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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
()
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