def path(prior,transition_matrix,emission_matrix,observation_vector,scaling=True):
print "Starting Viterbi"
print observation_vector.shape
number_of_hidden_states=len(prior)
number_of_observations=len(observation_vector)
shape_delta=(number_of_hidden_states,number_of_observations)
shape_psi=shape_delta
delta=np.zeros(shape_delta)
psi=np.zeros(shape_psi,dtype=np.int)
scale=np.ones(number_of_observations)
optimum_path=np.zeros(number_of_observations,dtype=np.int)
'''1.Initialization'''
first_observation=observation_vector[0]
# first_observation,"Frist "
#print prior,"Prior"
#print emission_matrix[first_observation:,0],"Emission"
#print prior*emission_matrix[first_observation][0],"Prod"
#print emission_matrix[5:,0],"ya"
#print emission_matrix[0][first_observation],emission_matrix[0][first_observation].shape
for i in range(number_of_hidden_states):
delta[i][0]=prior[i]*emission_matrix[i][first_observation]
psi[i,0]=0
#print delta
if scaling:
[delta[:,0], n] = normalize(delta[:,0])
scale[0] = 1/n
'''2.Recursion'''
'''Currently non vectorized'''
for t in range(1,number_of_observations):
for j in range(0,number_of_hidden_states):
p=0
for i in range(0,number_of_hidden_states):
p=delta[i][t-1]*transition_matrix[i][j]*emission_matrix[j][observation_vector[t]]
if p>delta[j][t]:
delta[j][t]=p
psi[j][t]=i
#print delta
if scaling:
[delta[:,t], n] = normalize(delta[:,t])
scale[t] = 1/n
'''3.Termination'''
p_star=max(delta[:,number_of_observations-1])
optimum_path[number_of_observations-1]=np.argmax(delta[:,number_of_observations-1])
'''4.Path Backtracking'''
for t in range(number_of_observations-2,-1,-1):
optimum_path[t]=psi[optimum_path[t+1]][t]
'''Log Probability'''
if scaling:
loglik=-sum(np.log(scale))
else:
loglik=np.log(p_star)
return [optimum_path,delta,loglik]
def dhmm_em(observation_i,prior,transition_matrix,emission_matrix,max_iter,thresh):
previous_loglik = -np.inf
loglik = 0
converged = False
num_iter = 1
LL = []
while (num_iter <= max_iter) and not converged :
#E step
[loglik,exp_num_visits1,exp_num_visitsT,exp_num_trans,exp_num_emit]=compute_ess_dhmm(observation_i,prior,transition_matrix,emission_matrix, 0)
#[loglik, prior,A,B] = compute_ess_dhmm(observation_i,hidden,prior,transition_matrix,emission_matrix, 0)
#print "-----------ITERATION "+str(num_iter)+"----------"
#M Step
#prior = prior
prior=normalize(exp_num_visits1)[0]
#print "AFTER M STEP:",prior
transition_matrix = mk_stochastic(exp_num_trans)
#emission_matrix = mk_stochastic(B)
emission_matrix=mk_stochastic(exp_num_emit)
num_iter = num_iter + 1
[converged,decrease] = em_converged(loglik, previous_loglik, thresh,False)
previous_loglik = loglik
LL.append(loglik)
#print "Log Likelihood:",LL
return [LL, prior, transition_matrix, emission_matrix, num_iter]
def forward(prior,transition_matrix,emission_matrix,observation_vector,scaling=True):
number_of_hidden_states=len(prior)
number_of_observations=len(observation_vector)
shape_alpha=(number_of_hidden_states,number_of_observations)
alpha=np.zeros(shape_alpha)
scale=np.ones(number_of_observations)
xi_summed = np.zeros((number_of_hidden_states,number_of_hidden_states))
'''1.Initialization'''
t=0
first_observation=observation_vector[t]
alpha[:,t]=prior*emission_matrix[first_observation:,t]
if scaling:
[alpha[:,0], n] = normalize(alpha[:,0])
scale[0] = 1/n;
'''2.Induction'''
'''Currently Non-vectorized'''
for t in range(1,number_of_observations):
for j in range(0,number_of_hidden_states):
prob_sum=0
for i in range(0,number_of_hidden_states):
prob_sum+=alpha[i][t-1]+transition_matrix[i][j]
alpha[j][t]=prob_sum*emission_matrix[j][observation_vector[t]]
if scaling:
[alpha[:,t], n] = normalize(alpha[:,t])
scale[t] = 1/n
xi_summed = xi_summed + normalise(np.dot(alpha[:,t-1] ,emission_matrix[:,t].H) * transition_matrix)
'''3.Termination'''
if scaling:
loglik=sum(np.log(scale))
else:
loglik=np.log(sum(alpha[:,number_of_observations]))
return alpha,loglik
def backward(prior,transition_matrix,emission_matrix,observation_vector,scaling=True):
number_of_hidden_states=len(prior)
number_of_observations=len(observation_vector)
shape_alpha=(number_of_hidden_states,number_of_observations)
beta=np.ones(shape_alpha)
scale=np.ones(number_of_observations)
'''1.Initialization'''
'''We have already set beta as a sequence of 1's.'''
'''2.Induction'''
'''Currently Non-vectorized'''
for t in range(number_of_observations-1,1,-1):
for i in range(0,number_of_hidden_states):
beta_sum=0
for j in range(0,number_of_hidden_states):
beta_sum+=beta[i][t-1]+transition_matrix[i][j]
beta[i][t]=beta_sum*emission_matrix[j][observation_vector[t]]
if scaling:
[beta[:,t], n] = normalize(beta[:,t]);
scale[t] = 1/n;
import numpy as np from underflow_normalize import normalize,mk_stochastic from sample import * from dhmm_em import dhmm_em O = 3 Q = 2 #"true" parameters prior0 = normalize(np.random.rand(Q,1))[0] prior0 =np.array([.5,.5]) transmat0 = mk_stochastic(np.random.rand(Q,Q)) transmat0=np.array([[.3 ,.7],[.7,.3]]) obsmat0 = mk_stochastic(np.random.rand(Q,O)) obsmat0=np.array([[.333,.333,.333],[.333,.333,.333]]) print "True Parameters" print "-"*80 print "Prior:",prior0 print "Observation",obsmat0 print "Transition:",transmat0 # training data T = 1 nex =5 [obs,hidden] = sample_dhmm(prior0, transmat0, obsmat0, T, nex) #print hidden,obs# initial guess of parameters prior1 = normalize(np.random.rand(Q,1))[0]
def compute_ess_dhmm(observation_vector,prior,transition_matrix,emission_matrix, dirichlet):
#print "__________________________________"
#print "Observation:",observation_vector,"\n","Hidden:",hidden,"\n","Prior",prior,"\n","Transition",transition_matrix,"\n","Emission",emission_matrix
(S,O)=np.shape(emission_matrix)
exp_num_trans=np.zeros((S,S))
exp_num_visits1=np.zeros((1,S)).flatten(1)
exp_num_visitsT=np.zeros((1,S)).flatten(1)
exp_num_emit = dirichlet*np.ones((S,O))
loglik = 0
num_sequences=len(observation_vector)
for i in range(num_sequences):
observation_i=observation_vector[i]
#Number of observations
T=len(observation_i)
obslik = evaluate_pdf_cond_multinomial(observation_i, emission_matrix)
#E
[alpha, beta, gamma, xi,xi_summed,current_ll] = forward_backward(prior, transition_matrix, emission_matrix,observation_i,True,obslik)
loglik = loglik + current_ll
exp_num_trans = exp_num_trans + xi_summed
#print "EXPETCED VISISTS 1 BEFORE",exp_num_visits1
exp_num_visits1 += gamma[:,0]
#print "EXPETCED VISISTS 1 AFTER",exp_num_visits1
exp_num_visitsT = exp_num_visitsT + gamma[:,T-1]
#print "Visits 1",exp_num_visits1
#print "Visits T",exp_num_visitsT
#print "EXP NUM TRANS",exp_num_trans
for t in range(0,T):
o = observation_i[t]
exp_num_emit[:,o] = exp_num_emit[:,o] + gamma[:,t]
#print "Log Likelihood:",loglik
#print "Exp Num Transitions",exp_num_trans
#print "Exp Num Visits 1",exp_num_visits1
#print "Exp Num Visits T",exp_num_visitsT
#print "Exp Num Emit",exp_num_emit
#print "Xi Summed",xi_summed
#print "Sequence",np.array(observation_i)+1
#print "Alpha",alpha
#print "Beta",beta
#raw_input('After iteration%s'%i)
new_pi=normalize(gamma[:,0])[0]
new_A=xi_summed/np.sum(gamma,1)
(number_of_hidden_states,number_of_observation_states)=np.shape(emission_matrix)
B_new = np.zeros(np.shape(emission_matrix))
for j in xrange(number_of_hidden_states):
for k in xrange(number_of_observation_states):
numer = 0.0
denom = 0.0
for t in xrange(T):
if observation_i[t] == k:
numer += gamma[j][t]
denom += gamma[j][t]
B_new[j][k] = numer/denom
#print "******************************"
#print "New Pi:",new_pi
#print "New A:",new_A
#print "After normalizing",mk_stochastic(new_A)
return [loglik,exp_num_visits1,exp_num_visitsT,exp_num_trans,exp_num_emit]
def forward_backward(prior,transition_matrix,emission_matrix,observation_vector,scaling,obslik):
number_of_hidden_states=len(prior)
number_of_observations=len(observation_vector)
shape_alpha=(number_of_hidden_states,number_of_observations)
alpha=np.zeros(shape_alpha)
scale=np.ones(number_of_observations)
xi = np.zeros((number_of_observations,number_of_hidden_states,number_of_hidden_states))
gamma=np.zeros(shape_alpha)
gamma2=np.zeros(shape_alpha)
xi_summed=np.zeros((number_of_hidden_states,number_of_hidden_states))
'''Forwards'''
'''1.Initialization'''
t=0
'''
first_observation=observation_vector[t]
print "Forward Backward"
print prior,emission_matrix[first_observation:,t]
print prior*emission_matrix[first_observation:,t],np.shape(prior*emission_matrix[first_observation:,t])
print
print np.dot(prior,emission_matrix[first_observation:,t])
alpha[:,t]=np.dot(prior,emission_matrix[first_observation:,t])
'''
for i in range(0,number_of_hidden_states):
alpha[i][0]=prior[i]*emission_matrix[i][observation_vector[0]]
#print "Prior_i",prior[i]
#print "Obs",observation_vector[0]
#print emission_matrix[i][observation_vector[0]]
if scaling:
[alpha[:,0], n] = normalize(alpha[:,0])
scale[0] = n
else:
pass
'''2.Induction'''
'''Currently Non-vectorized'''
for t in range(1,number_of_observations):
for j in range(0,number_of_hidden_states):
prob_sum=0
for i in range(0,number_of_hidden_states):
prob_sum+=alpha[i][t-1]*transition_matrix[i][j]
alpha[j][t]=prob_sum*emission_matrix[j][observation_vector[t]]
if scaling:
[alpha[:,t], n] = normalize(alpha[:,t])
scale[t] = n
'''3.Termination'''
if scaling:
#print scale,"SCALE"
loglik=sum(np.log(scale))
else:
loglik=np.log(sum(alpha[:,number_of_observations-1]))
'''Backwards'''
beta=np.ones(shape_alpha)
gamma[:,number_of_observations-1] = normalize(alpha[:,number_of_observations-1] * beta[:,number_of_observations-1])[0]
'''1.Initialization'''
'''We have already set beta as a sequence of 1's.'''
'''2.Induction'''
'''Currently Non-vectorized'''
for t in range(number_of_observations-2,-1,-1):
b = beta[:,t+1] * obslik[:,t+1]
for i in range(0,number_of_hidden_states):
beta_sum=0
for j in range(0,number_of_hidden_states):
beta_sum+=(beta[j][t+1]*transition_matrix[i][j]*emission_matrix[j][observation_vector[t+1]])
beta[i][t]=beta_sum
if scaling:
[beta[:,t], n] = normalize(beta[:,t])
scale[t] = n
gamma[:,t] = normalize(alpha[:,t] * beta[:,t])[0]
a=alpha[:,t].reshape(number_of_hidden_states,1)
#print transition_matrix
#print b
#print obslik[:,t+1],"OBSLIK"
#print np.dot(a, b.conj().T[np.newaxis])
#print np.mat(alpha[:,t])*np.mat(b.conj().T)
xi_summed = xi_summed + normalize((transition_matrix * np.dot(a, b.conj().T[np.newaxis])))[0]
'''Computing xi'''
for t in range(number_of_observations-1):
denom=0.0
for i in range(0,number_of_hidden_states):
for j in range(0,number_of_hidden_states):
denom+=alpha[i][t]*transition_matrix[i][j]*emission_matrix[j][observation_vector[t+1]]*beta[j][t+1]
for i in range(0,number_of_hidden_states):
for j in range(0,number_of_hidden_states):
numer=alpha[i][t]*transition_matrix[i][j]*emission_matrix[j][observation_vector[t+1]]*beta[j][t+1]
xi[t][i][j]=numer/denom
'''Computing xi_summed
for t in range(number_of_observations-1):
for i in range(number_of_hidden_states):
for j in range(number_of_hidden_states):
xi_summed[i][j]+=xi[t][i][j]
for t in xrange(number_of_observations):
for i in xrange(number_of_hidden_states):
gamma2[i][t] = sum(xi[t][i])'''
'''CHECKING'''
#print "Asserting"
for t in range(number_of_observations):
for i in range(0,number_of_hidden_states):
p=0.0
for j in range(number_of_hidden_states):
p+=xi[t][i][j]
#print p/gamma[i][t]
#assert(p==gamma[t][i])
return [alpha,beta,gamma,xi,xi_summed,loglik]