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

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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);
[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;

Accepted Answer

MathWorks Support Team
MathWorks Support Team on 30 Apr 2021 at 4:00
Edited: MathWorks Support Team on 30 Apr 2021 at 9:12
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.');
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;
% total quantization error in indexing
fprintf('Total quantization error in indexing: %f\n', (quant_error));
[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'))';
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));
title('Estimated Prob. Dist. Functions of State Emission values');
xlabel('Emission value');
ylabel('PDF value');
This toolbox may also be of interest:
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.
  1 Comment
haseeb shehzad
haseeb shehzad on 16 Nov 2018
Hi, would it make sense if I use the
in 'hmmdecode' or 'hmmviterbi' functions generated in 'run_hmm' function given that I have used the 'run_hmm' for continous values?

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