def test__example_1_3(self):
butler = Discrete.from_probs(data={
'yes': 0.6,
'no': 0.4
},
variables='butler')
maid = Discrete.from_probs(data={
'yes': 0.2,
'no': 0.8
},
variables='maid')
butler__and__maid = butler * maid
knife__given__butler__and__maid = Conditional.from_probs(
data={
('yes', 'no', 'no'): 0.3,
('yes', 'no', 'yes'): 0.2,
('yes', 'yes', 'no'): 0.6,
('yes', 'yes', 'yes'): 0.1,
('no', 'no', 'no'): 0.7,
('no', 'no', 'yes'): 0.8,
('no', 'yes', 'no'): 0.4,
('no', 'yes', 'yes'): 0.9,
},
joint_variables='knife_used',
conditional_variables=['butler', 'maid'])
butler__and__maid__and__knife = (knife__given__butler__and__maid *
butler__and__maid)
butler__given__knife = butler__and__maid__and__knife.given(
knife_used='yes').p(butler='yes')
self.assertAlmostEqual(0.728, butler__given__knife, 3)
def test__example_1_2(self):
has_kj = Discrete.from_probs(data={
'yes': 1e-5,
'no': 1 - 1e-5
},
variables='has_kj')
self.assertEqual(1e-5, has_kj.p(has_kj='yes'))
self.assertEqual(1 - 1e-5, has_kj.p(has_kj='no'))
eats_hbs__given__has_kj = Conditional.from_probs(
data={
('yes', 'yes'): 0.9,
('no', 'yes'): 0.1
},
joint_variables='eats_hbs',
conditional_variables='has_kj')
eats_hbs = Discrete.from_probs(data={
'yes': 0.5,
'no': 0.5
},
variables='eats_hbs')
# 1
has_kj__given__eats_hbs = eats_hbs__given__has_kj * has_kj / eats_hbs
self.assertEqual(
1.8e-5, has_kj__given__eats_hbs.p(has_kj='yes', eats_hbs='yes'))
# 2
eats_hbs = Discrete.from_probs(data={
'yes': 0.001,
'no': 0.999
},
variables='eats_hbs')
has_kj__given__eats_hbs = eats_hbs__given__has_kj * has_kj / eats_hbs
self.assertEqual(
9 / 1000, has_kj__given__eats_hbs.p(has_kj='yes', eats_hbs='yes'))
def setUp(self) -> None:
self.education = Discrete.from_counts(
data={
('Male', 'Never finished high school'): 112,
('Male', 'High school'): 231,
('Male', 'College'): 595,
('Male', 'Graduate school'): 242,
('Female', 'Never finished high school'): 136,
('Female', 'High school'): 189,
('Female', 'College'): 763,
('Female', 'Graduate school'): 172,
},
variables=['gender', 'highest_education'])
self.education__total = 112 + 231 + 595 + 242 + 136 + 189 + 763 + 172
self.total__high_school = 231 + 189
self.coin_dist = Discrete.from_probs(
data={
('H', 'H', 1, 1): 0.25,
('H', 'T', 1, 0): 0.25,
('T', 'H', 1, 0): 0.25,
('T', 'T', 0, 1): 0.25
},
variables=['coin_1', 'coin_2', 'x', 'y'])
def test_mode_nd_categorical(self):
counts = Series({('a', 'b'): 1, ('c', 'd'): 2, ('e', 'f'): 3})
discrete = Discrete.from_counts(counts, variables=['ace', 'bdf'])
expected = DataFrame([{'ace': 'e', 'bdf': 'f'}])
actual = discrete.mode()
self.assertTrue(expected.equals(actual))
def setUp(self) -> None:
self.darts = Discrete(data=Series(index=Index(data=range(1, 21),
name='region'),
data=1 / 20),
variables='region',
states=list(range(1, 21)))
def test_mode_nd_multi_value(self):
counts = Series({('a', 'b'): 1, ('c', 'd'): 3, ('e', 'f'): 3})
expected = DataFrame({'ace': ['c', 'e'], 'bdf': ['d', 'f']}, )
discrete = Discrete.from_counts(counts, variables=['ace', 'bdf'])
actual = discrete.mode()
self.assertTrue(expected.equals(actual))
def test_max_numeric(self):
discrete = Discrete.from_probs(data={
0: 0.7,
1000: 0.2,
2000: 0.1
},
variables='a')
self.assertAlmostEqual(2000, discrete.max())
discrete_2 = Discrete.from_probs(data={
0: 0.7,
1000: 0.3,
2000: 0
},
variables='a')
self.assertAlmostEqual(1000, discrete_2.max())
def test__example_1_7(self):
c__given__a__and__b = Conditional.binary_from_probs(
data={
(0, 0): 0.1,
(0, 1): 0.99,
(1, 0): 0.8,
(1, 1): 0.25,
},
joint_variable='C',
conditional_variables=['A', 'B'])
a = Discrete.binary(0.65, 'A')
b = Discrete.binary(0.77, 'B')
a__and__b = a * b
a__and__b__and__c = a__and__b * c__given__a__and__b
self.assertAlmostEqual(0.8436, a__and__b__and__c.given(C=0).p(A=1), 4)
def test__example_1_4(self):
occupied__given__alice__and__bob = Conditional.from_probs(
{
(True, False, False): 1,
(True, False, True): 1,
(True, True, False): 1,
(True, True, True): 0,
},
joint_variables='occupied',
conditional_variables=['alice', 'bob'])
alice__and__bob = Discrete.from_probs(
{
(False, False): 0.25,
(False, True): 0.25,
(True, False): 0.25,
(True, True): 0.25,
},
variables=['alice', 'bob'])
alice__and__bob__and__occupied = (occupied__given__alice__and__bob *
alice__and__bob)
self.assertEqual(
1,
alice__and__bob__and__occupied.given(alice=True,
occupied=True).p(bob=False))
def test_from_counts__1_var__vars_as_arg(self):
counts = Series({'a': 1, 'b': 2, 'c': 3})
discrete = Discrete.from_counts(counts, variables='abc')
self.assertEqual(['abc'], discrete.variables)
self.assertEqual({'abc': ['a', 'b', 'c']}, discrete.states)
self.assertEqual(1 / 6, discrete.p(abc='a'))
self.assertEqual(2 / 6, discrete.p(abc='b'))
self.assertEqual(3 / 6, discrete.p(abc='c'))
def test_max_categorical(self):
discrete = Discrete.from_probs(data={
'a': 0.7,
'b': 0.2,
'c': 0.1
},
variables='x')
self.assertRaises(TypeError, discrete.max)
def test_mode_1d_numeric(self):
discrete = Discrete.from_probs(data={
0: 0.7,
1000: 0.2,
2000: 0.1
},
variables='a')
self.assertEqual(0, discrete.mode())
def setUp(self) -> None:
# cookies
self.bowl_1_and_chocolate = 0.125
self.bowl_1_and_vanilla = 0.375
self.bowl_2_and_chocolate = 0.25
self.bowl_2_and_vanilla = 0.25
cookie_data = TestChapter01.make_cookies_observations()
self.cookies = Discrete.from_observations(cookie_data)
self.vanilla = self.cookies.p(flavor='vanilla')
self.vanilla__bowl_1 = self.cookies.given(bowl='bowl 1').p(
flavor='vanilla')
self.vanilla__bowl_2 = self.cookies.given(bowl='bowl 2').p(
flavor='vanilla')
self.bowl = Discrete.from_probs({
'bowl 1': 0.5,
'bowl 2': 0.5
},
variables=['bowl'])
self.bowl_1 = self.bowl.p(bowl='bowl 1')
self.bowl_2 = self.bowl.p(bowl='bowl 2')
# m & m's
self.mix_1994 = Discrete.from_probs(
{
'brown': 0.3,
'yellow': 0.2,
'red': 0.2,
'green': 0.1,
'orange': 0.1,
'tan': 0.1
},
variables='color')
self.mix_1996 = Discrete.from_probs(
{
'blue': 0.24,
'green': 0.2,
'orange': 0.16,
'yellow': 0.14,
'red': 0.13,
'brown': 0.13
},
variables='color')
self.bag = Discrete.from_probs({1994: 0.5, 1996: 0.5}, variables='bag')
def test_from_counts__1_var__vars_on_index(self):
counts = Series({'a': 1, 'b': 2, 'c': 3})
counts.index.name = 'abc'
discrete = Discrete.from_counts(counts)
self.assertEqual(['abc'], discrete.variables)
self.assertEqual({'abc': ['a', 'b', 'c']}, discrete.states)
self.assertEqual(1 / 6, discrete.p(abc='a'))
self.assertEqual(2 / 6, discrete.p(abc='b'))
self.assertEqual(3 / 6, discrete.p(abc='c'))
def test_mean_numeric(self):
discrete = Discrete.from_probs(data={
0: 0.7,
1000: 0.2,
2000: 0.1
},
variables='a')
self.assertAlmostEqual(0 * 0.7 + 1000 * 0.2 + 2000 * 0.1,
discrete.mean())
def test_from_probs__with_dict(self):
bowl = Discrete.from_probs({
'bowl 1': 0.5,
'bowl 2': 0.5
},
variables=['bowl'])
self.assertIsInstance(bowl, Discrete)
mix_1994 = Discrete.from_probs(
{
'brown': 0.3,
'yellow': 0.2,
'red': 0.2,
'green': 0.1,
'orange': 0.1,
'tan': 0.1
},
variables='color')
self.assertIsInstance(mix_1994, Discrete)
def test_from_observations__1_var(self):
observations = DataFrame({
'ace': ['a', 'c', 'c', 'e', 'e', 'e'],
})
discrete = Discrete.from_observations(observations)
self.assertEqual(['ace'], discrete.variables)
self.assertEqual({'ace': ['a', 'c', 'e']}, discrete.states)
self.assertEqual(1 / 6, discrete.p(ace='a'))
self.assertEqual(2 / 6, discrete.p(ace='c'))
self.assertEqual(3 / 6, discrete.p(ace='e'))
def test_from_counts__2_vars__states_as_arg(self):
counts = Series({('a', 'b'): 1, ('c', 'd'): 2, ('e', 'f'): 3})
counts.index.names = ['ace', 'bdf']
states = {'ace': ['a', 'c', 'e', 'g'], 'bdf': ['b', 'd', 'f', 'h']}
discrete = Discrete.from_counts(counts, states=states)
self.assertEqual(['ace', 'bdf'], discrete.variables)
self.assertEqual(states, discrete.states)
self.assertEqual(1 / 6, discrete.p(ace='a', bdf='b'))
self.assertEqual(2 / 6, discrete.p(ace='c', bdf='d'))
self.assertEqual(3 / 6, discrete.p(ace='e', bdf='f'))
def test_from_observations__1_var__replace_vars(self):
observations = DataFrame({
'ace': ['a', 'c', 'c', 'e', 'e', 'e'],
})
discrete = Discrete.from_observations(observations, variables='ACE')
self.assertEqual(['ACE'], discrete.variables)
self.assertEqual({'ACE': ['a', 'c', 'e']}, discrete.states)
self.assertEqual(1 / 6, discrete.p(ACE='a'))
self.assertEqual(2 / 6, discrete.p(ACE='c'))
self.assertEqual(3 / 6, discrete.p(ACE='e'))
def test__1_3_1(self):
t = Discrete.from_observations(data=DataFrame({
't': [s_a + s_b for s_a, s_b in product(range(1, 7), range(1, 7))]
}))
s_a__s_b = Discrete.from_probs(data={
(a, b): 1 / 36
for a, b in product(range(1, 7), range(1, 7))
},
variables=['s_a', 's_b'])
t_9__given__s_a__s_b = Conditional.from_probs(
data={(9, a, b): int(a + b == 9)
for a, b in product(range(1, 7), range(1, 7))},
joint_variables=['t'],
conditional_variables=['s_a', 's_b'])
t_9__s_a__s_b = t_9__given__s_a__s_b * s_a__s_b
t_9 = t_9__s_a__s_b / t.p(t=9)
for s_a, s_b in product(range(1, 6), range(1, 6)):
self.assertEqual(t_9.p(s_a=s_a, s_b=s_b),
0.25 if s_a + s_b == 9 else 0)
def test__1_1_2(self):
population_counts = Series({
'England': 60_776_238,
'Scotland': 5_116_900,
'Wales': 2_980_700
})
population_counts.index.name = 'country'
populations = Discrete.from_counts(data=population_counts)
self.assertAlmostEqual(0.882, populations.p(country='England'), 3)
self.assertAlmostEqual(0.074, populations.p(country='Scotland'), 3)
self.assertAlmostEqual(0.043, populations.p(country='Wales'), 3)
language_probs = DataFrame.from_dict(
{
'England': {
'English': 0.95,
'Scottish': 0.04,
'Welsh': 0.01
},
'Scotland': {
'English': 0.7,
'Scottish': 0.3,
'Welsh': 0.0
},
'Wales': {
'English': 0.6,
'Scottish': 0.0,
'Welsh': 0.4
}
},
orient='columns')
language_probs.index.name = 'language'
language_probs.columns.name = 'country'
language__given__country = Conditional(data=language_probs)
self.assertIsInstance(language__given__country.data, DataFrame)
self.assertListEqual(['language'],
language__given__country.joint_variables)
self.assertListEqual(['country'],
language__given__country.conditional_variables)
country__language = language__given__country * populations
for prob, country, language in [
(0.838, 'England', 'English'),
(0.035, 'England', 'Scottish'),
(0.009, 'England', 'Welsh'),
(0.052, 'Scotland', 'English'),
(0.022, 'Scotland', 'Scottish'),
(0.0, 'Scotland', 'Welsh'),
(0.026, 'Wales', 'English'),
(0.0, 'Wales', 'Scottish'),
(0.017, 'Wales', 'Welsh'),
]:
self.assertAlmostEqual(
prob, country__language.p(country=country, language=language),
3)
def test_from_counts__2_vars__vars_as_arg(self):
counts = Series({('a', 'b'): 1, ('c', 'd'): 2, ('e', 'f'): 3})
discrete = Discrete.from_counts(counts, variables=['ace', 'bdf'])
self.assertEqual(['ace', 'bdf'], discrete.variables)
self.assertEqual({
'ace': ['a', 'c', 'e'],
'bdf': ['b', 'd', 'f']
}, discrete.states)
self.assertEqual(1 / 6, discrete.p(ace='a', bdf='b'))
self.assertEqual(2 / 6, discrete.p(ace='c', bdf='d'))
self.assertEqual(3 / 6, discrete.p(ace='e', bdf='f'))
def test_from_observations__2_vars__extra_states(self):
observations = DataFrame({
'ace': ['a', 'c', 'c', 'e', 'e', 'e'],
'bdf': ['b', 'd', 'd', 'f', 'f', 'f']
})
states = {'ace': ['a', 'c', 'e', 'g'], 'bdf': ['b', 'd', 'f', 'h']}
discrete = Discrete.from_observations(observations, states=states)
self.assertEqual(['ace', 'bdf'], discrete.variables)
self.assertEqual(states, discrete.states)
self.assertEqual(1 / 6, discrete.p(ace='a', bdf='b'))
self.assertEqual(2 / 6, discrete.p(ace='c', bdf='d'))
self.assertEqual(3 / 6, discrete.p(ace='e', bdf='f'))
def test_given_all_variables(self):
expected = Discrete.binary(0, 'A_xor_B').data
xor = Conditional.binary_from_probs(data={
(0, 0): 0,
(0, 1): 1,
(1, 0): 1,
(1, 1): 0,
},
joint_variable='A_xor_B',
conditional_variables=['A', 'B'])
actual = xor.given(A=1, B=1).data
self.assertTrue(expected.equals(actual))
def test_from_observations__2_vars__replace_vars(self):
observations = DataFrame({
'ace': ['a', 'c', 'c', 'e', 'e', 'e'],
'bdf': ['b', 'd', 'd', 'f', 'f', 'f']
})
discrete = Discrete.from_observations(observations,
variables=['ACE', 'BDF'])
self.assertEqual(['ACE', 'BDF'], discrete.variables)
self.assertEqual({
'ACE': ['a', 'c', 'e'],
'BDF': ['b', 'd', 'f']
}, discrete.states)
self.assertEqual(1 / 6, discrete.p(ACE='a', BDF='b'))
self.assertEqual(2 / 6, discrete.p(ACE='c', BDF='d'))
self.assertEqual(3 / 6, discrete.p(ACE='e', BDF='f'))
def test_mean_categorical(self):
counts = Series({'a': 1, 'c': 2, 'e': 3})
discrete = Discrete.from_counts(counts, variables='x')
self.assertRaises(TypeError, discrete.mean)
def test_mode_1d_categorical(self):
counts = Series({'a': 1, 'c': 2, 'e': 3})
discrete = Discrete.from_counts(counts, variables='x')
self.assertEqual('e', discrete.mode())
def test_mode_1d_multi_value(self):
counts = Series({'a': 2, 'b': 2, 'c': 1})
discrete = Discrete.from_counts(counts, variables='x')
self.assertListEqual(['a', 'b'], discrete.mode())