def learn(self, oseq, nbIter=1):
'''
Build the new model that increase the probability of observing the sequence o
'''
T = len(oseq)
#self.N = hmm.stateSize
oseqInd = range( T )
#self.stateInd = range( self.N )
#interInd = range( nbIter )
xi = np.zeros((T-1, self.N, self.N)) # 3-D arrays : (T-1) * self.N * self.N
gamma = np.zeros((T, self.N))
sumXi = np.zeros((self.N, self.N))
sumGamma = np.zeros(self.N)
fwbw = ForwardBackward(self.hmm, oseq, True, True)
def calculateXi() :
'''
Compute the xi arrays
'''
po = fwbw.probability
for t in oseqInd[:T-1] : # last transition start at T-1 to T.
# we have T-1 possible transitions
for i in self.self.stateInd :
for j in self.stateInd : # x[t][i][j] probability of being in state i at time t and in state j at time t+1
xi[t, i, j] = fwbw.getAlphati(t, i) * self.hmm.getAij(i, j) * self.hmm.getBik(j, oseq[t]) * fwbw.getBetatj(t+1, j) / po
def calculateGamma() :
'''
Compute the gamma array
'''
for t in oseqInd[:T-1] :
for i in self.stateInd :
for j in self.stateInd :
gamma[t, i] += xi[t, i, j] # The nb transition from i at time t
t += 1
for j in self.stateInd : # t = T, probability that the last observable will be produce by State j
for i in self.stateInd :
gamma[t][j] = xi[t-1][i][j];
calculateXi()
calculateGamma()
for i in self.stateInd : # compute the number of transition from state i to state j
for j in self.stateInd :
for t in oseqInd[:T-1] :
sumXi[i, j] += xi[t, i, j];
for i in self.stateInd : # compute the number of transition from state i
for t in oseqInd[:T-1] :
sumGamma[i] += gamma[t, i];
newHmm = HMM(self.hmm.stateSize, self.hmm.obsSize)
for i in self.stateInd :
newHmm.setPii( i, gamma[1, i] )
for j in self.stateInd :
newHmm.setAij(i, j, sumXi[i, j] / sumGamma[i] ); # aij
for k in range(newHmm.obsSize) : #compute bik
sumGammaOk = 0.0;
t = 0;
for t in oseqInd : #compute the number of times ot is produced by state i
ot = oseq[t]
if ot == k :
sumGammaOk += gamma[t][i];
#System.out.println(" obs " + ot );
newHmm.setBik(i, k, sumGammaOk / ( sumGamma[i] + gamma[T-1][i] ) ) # we add the last
return newHmm
pi = 0.3333333333 # Equi probabilty
aij = 0.3333333333 # Equi probability
nbState = 3
nbObs = 2
obs = ["H", "T"]
opdf = " 0.5 0.5\n 0.75 0.25\n 0.25 0.75"
bik = np.genfromtxt(StringIO(opdf), delimiter=' ')
oseq = np.array([0, 0, 0, 0, 1, 0, 1, 1, 1, 1])
hmm = HMM(nbState, nbObs)
for i in range( nbState ):
hmm.setPii(i, pi)
for k in range( nbObs ):
hmm.setBik( i, k, bik[i,k] )
for i in range( nbState ):
for j in range( nbState ):
hmm.setAij(i, j, aij)
hmm.display()
bestPath = viterbi.viterbiProcessing(hmm, oseq)
print("Best Path : {0}, p = {1}".format(bestPath[0], bestPath[1]))
fwbw = ForwardBackward(hmm, oseq, False, True)