trans, emissions = model.forward_backward(sequence)
print trans
print emissions
print "Viterbi"
prob, states = model.viterbi(sequence)
print "Prob: {}".format(prob)
print "\n".join(state[1].name for state in states)
print
print "MAP"
prob, states = model.maximum_a_posteriori(sequence)
print "Prob: {}".format(prob)
print "\n".join(state[1].name for state in states)
print "Showing that sampling can reproduce the original transition probs."
print "Should produce a matrix close to the following: "
print " [ [ 0.60, 0.10, 0.30 ] "
print " [ 0.40, 0.40, 0.20 ] "
print " [ 0.05, 0.15, 0.80 ] ] "
print
print "Tranition Matrix From 100000 Samples:"
sample, path = model.sample(100000, path=True)
trans = np.zeros((3, 3))
for state, n_state in it.izip(path[1:-2], path[2:-1]):
state_name = float(state.name[1:]) - 1
n_state_name = float(n_state.name[1:]) - 1
trans[state_name, n_state_name] += 1
trans = (trans.T / trans.sum(axis=1)).T
print trans
silent = State(None, name="silent") model.add_state(state) model.add_state(state2) model.add_transition(state, state, 0.4) model.add_transition(state, state2, 0.4) model.add_transition(state2, state2, 0.4) model.add_transition(state2, state, 0.4) model.add_transition(model.start, state, 0.5) model.add_transition(model.start, state2, 0.5) model.add_transition(state, model.end, 0.2) model.add_transition(state2, model.end, 0.2) model.bake() sequence = model.sample() print sequence print print model.forward(sequence)[ len(sequence), model.end_index ] print model.backward(sequence)[0,model.start_index] print trans, ems = model.forward_backward(sequence) print trans print ems print model.train( [ sequence ] ) print print model.forward(sequence)[ len(sequence), model.end_index ] print model.backward(sequence)[0,model.start_index]
# Transition matrix, with 0.05 subtracted from each probability to add to
# the probability of exiting the hmm
model.add_transition(rainy, rainy, 0.65)
model.add_transition(rainy, sunny, 0.25)
model.add_transition(sunny, rainy, 0.35)
model.add_transition(sunny, sunny, 0.55)
# Add transitions to the end of the model
model.add_transition(rainy, model.end, 0.1)
model.add_transition(sunny, model.end, 0.1)
# Finalize the model structure
model.bake(verbose=True)
# Lets sample from this model.
print model.sample()
# Lets call Bob every hour and see what he's doing!
# (aka build up a sequence of observations)
sequence = ['walk', 'shop', 'clean', 'clean', 'clean', 'walk', 'clean']
# What is the probability of seeing this sequence?
print "Probability of Sequence: ", \
math.e**model.forward( sequence )[ len(sequence), model.end_index ]
print "Probability of Cleaning at Time Step 3 Given This Sequence: ", \
math.e**model.forward_backward( sequence )[1][ 2, model.states.index( rainy ) ]
print "Probability of the Sequence Given It's Sunny at Time Step 4: ", \
math.e**model.backward( sequence )[ 3, model.states.index( sunny ) ]
print " ".join(state.name
for i, state in model.maximum_a_posteriori(sequence)[1])
# Transition matrix, with 0.05 subtracted from each probability to add to # the probability of exiting the hmm model.add_transition( rainy, rainy, 0.65 ) model.add_transition( rainy, sunny, 0.25 ) model.add_transition( sunny, rainy, 0.35 ) model.add_transition( sunny, sunny, 0.55 ) # Add transitions to the end of the model model.add_transition( rainy, model.end, 0.1 ) model.add_transition( sunny, model.end, 0.1 ) # Finalize the model structure model.bake( verbose=True ) # Lets sample from this model. print model.sample() # Lets call Bob every hour and see what he's doing! # (aka build up a sequence of observations) sequence = [ 'walk', 'shop', 'clean', 'clean', 'clean', 'walk', 'clean' ] # What is the probability of seeing this sequence? print "Probability of Sequence: ", \ math.e**model.forward( sequence )[ len(sequence), model.end_index ] print "Probability of Cleaning at Time Step 3 Given This Sequence: ", \ math.e**model.forward_backward( sequence )[1][ 2, model.states.index( rainy ) ] print "Probability of the Sequence Given It's Sunny at Time Step 4: ", \ math.e**model.backward( sequence )[ 3, model.states.index( sunny ) ] print " ".join( state.name for i, state in model.maximum_a_posteriori( sequence )[1] )
trans, emissions = model.forward_backward( sequence )
print trans
print emissions
print "Viterbi"
prob, states = model.viterbi( sequence )
print "Prob: {}".format( prob )
print "\n".join( state[1].name for state in states )
print
print "MAP"
prob, states = model.maximum_a_posteriori( sequence )
print "Prob: {}".format( prob )
print "\n".join( state[1].name for state in states )
print "Showing that sampling can reproduce the original transition probs."
print "Should produce a matrix close to the following: "
print " [ [ 0.60, 0.10, 0.30 ] "
print " [ 0.40, 0.40, 0.20 ] "
print " [ 0.05, 0.15, 0.80 ] ] "
print
print "Tranition Matrix From 100000 Samples:"
sample, path = model.sample( 100000, path=True )
trans = np.zeros((3,3))
for state, n_state in it.izip( path[1:-2], path[2:-1] ):
state_name = float( state.name[1:] )-1
n_state_name = float( n_state.name[1:] )-1
trans[ state_name, n_state_name ] += 1
trans = (trans.T / trans.sum( axis=1 )).T
print trans
silent = State(None, name="silent") model.add_state(state) model.add_state(state2) model.add_transition(state, state, 0.4) model.add_transition(state, state2, 0.4) model.add_transition(state2, state2, 0.4) model.add_transition(state2, state, 0.4) model.add_transition(model.start, state, 0.5) model.add_transition(model.start, state2, 0.5) model.add_transition(state, model.end, 0.2) model.add_transition(state2, model.end, 0.2) model.bake() sequence = model.sample() print sequence print print model.forward(sequence)[len(sequence), model.end_index] print model.backward(sequence)[0, model.start_index] print trans, ems = model.forward_backward(sequence) print trans print ems print model.train([sequence]) print print model.forward(sequence)[len(sequence), model.end_index] print model.backward(sequence)[0, model.start_index]