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fixed viterbi algorithm (issue #1126) #1129

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Merged
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Oct 29, 2019
Merged

fixed viterbi algorithm (issue #1126) #1129

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27 changes: 21 additions & 6 deletions probability.py
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Original file line number Diff line number Diff line change
Expand Up @@ -11,6 +11,7 @@
import random
from collections import defaultdict
from functools import reduce
import numpy as np


# ______________________________________________________________________________
Expand Down Expand Up @@ -687,28 +688,42 @@ def forward_backward(HMM, ev):

def viterbi(HMM, ev):
"""[Equation 15.11]
Viterbi algorithm to find the most likely sequence. Computes the best path,
Viterbi algorithm to find the most likely sequence. Computes the best path and the corresponding probabilities,
given an HMM model and a sequence of observations."""
t = len(ev)
ev = ev.copy()
ev.insert(0, None)

m = [[0.0, 0.0] for _ in range(len(ev) - 1)]

# the recursion is initialized with m1 = forward(P(X0), e1)
m[0] = forward(HMM, HMM.prior, ev[1])
# keep track of maximizing predecessors
backtracking_graph = []

for i in range(1, t):
m[i] = element_wise_product(HMM.sensor_dist(ev[i + 1]),
[max(element_wise_product(HMM.transition_model[0], m[i - 1])),
max(element_wise_product(HMM.transition_model[1], m[i - 1]))])
backtracking_graph.append([np.argmax(element_wise_product(HMM.transition_model[0], m[i - 1])),
np.argmax(element_wise_product(HMM.transition_model[1], m[i - 1]))])

# computed probabilities
ml_probabilities = [0.0] * (len(ev) - 1)
# most likely sequence
ml_path = [True] * (len(ev) - 1)

path = [0.0] * (len(ev) - 1)
# the construction of the most likely sequence starts in the final state with the largest probability,
# and runs backwards; the algorithm needs to store for each xt its best predecessor xt-1
for i in range(t, -1, -1):
path[i - 1] = max(m[i - 1])
# and runs backwards; the algorithm needs to store for each xt its predecessor xt-1 maximizing its probability
i_max = np.argmax(m[-1])

for i in range(t - 1, -1, -1):
ml_probabilities[i] = m[i][i_max]
ml_path[i] = True if i_max == 0 else False
if i > 0:
i_max = backtracking_graph[i - 1][i_max]

return path
return ml_path, ml_probabilities


# _________________________________________________________________________
Expand Down
6 changes: 4 additions & 2 deletions tests/test_probability.py
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Original file line number Diff line number Diff line change
Expand Up @@ -288,10 +288,12 @@ def test_viterbi():
umbrellaHMM = HiddenMarkovModel(umbrella_transition, umbrella_sensor)

umbrella_evidence = [T, T, F, T, T]
assert rounder(viterbi(umbrellaHMM, umbrella_evidence)) == [0.8182, 0.5155, 0.1237, 0.0334, 0.0210]
assert viterbi(umbrellaHMM, umbrella_evidence)[0] == [T, T, F, T, T]
assert rounder(viterbi(umbrellaHMM, umbrella_evidence)[1]) == [0.8182, 0.5155, 0.1237, 0.0334, 0.0210]

umbrella_evidence = [T, F, T, F, T]
assert rounder(viterbi(umbrellaHMM, umbrella_evidence)) == [0.8182, 0.1964, 0.053, 0.0154, 0.0042]
assert viterbi(umbrellaHMM, umbrella_evidence)[0] == [T, F, F, F, T]
assert rounder(viterbi(umbrellaHMM, umbrella_evidence)[1]) == [0.8182, 0.1964, 0.0275, 0.0154, 0.0042]


def test_fixed_lag_smoothing():
Expand Down