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Implementation of Particle Filtering #151

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Mar 17, 2016
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Implementation of Particle Filtering #151

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12a4e92
Particle filtering
Schrodinger1926 Mar 17, 2016
a244992
pep8 compliance
Schrodinger1926 Mar 17, 2016
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85 changes: 76 additions & 9 deletions probability.py
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Original file line number Diff line number Diff line change
Expand Up @@ -526,6 +526,7 @@ def markov_blanket_sample(X, e, bn):

# Umbrella Example [Fig. 15.2]


class HiddenMarkovModel:

""" A Hidden markov model which takes Transition model and Sensor model as inputs"""
Expand All @@ -546,17 +547,18 @@ def sensor_dist(self, ev):

def forward(HMM, fv, ev):
prediction = vector_add(scalar_vector_product(fv[0], HMM.transition_model[0]),
scalar_vector_product(fv[1], HMM.transition_model[1]))
scalar_vector_product(fv[1], HMM.transition_model[1]))
sensor_dist = HMM.sensor_dist(ev)

return(normalize(element_wise_product(sensor_dist, prediction)))


def backward(HMM, b, ev):
sensor_dist = HMM.sensor_dist(ev)
prediction = element_wise_product(sensor_dist, b)

return(normalize(vector_add(scalar_vector_product(prediction[0], HMM.transition_model[0]),
scalar_vector_product(prediction[1], HMM.transition_model[1]))))
scalar_vector_product(prediction[1], HMM.transition_model[1]))))


def forward_backward(HMM, ev, prior):
Expand All @@ -571,7 +573,8 @@ def forward_backward(HMM, ev, prior):
umbrellaHMM = HiddenMarkovModel(umbrella_transition, umbrella_sensor)

>>> forward_backward(umbrellaHMM, umbrella_evidence, umbrella_prior)
[[0.6469, 0.3531], [0.8673, 0.1327], [0.8204, 0.1796], [0.3075, 0.6925], [0.8204, 0.1796], [0.8673, 0.1327]]
[[0.6469, 0.3531], [0.8673, 0.1327], [0.8204, 0.1796],
[0.3075, 0.6925], [0.8204, 0.1796], [0.8673, 0.1327]]
"""
t = len(ev)
ev.insert(0, None) # to make the code look similar to pseudo code
Expand All @@ -583,10 +586,10 @@ def forward_backward(HMM, ev, prior):

fv[0] = prior

for i in range(1, t+ 1):
fv[i] = forward(HMM, fv[i- 1], ev[i])
for i in range(1, t + 1):
fv[i] = forward(HMM, fv[i - 1], ev[i])
for i in range(t, -1, -1):
sv[i- 1] = normalize(element_wise_product(fv[i], b))
sv[i - 1] = normalize(element_wise_product(fv[i], b))
b = backward(HMM, b, ev[i])
bv.append(b)

Expand All @@ -600,14 +603,78 @@ def forward_backward(HMM, ev, prior):

# _________________________________________________________________________


def fixed_lag_smoothing(e_t, hmm, d):
"""[Fig. 15.6]"""
unimplemented()


def particle_filtering(e, N, dbn):
"""[Fig. 15.17]"""
unimplemented()
def particle_filtering(e, N, HMM):
"""
Particle filtering considering two states variables
N = 10
umbrella_evidence = T
umbrella_prior = [0.5, 0.5]
umbrella_transition = [[0.7, 0.3], [0.3, 0.7]]
umbrella_sensor = [[0.9, 0.2], [0.1, 0.8]]
umbrellaHMM = HiddenMarkovModel(umbrella_transition, umbrella_sensor)

>>> particle_filtering(umbrella_evidence, N, umbrellaHMM)
['A', 'A', 'A', 'B', 'A', 'A', 'B', 'A', 'A', 'A', 'B']

NOTE: Output is an probabilistic answer, therfore can vary
"""
s = []
dist = [0.5, 0.5]
# State Initialization
s = ['A' if probability(dist[0]) else 'B' for i in range(N)]
# Weight Initialization
w = [0 for i in range(N)]
# STEP 1
# Propagate one step using transition model given prior state
dist = vector_add(scalar_vector_product(dist[0], HMM.transition_model[0]),
scalar_vector_product(dist[1], HMM.transition_model[1]))
# Assign state according to probability
s = ['A' if probability(dist[0]) else 'B' for i in range(N)]
w_tot = 0
# Calculate importance weight given evidence e
for i in range(N):
if s[i] == 'A':
# P(U|A)*P(A)
w_i = HMM.sensor_dist(e)[0]*dist[0]
if s[i] == 'B':
# P(U|B)*P(B)
w_i = HMM.sensor_dist(e)[1]*dist[1]
w[i] = w_i
w_tot += w_i

# Normalize all the weights
for i in range(N):
w[i] = w[i]/w_tot

# Limit weights to 4 digits
for i in range(N):
w[i] = float("{0:.4f}".format(w[i]))

# STEP 2
s = weighted_sample_with_replacement(N, s, w)
return s


def weighted_sample_with_replacement(N, s, w):
"""
Performs Weighted sampling over the paricles given weights of each particle.
We keep on picking random states unitll we fill N number states in new distribution
"""
s_wtd = []
cnt = 0
while (cnt <= N):
# Generate a random number from 0 to N-1
i = random.randint(0, N-1)
if (probability(w[i])):
s_wtd.append(s[i])
cnt += 1
return s_wtd

# _________________________________________________________________________
__doc__ += """
Expand Down