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test_probability4e.py
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349 lines (276 loc) · 12.1 KB
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import pytest
from probability4e import *
random.seed("aima-python")
def tests():
cpt = burglary.variable_node('Alarm')
event = {'Burglary': True, 'Earthquake': True}
assert cpt.p(True, event) == 0.95
event = {'Burglary': False, 'Earthquake': True}
assert cpt.p(False, event) == 0.71
# enumeration_ask('Earthquake', {}, burglary)
s = {'A': True, 'B': False, 'C': True, 'D': False}
assert consistent_with(s, {})
assert consistent_with(s, s)
assert not consistent_with(s, {'A': False})
assert not consistent_with(s, {'D': True})
random.seed(21)
p = rejection_sampling('Earthquake', {}, burglary, 1000)
assert p[True], p[False] == (0.001, 0.999)
random.seed(71)
p = likelihood_weighting('Earthquake', {}, burglary, 1000)
assert p[True], p[False] == (0.002, 0.998)
# test ProbDist
def test_probdist_basic():
P = ProbDist('Flip')
P['H'], P['T'] = 0.25, 0.75
assert P['H'] == 0.25
assert P['T'] == 0.75
assert P['X'] == 0.00
P = ProbDist('BiasedDie')
P['1'], P['2'], P['3'], P['4'], P['5'], P['6'] = 10, 15, 25, 30, 40, 80
P.normalize()
assert P['2'] == 0.075
assert P['4'] == 0.15
assert P['6'] == 0.4
def test_probdist_frequency():
P = ProbDist('X', {'lo': 125, 'med': 375, 'hi': 500})
assert (P['lo'], P['med'], P['hi']) == (0.125, 0.375, 0.5)
P = ProbDist('Pascal-5', {'x1': 1, 'x2': 5, 'x3': 10, 'x4': 10, 'x5': 5, 'x6': 1})
assert (P['x1'], P['x2'], P['x3'], P['x4'], P['x5'], P['x6']) == (
0.03125, 0.15625, 0.3125, 0.3125, 0.15625, 0.03125)
def test_probdist_normalize():
P = ProbDist('Flip')
P['H'], P['T'] = 35, 65
P = P.normalize()
assert (P.prob['H'], P.prob['T']) == (0.350, 0.650)
P = ProbDist('BiasedDie')
P['1'], P['2'], P['3'], P['4'], P['5'], P['6'] = 10, 15, 25, 30, 40, 80
P = P.normalize()
assert (P.prob['1'], P.prob['2'], P.prob['3'], P.prob['4'], P.prob['5'], P.prob['6']) == (
0.05, 0.075, 0.125, 0.15, 0.2, 0.4)
# test JoinProbDist
def test_jointprob():
P = JointProbDist(['X', 'Y'])
P[1, 1] = 0.25
assert P[1, 1] == 0.25
P[dict(X=0, Y=1)] = 0.5
assert P[dict(X=0, Y=1)] == 0.5
def test_event_values():
assert event_values({'A': 10, 'B': 9, 'C': 8}, ['C', 'A']) == (8, 10)
assert event_values((1, 2), ['C', 'A']) == (1, 2)
def test_enumerate_joint():
P = JointProbDist(['X', 'Y'])
P[0, 0] = 0.25
P[0, 1] = 0.5
P[1, 1] = P[2, 1] = 0.125
assert enumerate_joint(['Y'], dict(X=0), P) == 0.75
assert enumerate_joint(['X'], dict(Y=2), P) == 0
assert enumerate_joint(['X'], dict(Y=1), P) == 0.75
Q = JointProbDist(['W', 'X', 'Y', 'Z'])
Q[0, 1, 1, 0] = 0.12
Q[1, 0, 1, 1] = 0.4
Q[0, 0, 1, 1] = 0.5
Q[0, 0, 1, 0] = 0.05
Q[0, 0, 0, 0] = 0.675
Q[1, 1, 1, 0] = 0.3
assert enumerate_joint(['W'], dict(X=0, Y=0, Z=1), Q) == 0
assert enumerate_joint(['W'], dict(X=0, Y=0, Z=0), Q) == 0.675
assert enumerate_joint(['W'], dict(X=0, Y=1, Z=1), Q) == 0.9
assert enumerate_joint(['Y'], dict(W=1, X=0, Z=1), Q) == 0.4
assert enumerate_joint(['Z'], dict(W=0, X=0, Y=0), Q) == 0.675
assert enumerate_joint(['Z'], dict(W=1, X=1, Y=1), Q) == 0.3
def test_enumerate_joint_ask():
P = JointProbDist(['X', 'Y'])
P[0, 0] = 0.25
P[0, 1] = 0.5
P[1, 1] = P[2, 1] = 0.125
assert enumerate_joint_ask(
'X', dict(Y=1), P).show_approx() == '0: 0.667, 1: 0.167, 2: 0.167'
def test_is_independent():
P = JointProbDist(['X', 'Y'])
P[0, 0] = P[0, 1] = P[1, 1] = P[1, 0] = 0.25
assert enumerate_joint_ask(
'X', dict(Y=1), P).show_approx() == '0: 0.5, 1: 0.5'
assert is_independent(['X', 'Y'], P)
# test BayesNode
def test_bayesnode_p():
bn = BayesNode('X', 'Burglary', {T: 0.2, F: 0.625})
assert bn.p(True, {'Burglary': True, 'Earthquake': False}) == 0.2
assert bn.p(False, {'Burglary': False, 'Earthquake': True}) == 0.375
assert BayesNode('W', '', 0.75).p(False, {'Random': True}) == 0.25
def test_bayesnode_sample():
X = BayesNode('X', 'Burglary', {T: 0.2, F: 0.625})
assert X.sample({'Burglary': False, 'Earthquake': True}) in [True, False]
Z = BayesNode('Z', 'P Q', {(True, True): 0.2, (True, False): 0.3,
(False, True): 0.5, (False, False): 0.7})
assert Z.sample({'P': True, 'Q': False}) in [True, False]
# test continuous variable bayesian net
def test_gaussian_probability():
param = {'sigma': 0.5, 'b': 1, 'a': {'h': 0.5}}
event = {'h': 0.6}
assert gaussian_probability(param, event, 1) == 0.6664492057835993
def test_logistic_probability():
param = {'mu': 0.5, 'sigma': 0.1}
event = {'h': 0.6}
assert logistic_probability(param, event, True) == 0.16857376940725355
assert logistic_probability(param, event, False) == 0.8314262305927465
def test_enumeration_ask():
assert enumeration_ask(
'Burglary', dict(JohnCalls=T, MaryCalls=T),
burglary).show_approx() == 'False: 0.716, True: 0.284'
assert enumeration_ask(
'Burglary', dict(JohnCalls=T, MaryCalls=F),
burglary).show_approx() == 'False: 0.995, True: 0.00513'
assert enumeration_ask(
'Burglary', dict(JohnCalls=F, MaryCalls=T),
burglary).show_approx() == 'False: 0.993, True: 0.00688'
assert enumeration_ask(
'Burglary', dict(JohnCalls=T),
burglary).show_approx() == 'False: 0.984, True: 0.0163'
assert enumeration_ask(
'Burglary', dict(MaryCalls=T),
burglary).show_approx() == 'False: 0.944, True: 0.0561'
def test_elimination_ask():
assert elimination_ask(
'Burglary', dict(JohnCalls=T, MaryCalls=T),
burglary).show_approx() == 'False: 0.716, True: 0.284'
assert elimination_ask(
'Burglary', dict(JohnCalls=T, MaryCalls=F),
burglary).show_approx() == 'False: 0.995, True: 0.00513'
assert elimination_ask(
'Burglary', dict(JohnCalls=F, MaryCalls=T),
burglary).show_approx() == 'False: 0.993, True: 0.00688'
assert elimination_ask(
'Burglary', dict(JohnCalls=T),
burglary).show_approx() == 'False: 0.984, True: 0.0163'
assert elimination_ask(
'Burglary', dict(MaryCalls=T),
burglary).show_approx() == 'False: 0.944, True: 0.0561'
# test sampling
def test_prior_sample():
random.seed(42)
all_obs = [prior_sample(burglary) for x in range(1000)]
john_calls_true = [observation for observation in all_obs if observation['JohnCalls'] is True]
mary_calls_true = [observation for observation in all_obs if observation['MaryCalls'] is True]
burglary_and_john = [observation for observation in john_calls_true if observation['Burglary'] is True]
burglary_and_mary = [observation for observation in mary_calls_true if observation['Burglary'] is True]
assert len(john_calls_true) / 1000 == 46 / 1000
assert len(mary_calls_true) / 1000 == 13 / 1000
assert len(burglary_and_john) / len(john_calls_true) == 1 / 46
assert len(burglary_and_mary) / len(mary_calls_true) == 1 / 13
def test_prior_sample2():
random.seed(128)
all_obs = [prior_sample(sprinkler) for x in range(1000)]
rain_true = [observation for observation in all_obs if observation['Rain'] is True]
sprinkler_true = [observation for observation in all_obs if observation['Sprinkler'] is True]
rain_and_cloudy = [observation for observation in rain_true if observation['Cloudy'] is True]
sprinkler_and_cloudy = [observation for observation in sprinkler_true if observation['Cloudy'] is True]
assert len(rain_true) / 1000 == 0.476
assert len(sprinkler_true) / 1000 == 0.291
assert len(rain_and_cloudy) / len(rain_true) == 376 / 476
assert len(sprinkler_and_cloudy) / len(sprinkler_true) == 39 / 291
def test_rejection_sampling():
random.seed(47)
assert rejection_sampling(
'Burglary', dict(JohnCalls=T, MaryCalls=T),
burglary, 10000).show_approx() == 'False: 0.7, True: 0.3'
assert rejection_sampling(
'Burglary', dict(JohnCalls=T, MaryCalls=F),
burglary, 10000).show_approx() == 'False: 1, True: 0'
assert rejection_sampling(
'Burglary', dict(JohnCalls=F, MaryCalls=T),
burglary, 10000).show_approx() == 'False: 0.987, True: 0.0128'
assert rejection_sampling(
'Burglary', dict(JohnCalls=T),
burglary, 10000).show_approx() == 'False: 0.982, True: 0.0183'
assert rejection_sampling(
'Burglary', dict(MaryCalls=T),
burglary, 10000).show_approx() == 'False: 0.965, True: 0.0348'
def test_rejection_sampling2():
random.seed(42)
assert rejection_sampling(
'Cloudy', dict(Rain=T, Sprinkler=T),
sprinkler, 10000).show_approx() == 'False: 0.56, True: 0.44'
assert rejection_sampling(
'Cloudy', dict(Rain=T, Sprinkler=F),
sprinkler, 10000).show_approx() == 'False: 0.119, True: 0.881'
assert rejection_sampling(
'Cloudy', dict(Rain=F, Sprinkler=T),
sprinkler, 10000).show_approx() == 'False: 0.951, True: 0.049'
assert rejection_sampling(
'Cloudy', dict(Rain=T),
sprinkler, 10000).show_approx() == 'False: 0.205, True: 0.795'
assert rejection_sampling(
'Cloudy', dict(Sprinkler=T),
sprinkler, 10000).show_approx() == 'False: 0.835, True: 0.165'
def test_likelihood_weighting():
random.seed(1017)
assert likelihood_weighting(
'Burglary', dict(JohnCalls=T, MaryCalls=T),
burglary, 10000).show_approx() == 'False: 0.702, True: 0.298'
assert likelihood_weighting(
'Burglary', dict(JohnCalls=T, MaryCalls=F),
burglary, 10000).show_approx() == 'False: 0.993, True: 0.00656'
assert likelihood_weighting(
'Burglary', dict(JohnCalls=F, MaryCalls=T),
burglary, 10000).show_approx() == 'False: 0.996, True: 0.00363'
assert likelihood_weighting(
'Burglary', dict(JohnCalls=F, MaryCalls=F),
burglary, 10000).show_approx() == 'False: 1, True: 0.000126'
assert likelihood_weighting(
'Burglary', dict(JohnCalls=T),
burglary, 10000).show_approx() == 'False: 0.979, True: 0.0205'
assert likelihood_weighting(
'Burglary', dict(MaryCalls=T),
burglary, 10000).show_approx() == 'False: 0.94, True: 0.0601'
def test_likelihood_weighting2():
random.seed(42)
assert likelihood_weighting(
'Cloudy', dict(Rain=T, Sprinkler=T),
sprinkler, 10000).show_approx() == 'False: 0.559, True: 0.441'
assert likelihood_weighting(
'Cloudy', dict(Rain=T, Sprinkler=F),
sprinkler, 10000).show_approx() == 'False: 0.12, True: 0.88'
assert likelihood_weighting(
'Cloudy', dict(Rain=F, Sprinkler=T),
sprinkler, 10000).show_approx() == 'False: 0.951, True: 0.0486'
assert likelihood_weighting(
'Cloudy', dict(Rain=T),
sprinkler, 10000).show_approx() == 'False: 0.198, True: 0.802'
assert likelihood_weighting(
'Cloudy', dict(Sprinkler=T),
sprinkler, 10000).show_approx() == 'False: 0.833, True: 0.167'
def test_gibbs_ask():
g_solution = gibbs_ask('Cloudy', dict(Rain=True), sprinkler, 1000)
assert abs(g_solution.prob[False] - 0.2) < 0.05
assert abs(g_solution.prob[True] - 0.8) < 0.05
# The following should probably go in .ipynb:
"""
# We can build up a probability distribution like this (p. 469):
>>> P = ProbDist()
>>> P['sunny'] = 0.7
>>> P['rain'] = 0.2
>>> P['cloudy'] = 0.08
>>> P['snow'] = 0.02
# and query it like this: (Never mind this ELLIPSIS option
# added to make the doctest portable.)
>>> P['rain'] #doctest:+ELLIPSIS
0.2...
# A Joint Probability Distribution is dealt with like this [Figure 13.3]:
>>> P = JointProbDist(['Toothache', 'Cavity', 'Catch'])
>>> T, F = True, False
>>> P[T, T, T] = 0.108; P[T, T, F] = 0.012; P[F, T, T] = 0.072; P[F, T, F] = 0.008
>>> P[T, F, T] = 0.016; P[T, F, F] = 0.064; P[F, F, T] = 0.144; P[F, F, F] = 0.576
>>> P[T, T, T]
0.108
# Ask for P(Cavity|Toothache=T)
>>> PC = enumerate_joint_ask('Cavity', {'Toothache': T}, P)
>>> PC.show_approx()
'False: 0.4, True: 0.6'
>>> 0.6-epsilon < PC[T] < 0.6+epsilon
True
>>> 0.4-epsilon < PC[F] < 0.4+epsilon
True
"""
if __name__ == '__main__':
pytest.main()