def mixed_estimator(C, Y, estimator, G=None, max_number_partitions=None, sorting=False):
"""
THe mixed estimator for mutual information of Mandros et al. KDD'2020. Discretizes with
equal-frequency. Estimator is the mutual information estimator of choice, G is the set of already
discrete variables. Will perfom an initial sorting on marginal mutual informations in two bins
if sorting=True"""
if isinstance(C, pd.Series) or isinstance(C, pd.DataFrame):
C = C.to_numpy()
if isinstance(Y, pd.Series) or isinstance(Y, pd.DataFrame):
Y = Y.to_numpy()
number_of_attributes_in_C = number_of_columns(C)
num_samples = len(C)
if max_number_partitions is None:
max_number_partitions = math.ceil(math.log10(len(C)))
# sorting in decreasing marginal mutual information
if sorting and number_of_attributes_in_C > 1:
generator = sort_generator(
estimator=estimator,
G=G,
Y=Y,
X=C,
)
sorted_attributes = sorted(generator, key=itemgetter(0))
sorted_column_indices = [row[1] for row in sorted_attributes]
C = C[:, sorted_column_indices]
discrete_C = None
best_score = float("-inf")
for i in range(number_of_attributes_in_C):
generator = max_generator(
estimator=estimator,
G=G,
Y=Y,
X=get_column(C, i),
max_number_partitions=max_number_partitions
)
top_score, top_discretized_attribute = max(generator, key=itemgetter(0))
if top_score > best_score:
best_score = top_score
discrete_C = append_two_arrays(discrete_C, top_discretized_attribute)
else:
discrete_C = append_two_arrays(discrete_C, np.zeros((num_samples, 1)))
return top_score, discrete_C
def fraction_of_information_plugin(X,
Y,
with_cross_tab=False,
contingency_table=None,
entropy_Y=None):
"""
The plugin estimator for the fraction of information F(X;Y)=I(X,Y)/H(Y).
It can be computed either using cross_tab from Pandas, or with
numpy. A precomputed contingency table and entropy of Y can be provided if
it is available"""
if isinstance(X, pd.Series) or isinstance(X, pd.DataFrame):
X = X.to_numpy()
if isinstance(Y, pd.Series) or isinstance(Y, pd.DataFrame):
Y = Y.to_numpy()
if with_cross_tab == True or contingency_table != None:
return fraction_of_information_from_cross_tab(
X, Y, contingency_table=contingency_table, entropy_Y=entropy_Y)
else:
entropyX = entropy_plugin(X)
if entropy_Y == None:
entropy_Y = entropy_plugin(Y)
dataXY = append_two_arrays(X, Y)
entropyXY = entropy_plugin(dataXY)
return (entropyX + entropy_Y - entropyXY) / entropy_Y
def test_mixed_fraction_information_permutation_another():
""" Tests choose_no_overflow for simple cases """
# input
X = np.arange(8)
Y = np.array([1, 1, 2, 2, 3, 3, 4, 4])
error = 1e-10
# do
res = mixed_estimator(append_two_arrays(X, X), Y, fraction_of_information_permutation, max_number_partitions=4)
# assert
assert res[0] == approx(0.4285714285714287, rel=error)
assert (np.array_equal(res[1][:, 0], [0, 0, 1, 1, 2, 2, 3, 3]))
assert (np.array_equal(res[1][:, 1], [0, 0, 0, 0, 0, 0, 0, 0]))
def mutual_information_plugin(X,
Y,
with_cross_tab=False,
contingency_table=None):
"""
The plugin estimator for mutual information I(X;Y) between two attribute sets X
and Y. It can be computed either using cross_tab from Pandas, or with
numpy. A precomputed contingency table can be provided if it is available"""
if isinstance(X, pd.Series) or isinstance(X, pd.DataFrame):
X = X.to_numpy()
if isinstance(Y, pd.Series) or isinstance(Y, pd.DataFrame):
Y = Y.to_numpy()
if with_cross_tab == True or contingency_table != None:
return mutual_information_from_cross_tab(
X, Y, contingency_table=contingency_table)
else:
entropyX = entropy_plugin(X)
entropy_Y = entropy_plugin(Y)
dataXY = append_two_arrays(X, Y)
entropyXY = entropy_plugin(dataXY)
return entropyX + entropy_Y - entropyXY
def sort_generator(estimator, G, Y, X):
for i in range(number_of_columns(X)):
discrete_candidate = pd.qcut(get_column(X, i), 2, labels=False, duplicates='drop')
joint_columns = append_two_arrays(discrete_candidate, G)
result = estimator(joint_columns, Y)
yield result, i
def max_generator(estimator, G, Y, X, max_number_partitions):
for num_bins in range(2, max_number_partitions + 1):
discrete_candidate = pd.qcut(X, num_bins, labels=False, duplicates='drop')
joint_columns = append_two_arrays(discrete_candidate, G)
result = estimator(joint_columns, Y)
yield result, discrete_candidate