legend string
    legend_str{i} = strcat('State ', num2str(i));
end

grid;

legend(legend_str);
title('Estimated Prob. Dist. Functions of State Emission values');
xlabel('Emission value');
ylabel('PDF value');

end

This toolbox may also be of interest:

https://www.cs.ubc.ca/~murphyk/Software/HMM/hmm.html

Note that The MathWorks does not guarantee or warrant the use or content of these submissions. Any questions, issues, or complaints should be directed to the contributing author.