def test_mi_uninformative():
x = np.reshape(np.arange(1, 101), (-1, 1))
y = np.ones((100, 1))
mi = estimate_mutual_information(x, y)
h_z = estimate_entropy(x)
assert h_z / 4 > mi, \
'uninformative column should have no information'
def test_mi_informative():
x = np.reshape(np.arange(1, 101), (-1, 1))
y = np.reshape(np.arange(1, 101), (-1, 1))
mi = estimate_mutual_information(x, y)
h_y = estimate_entropy(y)
assert mi > h_y / 4, \
'exact copy columns should have high information'
def test_mi_informative(self):
x = np.reshape(np.arange(1, 101), (-1, 1))
y = np.reshape(np.arange(1, 101), (-1, 1))
mi = estimate_mutual_information(x, y)
h_y = estimate_entropy(y)
self.assertGreater(mi, h_y / 4,
'exact copy columns should have high information')
def test_mi_uninformative(self):
x = np.reshape(np.arange(1, 101), (-1, 1))
y = np.ones((100, 1))
mi = estimate_mutual_information(x, y)
h_z = estimate_entropy(x)
self.assertGreater(h_z / 4, mi,
'uninformative column should have no information')
def test_cmi_high_info_uninformative_z():
# redundant copies have little information
x = np.reshape(np.arange(1, 101), (-1, 1))
y = np.reshape(np.arange(1, 101), (-1, 1))
# exact copies of y should have lots of information
useless_z = np.ones((100, 1))
cmi = estimate_conditional_information(x, y, useless_z)
mi = estimate_mutual_information(x, y)
assert round(abs(cmi - mi)) == 0, \
'uninformative z should not affect mutual information score'
def test_cmi_high_info_uninformative_z(self):
# redundant copies have little information
x = np.reshape(np.arange(1, 101), (-1, 1))
y = np.reshape(np.arange(1, 101), (-1, 1))
# exact copies of y should have lots of information
useless_z = np.ones((100, 1))
cmi = estimate_conditional_information(x, y, useless_z)
mi = estimate_mutual_information(x, y)
self.assertAlmostEqual(
cmi, mi,
'uninformative z should not affect mutual information score')
def judge(self):
logger.info(f'Judging feature using {self}')
z = (self.candidate_feature.as_feature_engineering_pipeline().fit(
self.X_df, y=self.y_df).transform(self.X_df_val))
y = self.y_val
z, y = asarray2d(z), asarray2d(y)
z, y = self._handle_nans(z, y)
if z is None and y is None:
# nans were found and handle_nan_targets == 'fail'
return False
mi = estimate_mutual_information(z, y)
delta = mi - self.threshold
outcome = delta > 0
logger.info(f'Mutual information with target I(Z;Y) is {mi} vs. '
f'threshold {self.threshold} ({delta} above threshold)')
return outcome
def _summarize_feature(
feature: 'ballet.feature.Feature',
values: Optional[Dict['ballet.feature.Feature', Optional[np.ndarray]]],
y: Optional[np.ndarray],
expensive_stats: bool,
) -> dict:
"""Summarize a single feature"""
result = {
'name':
feature.name,
'description':
feature.description,
'input': [feature.input] if isinstance(feature.input, str) else
feature.input if not callable(feature.input) else [],
'transformer':
repr(feature.transformer),
'primitives':
get_transformer_primitives(feature.transformer),
'output':
feature.output,
'author':
feature.author,
'source':
feature.source,
'mutual_information':
np.nan,
'conditional_mutual_information':
np.nan,
'ninputs':
np.nan,
'nvalues':
np.nan,
'ncontinuous':
np.nan,
'ndiscrete':
np.nan,
'mean':
np.nan,
'std':
np.nan,
'variance':
np.nan,
'min':
np.nan,
'median':
np.nan,
'max':
np.nan,
'nunique':
np.nan,
}
# if feature values are missing here, the values are left at nans from
# above
if values is not None and y is not None:
z = values[feature]
if z is not None:
feature_values_list = [
feature_values
for other_feature, feature_values in values.items()
if other_feature is not feature and feature_values is not None
]
if feature_values_list:
x = np.concatenate(feature_values_list, axis=1)
else:
x = np.empty((z.shape[0], 0))
_y, _z = skipna(y, z, how='left')
result['mutual_information'] = estimate_mutual_information(_z, _y)
if not callable(feature.input):
if isinstance(feature.input, str):
result['ninputs'] = 1
else:
result['ninputs'] = len(feature.input)
result['nvalues'] = z.shape[1]
result['ncontinuous'] = np.sum(_get_cont_columns(z))
result['ndiscrete'] = np.sum(_get_disc_columns(z))
result['mean'] = np.mean(np.mean(z, axis=0)) # same thing anyway
result['std'] = np.mean(np.std(z, axis=0))
result['variance'] = np.mean(np.var(z, axis=0))
result['min'] = np.min(z)
result['median'] = np.median(np.median(z, axis=0))
result['max'] = np.max(z)
result['nunique'] = np.mean(countunique(z, axis=0))
if expensive_stats or x.shape[1] < EXPENSIVE_STATS_CMI_MAX_COLS_X:
_y, _z, _x = skipna(y, z, x, how='left')
result['conditional_mutual_information'] = \
estimate_conditional_information(_z, _y, _x)
return result
def I(a, b, c=None): # noqa
if c is None:
return estimate_mutual_information(a, b)
else:
return estimate_conditional_information(a, b, c)