def test_a_b_mutual_information_declining(self):
'''
1. Start with 99 rows, two vars, 3 categories, perfectly correlated
2. Add 100 rows, randomly generated (different random seed for each var), see that mutual information is smaller
3. Repeat 2, and see that mutual information is smaller yet
'''
# Create perfectly correlated df
df = pd.DataFrame([], columns=list('ab'))
for i in range(33):
df1 = pd.DataFrame([['1', '1'], ['2', '2'], ['3', '3']],
columns=list('ab'))
df = df.append(df1, ignore_index=True)
sase = SampleSet(df)
mi1 = sase.mutual_information(['a'], ['b'])['mi']
self.assertAlmostEqual(mi1, np.log2(3))
# Append 100 uncorrelated rows
rows = [[str(random.randint(1, 3)),
str(random.randint(1, 3))] for i in range(100)]
randDf = pd.DataFrame(rows, columns=list('ab'))
df = df.append(randDf, ignore_index=True)
sase = SampleSet(df)
mi2 = sase.mutual_information(['a'], ['b'])['mi']
self.assertTrue(mi2 < mi1)
# Append another 100 uncorrelated rows
rows = [[str(random.randint(1, 3)),
str(random.randint(1, 3))] for i in range(100)]
randDf = pd.DataFrame(rows, columns=list('ab'))
df = df.append(randDf, ignore_index=True)
sase = SampleSet(df)
mi3 = sase.mutual_information(['a'], ['b'])['mi']
self.assertTrue(mi3 < mi2)
def test_separate_categories(self):
'''
Test that if categories are not separate an exception is thrown
'''
rows_3_cats = [['1', '1'], ['2', '2'], ['3', '3']]
df = pd.DataFrame(rows_3_cats, columns=list('ab'))
sase = SampleSet(df)
with self.assertRaises(Exception):
sase.mutual_information(['a', 'b'], ['b'])
def test_mutual_information_vs_categories(self):
'''
Test that mutual information is similar to log(number of categories) for perfectly correlated sets
'''
# test for 3 categories
rows_3_cats = [['1', '1'], ['2', '2'], ['3', '3']]
df = pd.DataFrame(rows_3_cats, columns=list('ab'))
sase = SampleSet(df)
self.assertAlmostEqual(sase.mutual_information(['a'], ['b'])['mi'], np.log2(3))
# test for 100 categories
rows_100_cats = [[str(i), str(i)] for i in range(100)]
df = pd.DataFrame(rows_100_cats, columns=list('ab'))
sase = SampleSet(df)
self.assertAlmostEqual(sase.mutual_information(['a'], ['b'])['mi'], np.log2(100))
def test_a_b_given_c(self):
'''
The test file has 200 rows where c==1, and MI(a,b)==1,
and 100 rows where c==2 and MI(a,b)==0
'''
matrix = pd.read_csv('test_files/test_conditional_mutual_information.csv', dtype=np.str)
samples = SampleSet(matrix)
self.assertEqual(samples.mutual_information(['a'], ['b'], ['c'])['mi'], 0.6666666666666666)
def test_mutual_information_significance_extreme(self):
'''
Test that when generating A, B randomly according to P(A), P(B), the % of Type I errors matches the significance.
'''
errors = 0
tests = 10
significance = 0.95
for i in range(tests):
df = self.generate_random_a_b(100000, [0.01], [0.99])
sase = SampleSet(df)
p_val = sase.mutual_information(['a'], ['b'], debug=True)['p_val']
if p_val > significance:
errors += 1
std = np.sqrt((significance * (1 - significance)) / tests)
self.assertAlmostEqual(1 - significance, errors / tests, delta=3 * std)
def test_mutual_information_significance_with_conditional(self):
'''
Test that when generating A, B randomly according to P(A), P(B), for a numbr of categories of a conditional group C, the % of Type I errors matches the significance.
'''
errors = 0
tests = 10
significance = 0.95
for i in range(tests):
final = pd.DataFrame({'a': [], 'b': [], 'c': []})
for j in [0, 5, 10]:
df = self.generate_random_a_b(10000, [0.05 + j], [0.95 - j])
df['c'] = j
final = final.append(df)
sase = SampleSet(final)
p_val = sase.mutual_information(['a'], ['b'], ['c'],
debug=True)['p_val']
if p_val > significance:
errors += 1
std = np.sqrt((significance * (1 - significance)) / tests)
self.assertAlmostEqual(1 - significance, errors / tests, delta=3 * std)
def test_a_b_mutual_info(self):
matrix = pd.read_csv('test_files/test_mutual_information.csv',
dtype=np.str)
samples = SampleSet(matrix)
self.assertEqual(samples.mutual_information(['a'], ['b'])['mi'], 1)