def hc_rr(data,
M=5,
R=3,
metric='AIC',
max_iter=100,
debug=False,
restriction=None):
"""
Arguments
---------
*data* : a nested numpy array
The data from which the Bayesian network
structure will be learned.
*metric* : a string
Which score metric to use.
Options:
- AIC
- BIC / MDL
- LL (log-likelihood)
*max_iter* : an integer
The maximum number of iterations of the
hill-climbing algorithm to run. Note that
the algorithm will terminate on its own if no
improvement is made in a given iteration.
*debug* : boolean
Whether to print the scores/moves of the
algorithm as its happening.
*restriction* : a list of 2-tuples
For MMHC algorithm, the list of allowable edge additions.
Returns
-------
*bn* : a BayesNet object
"""
nrow = data.shape[0]
ncol = data.shape[1]
names = range(ncol)
# INITIALIZE NETWORK W/ NO EDGES
# maintain children and parents dict for fast lookups
c_dict = dict([(n, []) for n in names])
p_dict = dict([(n, []) for n in names])
# COMPUTE INITIAL LIKELIHOOD SCORE
value_dict = dict([(n, np.unique(data[:, i]))
for i, n in enumerate(names)])
bn = BayesNet(c_dict)
mle_estimator(bn, data)
max_score = info_score(bn, nrow, metric)
_iter = 0
improvement = True
_restarts = 0
while improvement:
improvement = False
max_delta = 0
if debug:
print 'ITERATION: ', _iter
### TEST ARC ADDITIONS ###
for u in bn.nodes():
for v in bn.nodes():
if v not in c_dict[u] and u != v and not would_cause_cycle(
c_dict, u, v):
# FOR MMHC ALGORITHM -> Edge Restrictions
if restriction is None or (u, v) in restriction:
# SCORE FOR 'V' -> gaining a parent
old_cols = (v, ) + tuple(
p_dict[v]) # without 'u' as parent
mi_old = mutual_information(data[:, old_cols])
new_cols = old_cols + (u, ) # with'u' as parent
mi_new = mutual_information(data[:, new_cols])
delta_score = nrow * (mi_old - mi_new)
if delta_score > max_delta:
if debug:
print 'Improved Arc Addition: ', (u, v)
print 'Delta Score: ', delta_score
max_delta = delta_score
max_operation = 'Addition'
max_arc = (u, v)
### TEST ARC DELETIONS ###
for u in bn.nodes():
for v in bn.nodes():
if v in c_dict[u]:
# SCORE FOR 'V' -> losing a parent
old_cols = (v, ) + tuple(p_dict[v]) # with 'u' as parent
mi_old = mutual_information(data[:, old_cols])
new_cols = tuple([i for i in old_cols
if i != u]) # without 'u' as parent
mi_new = mutual_information(data[:, new_cols])
delta_score = nrow * (mi_old - mi_new)
if delta_score > max_delta:
if debug:
print 'Improved Arc Deletion: ', (u, v)
print 'Delta Score: ', delta_score
max_delta = delta_score
max_operation = 'Deletion'
max_arc = (u, v)
### TEST ARC REVERSALS ###
for u in bn.nodes():
for v in bn.nodes():
if v in c_dict[u] and not would_cause_cycle(
c_dict, v, u, reverse=True):
# SCORE FOR 'U' -> gaining 'v' as parent
old_cols = (u, ) + tuple(
p_dict[v]) # without 'v' as parent
mi_old = mutual_information(data[:, old_cols])
new_cols = old_cols + (v, ) # with 'v' as parent
mi_new = mutual_information(data[:, new_cols])
delta1 = nrow * (mi_old - mi_new)
# SCORE FOR 'V' -> losing 'u' as parent
old_cols = (v, ) + tuple(p_dict[v]) # with 'u' as parent
mi_old = mutual_information(data[:, old_cols])
new_cols = tuple([u for i in old_cols
if i != u]) # without 'u' as parent
mi_new = mutual_information(data[:, new_cols])
delta2 = nrow * (mi_old - mi_new)
# COMBINED DELTA-SCORES
delta_score = delta1 + delta2
if delta_score > max_delta:
if debug:
print 'Improved Arc Reversal: ', (u, v)
print 'Delta Score: ', delta_score
max_delta = delta_score
max_operation = 'Reversal'
max_arc = (u, v)
### DETERMINE IF/WHERE IMPROVEMENT WAS MADE ###
if max_delta != 0:
improvement = True
u, v = max_arc
if max_operation == 'Addition':
if debug:
print 'ADDING: ', max_arc, '\n'
c_dict[u].append(v)
p_dict[v].append(u)
elif max_operation == 'Deletion':
if debug:
print 'DELETING: ', max_arc, '\n'
c_dict[u].remove(v)
p_dict[v].remove(u)
elif max_operation == 'Reversal':
if debug:
print 'REVERSING: ', max_arc, '\n'
c_dict[u].remove(v)
p_dict[v].remove(u)
c_dict[v].append(u)
p_dict[u].append(v)
else:
if debug:
print 'No Improvement on Iter: ', _iter
#### RESTART WITH RANDOM MOVES ####
if _restarts < R:
improvement = True # make another pass of hill climbing
_iter = 0 # reset iterations
if debug:
print 'Restart - ', _restarts
_restarts += 1
for _ in range(M):
# 0 = Addition, 1 = Deletion, 2 = Reversal
operation = np.random.choice([0, 1, 2])
if operation == 0:
while True:
u, v = np.random.choice(list(bn.nodes()),
size=2,
replace=False)
# IF EDGE DOESN'T EXIST, ADD IT
if u not in p_dict[
v] and u != v and not would_cause_cycle(
c_dict, u, v):
if debug:
print 'RESTART - ADDING: ', (u, v)
c_dict[u].append(v)
p_dict[v].append(u)
break
elif operation == 1:
while True:
u, v = np.random.choice(list(bn.nodes()),
size=2,
replace=False)
# IF EDGE EXISTS, DELETE IT
if u in p_dict[v]:
if debug:
print 'RESTART - DELETING: ', (u, v)
c_dict[u].remove(v)
p_dict[v].remove(u)
break
elif operation == 2:
while True:
u, v = np.random.choice(list(bn.nodes()),
size=2,
replace=False)
# IF EDGE EXISTS, REVERSE IT
if u in p_dict[v] and not would_cause_cycle(
c_dict, v, u, reverse=True):
if debug:
print 'RESTART - REVERSING: ', (u, v)
c_dict[u].remove(v)
p_dict[v].remove(u)
c_dict[v].append(u)
p_dict[u].append(v)
break
### TEST FOR MAX ITERATION ###
_iter += 1
if _iter > max_iter:
if debug:
print 'Max Iteration Reached'
break
bn = BayesNet(c_dict)
return bn
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 setUp(self): self.bn = BayesNet() self.dpath = os.path.join(dirname(dirname(dirname(dirname(__file__)))),'data') self.bn_bif = read_bn(os.path.join(self.dpath,'cancer.bif')) self.bn_bn = read_bn(os.path.join(self.dpath,'cmu.bn'))
def hc(data, metric='AIC', max_iter=100, debug=False, restriction=None):
"""
Greedy Hill Climbing search proceeds by choosing the move
which maximizes the increase in fitness of the
network at the current step. It continues until
it reaches a point where there does not exist any
feasible single move that increases the network fitness.
It is called "greedy" because it simply does what is
best at the current iteration only, and thus does not
look ahead to what may be better later on in the search.
For computational saving, a Priority Queue (python's heapq)
can be used to maintain the best operators and reduce the
complexity of picking the best operator from O(n^2) to O(nlogn).
This works by maintaining the heapq of operators sorted by their
delta score, and each time a move is made, we only have to recompute
the O(n) delta-scores which were affected by the move. The rest of
the operator delta-scores are not affected.
For additional computational efficiency, we can cache the
sufficient statistics for various families of distributions -
therefore, computing the mutual information for a given family
only needs to happen once.
The possible moves are the following:
- add edge
- delete edge
- invert edge
Arguments
---------
*data* : a nested numpy array
The data from which the Bayesian network
structure will be learned.
*metric* : a string
Which score metric to use.
Options:
- AIC
- BIC / MDL
- LL (log-likelihood)
*max_iter* : an integer
The maximum number of iterations of the
hill-climbing algorithm to run. Note that
the algorithm will terminate on its own if no
improvement is made in a given iteration.
*debug* : boolean
Whether to print the scores/moves of the
algorithm as its happening.
*restriction* : a list of 2-tuples
For MMHC algorithm, the list of allowable edge additions.
Returns
-------
*bn* : a BayesNet object
"""
nrow = data.shape[0]
ncol = data.shape[1]
names = range(ncol)
# INITIALIZE NETWORK W/ NO EDGES
# maintain children and parents dict for fast lookups
c_dict = dict([(n, []) for n in names])
p_dict = dict([(n, []) for n in names])
# COMPUTE INITIAL LIKELIHOOD SCORE
value_dict = dict([(n, np.unique(data[:, i]))
for i, n in enumerate(names)])
bn = BayesNet(c_dict)
mle_estimator(bn, data)
max_score = info_score(bn, nrow, metric)
# CREATE EMPIRICAL DISTRIBUTION OBJECT FOR CACHING
#ED = EmpiricalDistribution(data,names)
_iter = 0
improvement = True
while improvement:
improvement = False
max_delta = 0
if debug:
print 'ITERATION: ', _iter
### TEST ARC ADDITIONS ###
for u in bn.nodes():
for v in bn.nodes():
if v not in c_dict[u] and u != v and not would_cause_cycle(
c_dict, u, v):
# FOR MMHC ALGORITHM -> Edge Restrictions
if restriction is None or (u, v) in restriction:
# SCORE FOR 'V' -> gaining a parent
old_cols = (v, ) + tuple(
p_dict[v]) # without 'u' as parent
mi_old = mutual_information(data[:, old_cols])
new_cols = old_cols + (u, ) # with'u' as parent
mi_new = mutual_information(data[:, new_cols])
delta_score = nrow * (mi_old - mi_new)
if delta_score > max_delta:
#if debug:
# print 'Improved Arc Addition: ' , (u,v)
# print 'Delta Score: ' , delta_score
max_delta = delta_score
max_operation = 'Addition'
max_arc = (u, v)
### TEST ARC DELETIONS ###
for u in bn.nodes():
for v in bn.nodes():
if v in c_dict[u]:
# SCORE FOR 'V' -> losing a parent
old_cols = (v, ) + tuple(p_dict[v]) # with 'u' as parent
mi_old = mutual_information(data[:, old_cols])
new_cols = tuple([i for i in old_cols
if i != u]) # without 'u' as parent
mi_new = mutual_information(data[:, new_cols])
delta_score = nrow * (mi_old - mi_new)
if delta_score > max_delta:
#if debug:
# print 'Improved Arc Deletion: ' , (u,v)
# print 'Delta Score: ' , delta_score
max_delta = delta_score
max_operation = 'Deletion'
max_arc = (u, v)
### TEST ARC REVERSALS ###
for u in bn.nodes():
for v in bn.nodes():
if v in c_dict[u] and not would_cause_cycle(
c_dict, v, u, reverse=True):
# SCORE FOR 'U' -> gaining 'v' as parent
old_cols = (u, ) + tuple(
p_dict[v]) # without 'v' as parent
mi_old = mutual_information(data[:, old_cols])
new_cols = old_cols + (v, ) # with 'v' as parent
mi_new = mutual_information(data[:, new_cols])
delta1 = nrow * (mi_old - mi_new)
# SCORE FOR 'V' -> losing 'u' as parent
old_cols = (v, ) + tuple(p_dict[v]) # with 'u' as parent
mi_old = mutual_information(data[:, old_cols])
new_cols = tuple([u for i in old_cols
if i != u]) # without 'u' as parent
mi_new = mutual_information(data[:, new_cols])
delta2 = nrow * (mi_old - mi_new)
# COMBINED DELTA-SCORES
delta_score = delta1 + delta2
if delta_score > max_delta:
#if debug:
# print 'Improved Arc Reversal: ' , (u,v)
# print 'Delta Score: ' , delta_score
max_delta = delta_score
max_operation = 'Reversal'
max_arc = (u, v)
### DETERMINE IF/WHERE IMPROVEMENT WAS MADE ###
if max_delta != 0:
improvement = True
u, v = max_arc
if max_operation == 'Addition':
if debug:
print 'ADDING: ', max_arc, '\n'
c_dict[u].append(v)
p_dict[v].append(u)
elif max_operation == 'Deletion':
if debug:
print 'DELETING: ', max_arc, '\n'
c_dict[u].remove(v)
p_dict[v].remove(u)
elif max_operation == 'Reversal':
if debug:
print 'REVERSING: ', max_arc, '\n'
c_dict[u].remove(v)
p_dict[v].remove(u)
c_dict[v].append(u)
p_dict[u].append(v)
else:
if debug:
print 'No Improvement on Iter: ', _iter
### TEST FOR MAX ITERATION ###
_iter += 1
if _iter > max_iter:
if debug:
print 'Max Iteration Reached'
break
bn = BayesNet(c_dict)
return bn
