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Hidden markov model - for learning time dependend structures
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A=HMM(H) returns a hidden markov model object. Its based on code from a
lecture of Sam Roweis.
The data is assumed to be cell arrays or a matrix with positive numbers
as entries and zeros, where there is no sequence entry.
Example:
These representations are equivalent:
Y{1} = [1,2,3,1,4,1]
Y{2} = [1,1,1,3]
and
Y = [1,2,3,1,4,1;1,1,1,3,0,0]
The testing methode computes the most probable sequence of states for
given symbol sequence and its loglikelihood.
Hyperparameters, and their defaults
alpha = [] -- indices which refer to cell array components, that are
the charakters of the alphabet.
The training sequnces have to be vectors of indices.
tol = 1e-5 -- convergence criterion. fractional change of loglokelihood,
which stops the iteration
A = 2 -- number of states or the transition probabilities
updateflags = [1,1,1] -- controls the update of parameters
it is a three-vector whose elements
control the updating of [A,pi,B]
nonzero elements mean update that parameter
testing_mode=0 Determines the testing mode. testing_mode=0
estimates the most probable path with their loglikelihoods
given the sequences. testing_mode=1 generates
sequences with the model. In this case the data
object passed to the hmm should be d([m,l]),
where m is the number of training sequences to
be generated and l is the length of the
sequences
maxiter = 100 -- maximal number of iterations for EM-algorithm
Model
alpha.Y -- observation emission probabilities
alpha.X -- state transition probabilities
pi -- initial state prior probabilities
LL -- log likelihood curve
M -- number of symbols
Methods:
train, test
Example: simulating fair/unfair dice
prob distributions for fair and unfair die
unfair = [1,1,1,1,100,100]; unfair = unfair/sum(unfair);
fair = [1,1,1,1,1,1]; fair = fair/sum(fair);
max_l = 30; maximum sequence length
X = []; stay_prob = 0.9; probability to stay in the same state
for i = 1:200 generate 100 sequences
l = round(rand*10)+1;
fairdice = 1; we start with the fair dice
pi = []; seq = [];
for j = 1:l
tmp = rand;
if fairdice
for k = 1:length(fair), if tmp < sum(fair(1:k)), break; end , end
seq = [seq,k];
change dice?
if rand > stay_prob, fairdice = 0; end
else
for k = 1:length(unfair), if tmp < sum(unfair(1:k)),break; end , end
seq = [seq,k];
change dice?
if rand > stay_prob, fairdice = 1; , end
end
end
X = [X; seq , zeros(1,max_l+1-size(seq,2))];
end
d = data(X);
[r a] = train(hmm,d)
WARNING: If you get errors, it may be due to the fact, that data object
in spider are not suited to store cell arrays.
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Reference : A tutorial on Hidden Markov Models and Selected Applications in Speech Recognition |
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Author : Lawrence R. Rabiner |