def conditional_entropy(self, col_a, col_b, n_samples=1000):
""" Conditional entropy, H(A|B), of a given b.
Implementation notes
--------------------
Uses MonteCarlo integration at least in the joint entropy component.
Parameters
----------
col_a : indexer
The name of the first column
col_b : indexer
The name of the second column
n_samples : int
The number of samples to use for the Monte Carlo approximation
(if nored if `col` is categorical).
Returns
-------
h_c : float
The conditional entropy of `col_a` given `col_b`.
"""
col_idxs = [
self._converters['col2idx'][col_a],
self._converters['col2idx'][col_b]
]
h_ab = mu.joint_entropy(self._models, col_idxs, n_samples)
h_b = self.entropy(col_b, n_samples)
h_c = h_ab - h_b
return h_c
def conditional_entropy(self, col_a, col_b, n_samples=1000):
""" Conditional entropy, H(A|B), of a given b.
Implementation notes
--------------------
Uses MonteCarlo integration at least in the joint entropy component.
Parameters
----------
col_a : indexer
The name of the first column
col_b : indexer
The name of the second column
n_samples : int
The number of samples to use for the Monte Carlo approximation
(if nored if `col` is categorical).
Returns
-------
h_c : float
The conditional entropy of `col_a` given `col_b`.
"""
col_idxs = [self._converters['col2idx'][col_a],
self._converters['col2idx'][col_b]]
h_ab = mu.joint_entropy(self._models, col_idxs, n_samples)
h_b = self.entropy(col_b, n_samples)
h_c = h_ab - h_b
return h_c
def mutual_information(self,
col_a,
col_b,
normed=True,
linfoot=False,
n_samples=1000):
""" The mutual information, I(A, B), between two columns.
Parameters
----------
col_a : indexer
The name of the first column
col_b : indexer
The name of the second column
normed : bool
If True, the mutual information, I, is normed according to the
symmertic uncertainty, U = 2*I(A, B)/(H(A) + H(B)).
n_samples : int
The number of samples to use for the Monte Carlo approximation
(if nored if `col` is categorical).
Returns
-------
mi : float
The mutual information between `col_a` and `col_b`.
"""
if linfoot:
normed = False
idx_a = self._converters['col2idx'][col_a]
idx_b = self._converters['col2idx'][col_b]
models = []
for model in self._models:
if model['col_assignment'][idx_a] == \
model['col_assignment'][idx_b]:
models.append(model)
if len(models) == 0:
mi = 0.0
else:
h_a = self.entropy(col_a, n_samples=n_samples)
h_b = self.entropy(col_b, n_samples=n_samples)
h_ab = mu.joint_entropy(models, [idx_a, idx_b], n_samples)
mi = h_a + h_b - h_ab
# XXX: Differential entropy can be negative. Here we prevent
# negative mutual information.
mi = max(mi, 0.)
if normed:
# normalize using symmetric uncertainty
mi = 2. * mi / (h_a + h_b)
if linfoot:
mi = (1. - exp(-2 * mi))**.5
return mi
def mutual_information(self, col_a, col_b, normed=True, linfoot=False,
n_samples=1000):
""" The mutual information, I(A, B), between two columns.
Parameters
----------
col_a : indexer
The name of the first column
col_b : indexer
The name of the second column
normed : bool
If True, the mutual information, I, is normed according to the
symmertic uncertainty, U = 2*I(A, B)/(H(A) + H(B)).
n_samples : int
The number of samples to use for the Monte Carlo approximation
(if nored if `col` is categorical).
Returns
-------
mi : float
The mutual information between `col_a` and `col_b`.
"""
if linfoot:
normed = False
idx_a = self._converters['col2idx'][col_a]
idx_b = self._converters['col2idx'][col_b]
models = []
for model in self._models:
if model['col_assignment'][idx_a] == \
model['col_assignment'][idx_b]:
models.append(model)
if len(models) == 0:
mi = 0.0
else:
h_a = self.entropy(col_a, n_samples=n_samples)
h_b = self.entropy(col_b, n_samples=n_samples)
h_ab = mu.joint_entropy(models, [idx_a, idx_b], n_samples)
mi = h_a + h_b - h_ab
# XXX: Differential entropy can be negative. Here we prevent
# negative mutual information.
mi = max(mi, 0.)
if normed:
# normalize using symmetric uncertainty
mi = 2.*mi/(h_a + h_b)
if linfoot:
mi = (1. - exp(-2*mi))**.5
return mi
