def iamb(data, alpha=0.05, feature_selection=None, debug=False):
"""
IAMB Algorithm for learning the structure of a
Discrete Bayesian Network from data.
Arguments
---------
*data* : a nested numpy array
*alpha* : a float
The type II error rate.
*feature_selection* : None or a string
Whether to use IAMB as a structure learning
or feature selection algorithm.
Returns
-------
*bn* : a BayesNet object or
*mb* : the markov blanket of a node
Effects
-------
None
Notes
-----
- Works but there are definitely some bugs.
Speed Test:
*** 5 vars, 624 obs ***
- 196 ms
"""
n_rv = data.shape[1]
Mb = dict([(rv, []) for rv in range(n_rv)])
if feature_selection is None:
_T = range(n_rv)
else:
assert (not isinstance(feature_selection, list)
), 'feature_selection must be only one value'
_T = [feature_selection]
# LEARN MARKOV BLANKET
for T in _T:
V = set(range(n_rv)) - {T}
Mb_change = True
# GROWING PHASE
while Mb_change:
Mb_change = False
# find X_max in V-Mb(T)-{T} that maximizes
# mutual information of X,T|Mb(T)
# i.e. max of mi_test(data[:,(X,T,Mb(T))])
max_val = -1
max_x = None
for X in V - set(Mb[T]) - {T}:
cols = (X, T) + tuple(Mb[T])
mi_val = mi_test(data[:, cols], test=False)
if mi_val > max_val:
max_val = mi_val
max_x = X
# if Xmax is dependent on T given Mb(T)
cols = (max_x, T) + tuple(Mb[T])
if max_x is not None and are_independent(data[:, cols]):
Mb[T].append(X)
Mb_change = True
if debug:
print('Adding %s to MB of %s' % (str(X), str(T)))
# SHRINKING PHASE
for X in Mb[T]:
# if x is independent of t given Mb(T) - {x}
cols = (X, T) + tuple(set(Mb[T]) - {X})
if are_independent(data[:, cols], alpha):
Mb[T].remove(X)
if debug:
print('Removing %s from MB of %s' % (str(X), str(T)))
if feature_selection is None:
# RESOLVE GRAPH STRUCTURE
edge_dict = resolve_markov_blanket(Mb, data)
if debug:
print('Unoriented edge dict:\n %s' % str(edge_dict))
print('MB: %s' % str(Mb))
# ORIENT EDGES
oriented_edge_dict = orient_edges_gs2(edge_dict, Mb, data, alpha)
if debug:
print('Oriented edge dict:\n %s' % str(oriented_edge_dict))
# CREATE BAYESNET OBJECT
value_dict = dict(
zip(range(data.shape[1]),
[list(np.unique(col)) for col in data.T]))
bn = BayesNet(oriented_edge_dict, value_dict)
return bn
else:
return Mb[_T]
def gs(data, alpha=0.05, feature_selection=None, debug=False):
"""
Perform growshink algorithm over dataset to learn
Bayesian network structure.
This algorithm is clearly a good candidate for
numba JIT compilation...
STEPS
-----
1. Compute Markov Blanket
2. Compute Graph Structure
3. Orient Edges
4. Remove Cycles
5. Reverse Edges
6. Propagate Directions
Arguments
---------
*data* : a nested numpy array
Data from which you wish to learn structure
*alpha* : a float
Type I error rate for independence test
Returns
-------
*bn* : a BayesNet object
Effects
-------
None
Notes
-----
Speed Test:
*** 5 variables, 624 observations ***
- 63.7 ms
"""
n_rv = data.shape[1]
data, value_dict = replace_strings(data, return_values=True)
if feature_selection is None:
_T = range(n_rv)
else:
assert (not isinstance(feature_selection, list)), 'feature_selection must be only one value'
_T = [feature_selection]
# STEP 1 : COMPUTE MARKOV BLANKETS
Mb = dict([(rv,[]) for rv in range(n_rv)])
for X in _T:
S = []
grow_condition = True
while grow_condition:
grow_condition=False
for Y in range(n_rv):
if X!=Y and Y not in S:
# if there exists some Y such that Y is dependent on X given S,
# add Y to S
cols = (X,Y) + tuple(S)
pval = mi_test(data[:,cols])
if pval < alpha: # dependent
grow_condition=True # dependent -> continue searching
S.append(Y)
shrink_condition = True
while shrink_condition:
TEMP_S = []
shrink_condition=False
for Y in S:
s_copy = copy(S)
s_copy.remove(Y) # condition on S-{Y}
# if X independent of Y given S-{Y}, leave Y out
# if X dependent of Y given S-{Y}, keep it in
cols = (X,Y) + tuple(s_copy)
pval = mi_test(data[:,cols])
if pval < alpha: # dependent
TEMP_S.append(Y)
else: # independent -> condition searching
shrink_condition=True
Mb[X] = TEMP_S
if debug:
print 'Markov Blanket for %s : %s' % (X, str(TEMP_S))
if feature_selection is None:
# STEP 2: COMPUTE GRAPH STRUCTURE
# i.e. Resolve Markov Blanket
edge_dict = resolve_markov_blanket(Mb,data)
if debug:
print 'Unoriented edge dict:\n %s' % str(edge_dict)
# STEP 3: ORIENT EDGES
oriented_edge_dict = orient_edges_MB(edge_dict,Mb,data,alpha)
if debug:
print 'Oriented edge dict:\n %s' % str(oriented_edge_dict)
# CREATE BAYESNET OBJECT
bn=BayesNet(oriented_edge_dict,value_dict)
return bn
else:
return Mb[_T]
def gs(data, alpha=0.05, feature_selection=None, debug=False):
"""
Perform growshink algorithm over dataset to learn
Bayesian network structure.
This algorithm is clearly a good candidate for
numba JIT compilation...
STEPS
-----
1. Compute Markov Blanket
2. Compute Graph Structure
3. Orient Edges
4. Remove Cycles
5. Reverse Edges
6. Propagate Directions
Arguments
---------
*data* : a nested numpy array
Data from which you wish to learn structure
*alpha* : a float
Type I error rate for independence test
Returns
-------
*bn* : a BayesNet object
Effects
-------
None
Notes
-----
Speed Test:
*** 5 variables, 624 observations ***
- 63.7 ms
"""
n_rv = data.shape[1]
data, value_dict = replace_strings(data, return_values=True)
if feature_selection is None:
_T = range(n_rv)
else:
assert (not isinstance(feature_selection, list)), 'feature_selection must be only one value'
_T = [feature_selection]
# STEP 1 : COMPUTE MARKOV BLANKETS
Mb = dict([(rv,[]) for rv in range(n_rv)])
for X in _T:
S = []
grow_condition = True
while grow_condition:
grow_condition=False
for Y in range(n_rv):
if X!=Y and Y not in S:
# if there exists some Y such that Y is dependent on X given S,
# add Y to S
cols = (X,Y) + tuple(S)
pval = mi_test(data[:,cols])
if pval < alpha: # dependent
grow_condition=True # dependent -> continue searching
S.append(Y)
shrink_condition = True
while shrink_condition:
TEMP_S = []
shrink_condition=False
for Y in S:
s_copy = copy(S)
s_copy.remove(Y) # condition on S-{Y}
# if X independent of Y given S-{Y}, leave Y out
# if X dependent of Y given S-{Y}, keep it in
cols = (X,Y) + tuple(s_copy)
pval = mi_test(data[:,cols])
if pval < alpha: # dependent
TEMP_S.append(Y)
else: # independent -> condition searching
shrink_condition=True
Mb[X] = TEMP_S
if debug:
print('Markov Blanket for %s : %s' % (X, str(TEMP_S)))
if feature_selection is None:
# STEP 2: COMPUTE GRAPH STRUCTURE
# i.e. Resolve Markov Blanket
edge_dict = resolve_markov_blanket(Mb,data)
if debug:
print('Unoriented edge dict:\n %s' % str(edge_dict))
# STEP 3: ORIENT EDGES
oriented_edge_dict = orient_edges_MB(edge_dict,Mb,data,alpha)
if debug:
print('Oriented edge dict:\n %s' % str(oriented_edge_dict))
# CREATE BAYESNET OBJECT
bn=BayesNet(oriented_edge_dict,value_dict)
return bn
else:
return Mb[_T]
def iamb(data, alpha=0.05, feature_selection=None, debug=False):
"""
IAMB Algorithm for learning the structure of a
Discrete Bayesian Network from data.
Arguments
---------
*data* : a nested numpy array
*alpha* : a float
The type II error rate.
*feature_selection* : None or a string
Whether to use IAMB as a structure learning
or feature selection algorithm.
Returns
-------
*bn* : a BayesNet object or
*mb* : the markov blanket of a node
Effects
-------
None
Notes
-----
- Works but there are definitely some bugs.
Speed Test:
*** 5 vars, 624 obs ***
- 196 ms
"""
n_rv = data.shape[1]
Mb = dict([(rv,[]) for rv in range(n_rv)])
if feature_selection is None:
_T = range(n_rv)
else:
assert (not isinstance(feature_selection, list)), 'feature_selection must be only one value'
_T = [feature_selection]
# LEARN MARKOV BLANKET
for T in _T:
V = set(range(n_rv)) - {T}
Mb_change=True
# GROWING PHASE
while Mb_change:
Mb_change = False
# find X_max in V-Mb(T)-{T} that maximizes
# mutual information of X,T|Mb(T)
# i.e. max of mi_test(data[:,(X,T,Mb(T))])
max_val = -1
max_x = None
for X in V - set(Mb[T]) - {T}:
cols = (X,T)+tuple(Mb[T])
mi_val = mi_test(data[:,cols],test=False)
if mi_val > max_val:
max_val = mi_val
max_x = X
# if Xmax is dependent on T given Mb(T)
cols = (max_x,T) + tuple(Mb[T])
if max_x is not None and are_independent(data[:,cols]):
Mb[T].append(X)
Mb_change = True
if debug:
print 'Adding %s to MB of %s' % (str(X), str(T))
# SHRINKING PHASE
for X in Mb[T]:
# if x is independent of t given Mb(T) - {x}
cols = (X,T) + tuple(set(Mb[T]) - {X})
if are_independent(data[:,cols],alpha):
Mb[T].remove(X)
if debug:
print 'Removing %s from MB of %s' % (str(X), str(T))
if feature_selection is None:
# RESOLVE GRAPH STRUCTURE
edge_dict = resolve_markov_blanket(Mb, data)
if debug:
print 'Unoriented edge dict:\n %s' % str(edge_dict)
print 'MB: %s' % str(Mb)
# ORIENT EDGES
oriented_edge_dict = orient_edges_gs2(edge_dict,Mb,data,alpha)
if debug:
print 'Oriented edge dict:\n %s' % str(oriented_edge_dict)
# CREATE BAYESNET OBJECT
value_dict = dict(zip(range(data.shape[1]),
[list(np.unique(col)) for col in data.T]))
bn=BayesNet(oriented_edge_dict,value_dict)
return bn
else:
return Mb[_T]