def sprinkler_test_0(self):
'''
Simple network from "An introduction to graphical models" by Kevin P.
Murphy
C -> S
C -> R
S -> W
R -> W
'''
C = RandVar("Cloudy", ["F", "T"])
S = RandVar("Sprinkler", ["F", "T"])
R = RandVar("Rain", ["F", "T"])
W = RandVar("WetGrass", ["F", "T"])
Cf = Factor([C], [0.5, 0.5])
Sf = Factor([S, C], [0.5, 0.5, 0.9, 0.1])
Rf = Factor([R, C], [0.8, 0.2, 0.2, 0.5])
Wf = Factor([W, S, R], [1.0, 0.0, 0.1, 0.9, 0.1, 0.9, 0.01, 0.99])
SprinklerNW = bn.BayesianNetwork([(C, Cf, []), (S, Sf, [C]),
(R, Rf, [C]), (W, Wf, [S, R])])
cases = [(W, 1, [(S, "T"), (R, "F")], 0.9)]
for (qvar, qvalue, evidence, expect) in cases:
result = SprinklerNW.eliminationAsk(qvar, evidence)
print("qvar: %s\nevidence: %s\nexpect: %s\nresult: %s" %
(qvar.name, ",".join(
["%s=%s" % (x[0].name, x[1])
for x in evidence]), expect, result.values[qvalue]))
assert_almost_equal(result.values[qvalue], expect, places=3)
def ex1():
"""
Example of the Channel Capacity algorithm applied to a binary symmetric
channel. Such channels have an explicit way to have their channel capacity
computed. Which is:
C = 1 - H(p),
where p is the probability of error in the channel::
p
0 --- 0
\ / 1-p
/
/ \ 1-p
1 --- 1
p
In this example the probability of error is 0.1
"""
p = 0.9
Input = RandVar("Input", ["T", "F"])
Output = RandVar("Output", ["T", "F"])
Prior = Factor(Input, [0.5, 0.5])
Channel = Factor([Input, Output], [p, 1 - p, 1 - p, p])
cc = ChannelCapacity(Input, Output, Prior, Channel)
explicit = 1 - entropy(Factor(Input, [p, 1 - p]))
print("Channel Capacity of a binary symmetric channel")
print("Blahut-Arimoto:", cc)
print("Explicit: ", explicit)
def factor_test(self):
X = RandVar("X", [0, 1])
Y = RandVar("Y", [0, 1])
f1 = Factor(X, [0, 1])
f2 = Factor([X, Y], [0, 1, 2, 3])
assert(f1.__repr__() == "(X, [0, 1])")
assert(f2.__repr__() == "([X, Y], [0, 1, 2, 3])")
def ex2():
domain = [str(i) for i in range(2)]
Input = RandVar("Input", domain)
Output = RandVar("Output", domain)
Prior = Factor(Input, [1.0 / 2.0] * 2)
channel_dist = [random.random() for i in range(4)]
Channel = Factor([Input, Output], channel_dist).normalize(Input)
print(ChannelCapacity(Input, Output, Prior, Channel))
def min_test_2(self):
"""
Minimum with one variable
"""
for i, domain in enumerate(self.X.domain):
fac = Factor(self.X, [1, 2])
fac.values[i] = -10
assert(fac.min() == -10)
def max_test_0(self):
"""
Maximum with one variable
"""
for i, domain in enumerate(self.X.domain):
fac = Factor(self.X, [1, 2])
fac.values[i] = 10
assert(fac.max() == 10)
def max_test_1(self):
"""
Maximum with two variables
"""
for i, domainx in enumerate(self.X.domain):
for j, domainy in enumerate(self.Y.domain):
fac = Factor([self.X, self.Y], [1, 2, 3, 4])
fac.values[i + j*2] = 10
assert(fac.max() == 10)
def min_test_3(self):
"""
Minimum with two variables
"""
for i, domainx in enumerate(self.X.domain):
for j, domainy in enumerate(self.Y.domain):
fac = Factor([self.X, self.Y], [1, 2, 3, 4])
fac.values[i + j*2] = -10
assert(fac.min() == -10)
def argmin_test_6(self):
"""
Minimum argument with one variable
"""
for i, domain in enumerate(self.X.domain):
fac = Factor(self.X, [1, 2])
fac.values[i] = -10
event = Event([(self.X, domain)])
assert(fac.argmin() == event)
def argmin_test_7(self):
"""
Minimum argument with two variables
"""
for i, domainx in enumerate(self.X.domain):
for j, domainy in enumerate(self.Y.domain):
fac = Factor([self.X, self.Y], [1, 2, 3, 4])
fac.values[i + j*2] = -10
event = Event([(self.X, domainx), (self.Y, domainy)])
assert(fac.argmin() == event)
def student_test_0(self):
'''
Student network from "Probabilistic graphical models principles and
techniques" by Koller and Friedman
D -> G
I -> G
I -> S
G -> L
'''
D = RandVar("Difficulty", ["easy", "hard"])
I = RandVar("Intelligence", ["low", "high"])
G = RandVar("Grade", ["a", "b", "c"])
S = RandVar("SAT", ["low", "high"])
L = RandVar("Letter", ["weak", "good"])
Df = Factor([D], [0.6, 0.4])
If = Factor([I], [0.7, 0.3])
Gf = Factor([G, D, I], [
0.30, 0.40, 0.30, 0.05, 0.25, 0.70, 0.90, 0.08, 0.02, 0.50, 0.30,
0.20
])
Sf = Factor([S, I], [0.95, 0.05, 0.2, 0.8])
Lf = Factor([L, G], [0.1, 0.9, 0.4, 0.6, 0.99, 0.01])
StudentNW = bn.BayesianNetwork([(D, Df, []), (I, If, []),
(G, Gf, [D, I]), (S, Sf, [I]),
(L, Lf, [G])])
cases = [(L, 1, [(I, "low"), (D, "easy")], 0.513),
(I, 1, [(L, "weak")], 0.140),
(I, 1, [(G, "c"), (S, "high")], 0.578),
(L, 1, [(I, "low")], 0.389), (I, 1, [(G, "c")], 0.079)]
for (qvar, qvalue, evidence, expect) in cases:
result = StudentNW.eliminationAsk(qvar, evidence)
print("qvar: %s\nevidence: %s\nexpect: %s\nresult: %s" %
(qvar.name, ",".join(
["%s=%s" % (x[0].name, x[1])
for x in evidence]), expect, result.values[qvalue]))
assert_almost_equal(result.values[qvalue], expect, places=3)
def kullbackLeiblerDistance(fac1, fac2, base=2):
"""
Calculates the Kullback-Leibler Distance between fac1 and fac2. The factors
should represent probability distributions with the same variables, like
P(X) and Q(X), or P(X, Y) and Q(X, Y)
:param fac1: First factor in operation
:param fac2: Second factor in operation
:param base: Base of logarithms in the operations, defaults to 2
:returns: The Kullback-Leibler Distance
"""
kld = lambda f1, f2: f1 * log(f1 / f2) / log(base)
return sum(Factor.factorOp(fac1, fac2, kld).values)
def kullbackLeiblerDistance(fac1, fac2, base=2):
"""
Calculates the Kullback-Leibler Distance between fac1 and fac2. The factors
should represent probability distributions with the same variables, like
P(X) and Q(X), or P(X, Y) and Q(X, Y)
:param fac1: First factor in operation
:param fac2: Second factor in operation
:param base: Base of logarithms in the operations, defaults to 2
:returns: The Kullback-Leibler Distance
"""
kld = lambda f1, f2: f1 * log(f1 / f2) / log(base)
return sum(Factor.factorOp(fac1, fac2, kld).values)
def factor_test(self):
X = RandVar("X", [0, 1])
Y = RandVar("Y", [0, 1])
f1 = Factor(X, [0, 1])
f2 = Factor([X, Y], [0, 1, 2, 3])
assert (f1.__repr__() == "(X, [0, 1])")
assert (f2.__repr__() == "([X, Y], [0, 1, 2, 3])")
def __init__(self):
TestBase.__init__(self)
# factors for information theory testing
self.fX1 = Factor(self.X, [0.5, 0.5])
self.fX2 = Factor(self.X, [0.0, 1.0])
self.fX3 = Factor(self.X, [1.0, 0.0])
self.fXY1 = Factor([self.X, self.Y], [0.25, 0.25, 0.25, 0.25])
self.fXY2 = Factor([self.X, self.Y], [0.1, 0.2, 0.3, 0.4])
self.fXY3 = Factor([self.X, self.Y], [0.4, 0.3, 0.2, 0.1])
def rejectionSample(self, query_var, observed, samples_num):
"""
Implementation of the rejection sample algorithm. This algorithms
estimates a distribution P(X | e), where X is a query variable and e
are observations made in the network.
:param query_var: Random variable of type RandVar
:param observed: List of observations. Each element of the list
should be a tuple, which first element is a RandVar
and second element is the observed value for that
variable
:param samples_num: Number of samples the algorithm is going to take to
calculate the estimative
"""
# List of counts for each value of the domain. Initialized with 0
count = {i: 0 for i in query_var.domain}
# The samples_num of samples
for i in range(samples_num):
# Take a sample
sample = self.sample()
# Check if it should be rejected
rejected = False
for j in observed:
for k in sample:
# If the value of the sampled variable is different from
# the value of the observed one, rejected
if j[0].name == k[0].name and j[1] != k[1]:
rejected = True
break
# If the sample was already rejected, get out of the cycle
if rejected:
break
# If the sample is not rejected, increment the counts
if not rejected:
for j in sample:
if j[0].name == query_var.name:
count[j[1]] += 1
# Make resulting factor
values = [count[i] for i in query_var.domain]
return Factor([query_var], values).normalize(query_var)
def gibbsAsk(self, query_var, observed, samples_num):
# Result is a list of counts for each value in the domain of the query
# variable. Initialized with 0
res = {i: 0 for i in query_var.domain}
# Assure the observed argument is an Event
if type(observed) != Event:
observed = Event(observed)
# Create non evidence variable list, which are all the variables not
# present in the observations
non_evidence_vars = [i for i in self.network
if not observed.varInEvent(i.node)]
# Get markov blankets for each non evidence variable
mbs = dict()
for i in non_evidence_vars:
mbs[i.node.name] = self.markovBlanket(i)
# Make an initial sample
sample = self.sample(observed)
# Execute for samples_num samples
for i in range(samples_num):
for j in non_evidence_vars:
# Get distribution P(j | mb(j))
dist = j.factor
for k in mbs[j.node.name]:
dist *= k.factor
# Instantiate with previous sample, except for current j
# variable
sample.removeVar(j.node)
dist = dist.instVar(sample)
# Set new random value of current variable in sample
rvalue = self.pickRandomValue(dist.rand_vars[0].domain,
dist.values, random.random())
sample.setValue(j.node, rvalue)
# Increment count
res[rvalue] += 1
# Return the count list normalized
values = [res[i] for i in query_var.domain]
return Factor(query_var, values).normalize(query_var)
def __init__(self):
TestBase.__init__(self)
# factors for information theory testing
self.fX1 = Factor(self.X, [0.5, 0.5])
self.fX2 = Factor(self.X, [0.0, 1.0])
self.fX3 = Factor(self.X, [1.0, 0.0])
self.fXY1 = Factor([self.X, self.Y], [0.25, 0.25, 0.25, 0.25])
self.fXY2 = Factor([self.X, self.Y], [0.1, 0.2, 0.3, 0.4])
self.fXY3 = Factor([self.X, self.Y], [0.4, 0.3, 0.2, 0.1])
self.P1 = Factor([self.X], [0.5, 0.5])
self.Q1 = Factor([self.X], [0.9, 0.1])
self.P2 = Factor([self.X, self.Y], [0.25, 0.25, 0.25, 0.25])
self.Q2 = Factor([self.X, self.Y], [0.8, 0.05, 0.05, 0.8])
def inf_theory_test_7(self):
"""
I(X ; Y)
"""
joint = Factor([self.X, self.Y], [0.8, 0.05, 0.05, 0.8])
fac1 = self.fXY1.marginal(self.X)
fac2 = self.fXY1.marginal(self.Y)
res = [
mutualInformation(joint, fac1, fac2),
mutualInformation(joint, fac1, fac2, 10),
mutualInformation(joint, fac1, fac2, math.e)
]
assert_almost_equal(res[0], 2.4527, places=4)
assert_almost_equal(res[1], 0.73834, places=5)
assert_almost_equal(res[2], 1.7001, places=5)
def beliefProp(self):
"""
Belief propagation algorithm, also known as sum-product algorithm. The
result of the algorithm is stored in the *marginal* attribute of every
variable node which is part of the network. This implementation only
works with tree networks.
"""
# Select any root node
root_node = self.nodes[next(iter(self.nodes))]
# Get messages to this node
res = self.factorToVar(root_node.neighbors[0], root_node)
root_node.messages[0] = res
for i, neighbor in enumerate(root_node.neighbors[1:]):
msg = self.factorToVar(neighbor, root_node)
root_node.messages[i+1] = msg
res *= msg
for i in root_node.obs_factors:
res *= i
# Store the calculated marginal
root_node.setMarginal(res)
# Propagate this message to other nodes
for i, neighbor in enumerate(root_node.neighbors):
new_msg = Factor(root_node.var, [1, 1])
for j in range(len(root_node.neighbors)):
if i != j:
new_msg *= root_node.messages[j]
for j in root_node.obs_factors:
new_msg *= j
self.progMsgVarToFactor(neighbor, root_node, new_msg)
sys.path.insert(0, path.join("..", "ProbPy"))
# Import ProbPy modules
from ProbPy import RandVar, Factor, Event
from ProbPy import bn
if __name__ == "__main__":
# Variables for this example
cloudy = RandVar("cloudy", ["True", "False"])
sprinkler = RandVar("sprinkler", ["True", "False"])
rain = RandVar("rain", ["True", "False"])
wet_grass = RandVar("wet_grass", ["True", "False"])
# Factors representing the conditional distributions of this network
factor_cloudy = Factor(cloudy, [0.5, 0.5])
factor_sprinkler = Factor([sprinkler, cloudy], [0.1, 0.9, 0.5, 0.5])
factor_rain = Factor([rain, cloudy], [0.8, 0.2, 0.2, 0.8])
factor_wet_grass = Factor([wet_grass, rain, sprinkler],
[0.99, 0.01, 0.9, 0.1, 0.9, 0.1, 0.0, 1.0])
# Actual network representation
network = [(cloudy, factor_cloudy), (sprinkler, factor_sprinkler),
(rain, factor_rain), (wet_grass, factor_wet_grass)]
# Create a Bayesian Network
BN = bn.BayesianNetwork(network)
# Set one observation
observed = Event(var=sprinkler, val="True")
def __init__(self):
# Scalars
self.scalar = 10
self.scalarf = Factor([], [10])
# Binary variables
self.X = RandVar("X", ["T", "F"])
self.Y = RandVar("Y", ["T", "F"])
self.Z = RandVar("Z", ["T", "F"])
self.W = RandVar("W", ["T", "F"])
self.K = RandVar("K", ["T", "F"])
self.T = RandVar("T", ["T", "F"])
# Domains
self.X_domain = list(range(1, 3))
self.Y_domain = list(range(3, 5))
self.Z_domain = list(range(5, 7))
self.XY_domain = list(range(1, 5))
self.XZ_domain = list(range(5, 9))
self.ZW_domain = list(range(9, 13))
self.XYZ_domain = list(range(1, 9))
self.XYW_domain = list(range(9, 17))
self.XKW_domain = list(range(17, 25))
self.TKW_domain = list(range(25, 33))
# Factors
self.X_factor = Factor(self.X, self.X_domain)
self.Y_factor = Factor(self.Y, self.Y_domain)
self.Z_factor = Factor(self.Z, self.Z_domain)
self.XY_factor = Factor([self.X, self.Y], self.XY_domain)
self.XZ_factor = Factor([self.X, self.Z], self.XZ_domain)
self.ZW_factor = Factor([self.Z, self.W], self.ZW_domain)
self.XYZ_factor = Factor([self.X, self.Y, self.Z], self.XYZ_domain)
self.XYW_factor = Factor([self.X, self.Y, self.W], self.XYW_domain)
self.XKW_factor = Factor([self.X, self.K, self.W], self.XKW_domain)
self.TKW_factor = Factor([self.T, self.K, self.W], self.TKW_domain)
# Factors for normalization
self.X_factor_n = Factor(self.X, [1, 2])
self.XY_factor_n = Factor([self.X, self.Y], [1, 1, 2, 2])
self.XYZ_factor_n = Factor([self.X, self.Y, self.Z],
[1, 1, 2, 2, 3, 3, 4, 4])
# Distributions for expected value
self.X_dist = Factor(self.X, [0.8, 0.2])
self.Y_dist = Factor(self.Y, [0.1, 0.9])
self.XY_dist = Factor([self.X, self.Y], [0.1, 0.2, 0.3, 0.4])
# Function for expected values f(X)
self.x_ev = Factor(self.X, [10, 20])
self.y_ev = Factor(self.Y, [15, 25])
self.xy_ev = Factor([self.X, self.Y], [25, 35, 35, 45])
from ProbPy import RandVar, Factor, Event
from ProbPy import bn
if __name__ == "__main__":
# These are the variables in the network. The first argument is the actual
# name of the variable and the second is the domain of it
burglary = RandVar("burglary", ["True", "False"])
earthq = RandVar("earthq", ["True", "False"])
alarm = RandVar("alarm", ["True", "False"])
john = RandVar("john", ["True", "False"])
mary = RandVar("mary", ["True", "False"])
# These are the distributions. First argument are the variables, second is
# the values in the distribution
factor_burglary = Factor([burglary], [0.001, 0.999])
factor_earthq = Factor([earthq], [0.002, 0.998])
factor_alarm = Factor([alarm, earthq, burglary], [
0.95, 0.05, 0.94, 0.06, 0.29, 0.71, 0.001, 0.999
])
factor_john = Factor([john, alarm], [0.90, 0.10, 0.05, 0.95])
factor_mary = Factor([mary, alarm], [0.70, 0.30, 0.01, 0.99])
# This array has the nodes of the network. Each element is a tuple. In each
# tuple, the first argument is the variable of that node, the second is the
# distribution. Note that the nodes were place in the list at random
network = [
(earthq, factor_earthq),
(alarm, factor_alarm),
(john, factor_john),
(burglary, factor_burglary),
# Import ProbPy modules
from ProbPy import RandVar, Factor
if __name__ == "__main__":
"""
Supposing the following example
P(X | Y) P(Y) 1/P(X) = P(Y | X)
"""
# Random Variables
X = RandVar("X", ["T", "F"])
Y = RandVar("Y", ["T", "F"])
# Prior distribution, P(Y)
fy = Factor(Y, [0.2, 0.8])
# Conditional distribution, P(X | Y)
fx_y = Factor([X, Y], [0.1, 0.9, 0.5, 0.5])
# Bayes theorem to get P(Y | X)
fy_x = (fx_y * fy).normalize(Y)
print("P(X | Y) P(Y) 1/P(X) = P(Y | X)")
print(fy_x.values)
# Alternative way of getting P(Y | X) without using the normalize() method
fxy = fx_y * fy
fx = fxy.marginal(X)
fx_y = fxy / fx
class TestInfTheoryValue(TestBase):
def __init__(self):
TestBase.__init__(self)
# factors for information theory testing
self.fX1 = Factor(self.X, [0.5, 0.5])
self.fX2 = Factor(self.X, [0.0, 1.0])
self.fX3 = Factor(self.X, [1.0, 0.0])
self.fXY1 = Factor([self.X, self.Y], [0.25, 0.25, 0.25, 0.25])
self.fXY2 = Factor([self.X, self.Y], [0.1, 0.2, 0.3, 0.4])
self.fXY3 = Factor([self.X, self.Y], [0.4, 0.3, 0.2, 0.1])
self.P1 = Factor([self.X], [0.5, 0.5])
self.Q1 = Factor([self.X], [0.9, 0.1])
self.P2 = Factor([self.X, self.Y], [0.25, 0.25, 0.25, 0.25])
self.Q2 = Factor([self.X, self.Y], [0.8, 0.05, 0.05, 0.8])
def inf_theory_test_0(self):
"""
H(X)
"""
assert_almost_equal(entropy(self.fX1), 1.0, places=1)
assert_almost_equal(entropy(self.fX1, 10), 0.30103, places=5)
assert_almost_equal(entropy(self.fX1, math.e), 0.69315, places=5)
assert_almost_equal(entropy(self.fX2), 0.0, places=1)
assert_almost_equal(entropy(self.fX2, 10), 0.0, places=1)
assert_almost_equal(entropy(self.fX2, math.e), 0.0, places=1)
assert_almost_equal(entropy(self.fX3), 0.0, places=1)
assert_almost_equal(entropy(self.fX3, 10), 0.0, places=1)
assert_almost_equal(entropy(self.fX3, math.e), 0.0, places=1)
def inf_theory_test_1(self):
"""
H(X, Y)
"""
assert_almost_equal(entropy(self.fXY1), 2.0, places=1)
assert_almost_equal(entropy(self.fXY1, 10), 0.60206, places=5)
assert_almost_equal(entropy(self.fXY1, math.e), 1.3863, places=4)
assert_almost_equal(entropy(self.fXY2), 1.8464, places=4)
assert_almost_equal(entropy(self.fXY2, 10), 0.55583, places=5)
assert_almost_equal(entropy(self.fXY2, math.e), 1.2799, places=4)
assert_almost_equal(entropy(self.fXY3), 1.8464, places=4)
assert_almost_equal(entropy(self.fXY3, 10), 0.55583, places=5)
assert_almost_equal(entropy(self.fXY3, math.e), 1.2799, places=4)
def inf_theory_test_2(self):
"""
KLD(P1 | Q1)
"""
res = [
kullbackLeiblerDistance(self.P1, self.Q1),
kullbackLeiblerDistance(self.P1, self.Q1, 10),
kullbackLeiblerDistance(self.P1, self.Q1, math.e)
]
assert_almost_equal(res[0], 0.73697, places=4)
assert_almost_equal(res[1], 0.22185, places=4)
assert_almost_equal(res[2], 0.51083, places=4)
def inf_theory_test_3(self):
"""
KLD(P2 | Q2)
"""
res = [
kullbackLeiblerDistance(self.P2, self.Q2),
kullbackLeiblerDistance(self.P2, self.Q2, 10),
kullbackLeiblerDistance(self.P2, self.Q2, math.e)
]
assert_almost_equal(res[0], 0.32193, places=4)
assert_almost_equal(res[1], 0.09691, places=4)
assert_almost_equal(res[2], 0.22314, places=4)
def inf_theory_test_4(self):
"""
KLD(Q1 | P1)
"""
res = [
kullbackLeiblerDistance(self.Q1, self.P1),
kullbackLeiblerDistance(self.Q1, self.P1, 10),
kullbackLeiblerDistance(self.Q1, self.P1, math.e)
]
assert_almost_equal(res[0], 0.53100, places=5)
assert_almost_equal(res[1], 0.15985, places=5)
assert_almost_equal(res[2], 0.36806, places=5)
def inf_theory_test_5(self):
"""
KLD(Q2 | P2)
"""
res = [
kullbackLeiblerDistance(self.Q2, self.P2),
kullbackLeiblerDistance(self.Q2, self.P2, 10),
kullbackLeiblerDistance(self.Q2, self.P2, math.e)
]
assert_almost_equal(res[0], 2.4527, places=4)
assert_almost_equal(res[1], 0.73834, places=5)
assert_almost_equal(res[2], 1.7001, places=4)
def inf_theory_test_6(self):
"""
I(X ; Y)
"""
fac1 = self.fXY1.marginal(self.X)
fac2 = self.fXY1.marginal(self.Y)
res = [
mutualInformation(self.fXY1, fac1, fac2),
mutualInformation(self.fXY1, fac1, fac2, 10),
mutualInformation(self.fXY1, fac1, fac2, math.e)
]
assert_almost_equal(res[0], 0.0, places=1)
assert_almost_equal(res[1], 0.0, places=1)
assert_almost_equal(res[2], 0.0, places=1)
def inf_theory_test_7(self):
"""
I(X ; Y)
"""
joint = Factor([self.X, self.Y], [0.8, 0.05, 0.05, 0.8])
fac1 = self.fXY1.marginal(self.X)
fac2 = self.fXY1.marginal(self.Y)
res = [
mutualInformation(joint, fac1, fac2),
mutualInformation(joint, fac1, fac2, 10),
mutualInformation(joint, fac1, fac2, math.e)
]
assert_almost_equal(res[0], 2.4527, places=4)
assert_almost_equal(res[1], 0.73834, places=5)
assert_almost_equal(res[2], 1.7001, places=5)
class TestInfTheoryValue(TestBase):
def __init__(self):
TestBase.__init__(self)
# factors for information theory testing
self.fX1 = Factor(self.X, [0.5, 0.5])
self.fX2 = Factor(self.X, [0.0, 1.0])
self.fX3 = Factor(self.X, [1.0, 0.0])
self.fXY1 = Factor([self.X, self.Y], [0.25, 0.25, 0.25, 0.25])
self.fXY2 = Factor([self.X, self.Y], [0.1, 0.2, 0.3, 0.4])
self.fXY3 = Factor([self.X, self.Y], [0.4, 0.3, 0.2, 0.1])
self.P1 = Factor([self.X], [0.5, 0.5])
self.Q1 = Factor([self.X], [0.9, 0.1])
self.P2 = Factor([self.X, self.Y], [0.25, 0.25, 0.25, 0.25])
self.Q2 = Factor([self.X, self.Y], [0.8, 0.05, 0.05, 0.8])
def inf_theory_test_0(self):
"""
H(X)
"""
assert_almost_equal(entropy(self.fX1), 1.0, places=1)
assert_almost_equal(entropy(self.fX1, 10), 0.30103, places=5)
assert_almost_equal(entropy(self.fX1, math.e), 0.69315, places=5)
assert_almost_equal(entropy(self.fX2), 0.0, places=1)
assert_almost_equal(entropy(self.fX2, 10), 0.0, places=1)
assert_almost_equal(entropy(self.fX2, math.e), 0.0, places=1)
assert_almost_equal(entropy(self.fX3), 0.0, places=1)
assert_almost_equal(entropy(self.fX3, 10), 0.0, places=1)
assert_almost_equal(entropy(self.fX3, math.e), 0.0, places=1)
def inf_theory_test_1(self):
"""
H(X, Y)
"""
assert_almost_equal(entropy(self.fXY1), 2.0, places=1)
assert_almost_equal(entropy(self.fXY1, 10), 0.60206, places=5)
assert_almost_equal(entropy(self.fXY1, math.e), 1.3863, places=4)
assert_almost_equal(entropy(self.fXY2), 1.8464, places=4)
assert_almost_equal(entropy(self.fXY2, 10), 0.55583, places=5)
assert_almost_equal(entropy(self.fXY2, math.e), 1.2799, places=4)
assert_almost_equal(entropy(self.fXY3), 1.8464, places=4)
assert_almost_equal(entropy(self.fXY3, 10), 0.55583, places=5)
assert_almost_equal(entropy(self.fXY3, math.e), 1.2799, places=4)
def inf_theory_test_2(self):
"""
KLD(P1 | Q1)
"""
res = [kullbackLeiblerDistance(self.P1, self.Q1),
kullbackLeiblerDistance(self.P1, self.Q1, 10),
kullbackLeiblerDistance(self.P1, self.Q1, math.e)]
assert_almost_equal(res[0], 0.73697, places=4)
assert_almost_equal(res[1], 0.22185, places=4)
assert_almost_equal(res[2], 0.51083, places=4)
def inf_theory_test_3(self):
"""
KLD(P2 | Q2)
"""
res = [kullbackLeiblerDistance(self.P2, self.Q2),
kullbackLeiblerDistance(self.P2, self.Q2, 10),
kullbackLeiblerDistance(self.P2, self.Q2, math.e)]
assert_almost_equal(res[0], 0.32193, places=4)
assert_almost_equal(res[1], 0.09691, places=4)
assert_almost_equal(res[2], 0.22314, places=4)
def inf_theory_test_4(self):
"""
KLD(Q1 | P1)
"""
res = [kullbackLeiblerDistance(self.Q1, self.P1),
kullbackLeiblerDistance(self.Q1, self.P1, 10),
kullbackLeiblerDistance(self.Q1, self.P1, math.e)]
assert_almost_equal(res[0], 0.53100, places=5)
assert_almost_equal(res[1], 0.15985, places=5)
assert_almost_equal(res[2], 0.36806, places=5)
def inf_theory_test_5(self):
"""
KLD(Q2 | P2)
"""
res = [kullbackLeiblerDistance(self.Q2, self.P2),
kullbackLeiblerDistance(self.Q2, self.P2, 10),
kullbackLeiblerDistance(self.Q2, self.P2, math.e)]
assert_almost_equal(res[0], 2.4527, places=4)
assert_almost_equal(res[1], 0.73834, places=5)
assert_almost_equal(res[2], 1.7001, places=4)
def inf_theory_test_6(self):
"""
I(X ; Y)
"""
fac1 = self.fXY1.marginal(self.X)
fac2 = self.fXY1.marginal(self.Y)
res = [mutualInformation(self.fXY1, fac1, fac2),
mutualInformation(self.fXY1, fac1, fac2, 10),
mutualInformation(self.fXY1, fac1, fac2, math.e)]
assert_almost_equal(res[0], 0.0, places=1)
assert_almost_equal(res[1], 0.0, places=1)
assert_almost_equal(res[2], 0.0, places=1)
def inf_theory_test_7(self):
"""
I(X ; Y)
"""
joint = Factor([self.X, self.Y], [0.8, 0.05, 0.05, 0.8])
fac1 = self.fXY1.marginal(self.X)
fac2 = self.fXY1.marginal(self.Y)
res = [mutualInformation(joint, fac1, fac2),
mutualInformation(joint, fac1, fac2, 10),
mutualInformation(joint, fac1, fac2, math.e)]
assert_almost_equal(res[0], 2.4527, places=4)
assert_almost_equal(res[1], 0.73834, places=5)
assert_almost_equal(res[2], 1.7001, places=5)