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 fast_iamb(data, k=5, alpha=0.05, feature_selection=None, debug=False):
"""
From [1]:
"A novel algorithm for the induction of
Markov blankets from data, called Fast-IAMB, that employs
a heuristic to quickly recover the Markov blanket. Empirical
results show that Fast-IAMB performs in many cases
faster and more reliably than existing algorithms without
adversely affecting the accuracy of the recovered Markov
blankets."
Arguments
---------
*data* : a nested numpy array
*k* : an integer
The max number of edges to add at each iteration of
the algorithm.
*alpha* : a float
Probability of Type I error
Returns
-------
*bn* : a BayesNet object
Effects
-------
None
Notes
-----
- Currently does not work. I think it's stuck in an infinite loop...
"""
# get values
value_dict = dict(zip(range(data.shape[1]),
[list(np.unique(col)) for col in data.T]))
# replace strings
data = replace_strings(data)
n_rv = data.shape[1]
Mb = dict([(rv,[]) for rv in range(n_rv)])
N = data.shape[0]
card = dict(zip(range(n_rv),unique_bins(data)))
#card = dict(zip(range(data.shape[1]),np.amax(data,axis=0)))
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:
S = set(range(n_rv)) - {T}
for A in S:
if not are_independent(data[:,(A,T)]):
S.remove(A)
s_h_dict = dict([(s,0) for s in S])
while S:
insufficient_data = False
break_grow_phase = False
#### GROW PHASE ####
# Calculate mutual information for all variables
mi_dict = dict([(s,mi_test(data[:,(s,T)+tuple(Mb[T])])) for s in S])
for x_i in sorted(mi_dict, key=mi_dict.get,reverse=True):
# Add top MI-score variables until there isn't enough data for bins
if (N / card[x_i]*card[T]*np.prod([card[b] for b in Mb[T]])) >= k:
Mb[T].append(x_i)
else:
insufficient_data = True
break
#### SHRINK PHASE ####
removed_vars = False
for A in Mb[T]:
cols = (A,T) + tuple(set(Mb[T]) - {A})
# if A is independent of T given Mb[T], remove A
if are_independent(data[:,cols]):
Mb[T].remove(A)
removed_vars=True
#### FINALIZE BLANKET FOR "T" OR MAKE ANOTHER PASS ####
if insufficient_data and not removed_vars:
if debug:
print 'Breaking..'
break
else:
A = set(range(n_rv)) - {T} - set(Mb[T])
#A = set(nodes) - {T} - set(Mb[T])
S = set()
for a in A:
cols = (a,T) + tuple(Mb[T])
if are_independent(data[:,cols]):
S.add(a)
if debug:
print 'Done with %s' % T
if feature_selection is None:
# RESOLVE GRAPH STRUCTURE
edge_dict = resolve_markov_blanket(Mb, data)
# ORIENT EDGES
oriented_edge_dict = orient_edges_MB(edge_dict,Mb,data,alpha)
# CREATE BAYESNET OBJECT
bn=BayesNet(oriented_edge_dict,value_dict)
return BN
else:
return Mb[_T]
def fast_iamb(data, k=5, alpha=0.05, feature_selection=None, debug=False):
"""
From [1]:
"A novel algorithm for the induction of
Markov blankets from data, called Fast-IAMB, that employs
a heuristic to quickly recover the Markov blanket. Empirical
results show that Fast-IAMB performs in many cases
faster and more reliably than existing algorithms without
adversely affecting the accuracy of the recovered Markov
blankets."
Arguments
---------
*data* : a nested numpy array
*k* : an integer
The max number of edges to add at each iteration of
the algorithm.
*alpha* : a float
Probability of Type I error
Returns
-------
*bn* : a BayesNet object
Effects
-------
None
Notes
-----
- Currently does not work. I think it's stuck in an infinite loop...
"""
# get values
value_dict = dict(zip(range(data.shape[1]), [list(np.unique(col)) for col in data.T]))
# replace strings
data = replace_strings(data)
n_rv = data.shape[1]
Mb = dict([(rv, []) for rv in range(n_rv)])
N = data.shape[0]
card = dict(zip(range(n_rv), unique_bins(data)))
# card = dict(zip(range(data.shape[1]),np.amax(data,axis=0)))
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:
S = set(range(n_rv)) - {T}
for A in S:
if not are_independent(data[:, (A, T)]):
S.remove(A)
s_h_dict = dict([(s, 0) for s in S])
while S:
insufficient_data = False
break_grow_phase = False
#### GROW PHASE ####
# Calculate mutual information for all variables
mi_dict = dict([(s, mi_test(data[:, (s, T) + tuple(Mb[T])])) for s in S])
for x_i in sorted(mi_dict, key=mi_dict.get, reverse=True):
# Add top MI-score variables until there isn't enough data for bins
if (N / card[x_i] * card[T] * np.prod([card[b] for b in Mb[T]])) >= k:
Mb[T].append(x_i)
else:
insufficient_data = True
break
#### SHRINK PHASE ####
removed_vars = False
for A in Mb[T]:
cols = (A, T) + tuple(set(Mb[T]) - {A})
# if A is independent of T given Mb[T], remove A
if are_independent(data[:, cols]):
Mb[T].remove(A)
removed_vars = True
#### FINALIZE BLANKET FOR "T" OR MAKE ANOTHER PASS ####
if insufficient_data and not removed_vars:
if debug:
print "Breaking.."
break
else:
A = set(range(n_rv)) - {T} - set(Mb[T])
# A = set(nodes) - {T} - set(Mb[T])
S = set()
for a in A:
cols = (a, T) + tuple(Mb[T])
if are_independent(data[:, cols]):
S.add(a)
if debug:
print "Done with %s" % T
if feature_selection is None:
# RESOLVE GRAPH STRUCTURE
edge_dict = resolve_markov_blanket(Mb, data)
# ORIENT EDGES
oriented_edge_dict = orient_edges_MB(edge_dict, Mb, data, alpha)
# CREATE BAYESNET OBJECT
bn = BayesNet(oriented_edge_dict, value_dict)
return BN
else:
return Mb[_T]
