def marginal_ve_e(bn, target, evidence={}):
"""
Perform Sum-Product Variable Elimination on
a Discrete Bayesian Network.
Arguments
---------
*bn* : a BayesNet object
*target* : a list of target RVs
*evidence* : a dictionary, where
key = rv and value = rv value
Returns
-------
*marginal_dict* : a dictionary, where
key = an rv in target and value =
a numpy array containing the key's
marginal conditional probability distribution.
Notes
-----
- Mutliple pieces of evidence often returns "nan"...numbers too small?
- dividing by zero -> perturb values in Factor class
"""
_phi = Factorization(bn)
order = copy(list(bn.nodes()))
order.remove(target)
#### EVIDENCE PROCESSING ####
for E, e in evidence.items():
_phi -= (E,e)
order.remove(E)
#### SUM-PRODUCT ELIMINATE VAR ####
for var in order:
_phi /= var
# multiply phi's together if there is evidence
final_phi = _phi.consolidate()
return np.round(final_phi.cpt,4)
def marginal_ve_e(bn, target, evidence={}):
"""
Perform Sum-Product Variable Elimination on
a Discrete Bayesian Network.
Arguments
---------
*bn* : a BayesNet object
*target* : a list of target RVs
*evidence* : a dictionary, where
key = rv and value = rv value
Returns
-------
*marginal_dict* : a dictionary, where
key = an rv in target and value =
a numpy array containing the key's
marginal conditional probability distribution.
Notes
-----
- Mutliple pieces of evidence often returns "nan"...numbers too small?
- dividing by zero -> perturb values in Factor class
"""
_phi = Factorization(bn)
order = copy(list(bn.nodes()))
order.remove(target)
#### EVIDENCE PROCESSING ####
for E, e in evidence.items():
_phi -= (E,e)
order.remove(E)
#### SUM-PRODUCT ELIMINATE VAR ####
for var in order:
_phi /= var
# multiply phi's together if there is evidence
final_phi = _phi.consolidate()
return np.round(final_phi.cpt,4)
def ve_map(bn,
evidence={},
target=None,
prob=False):
"""
Perform Max-Sum Variable Elimination over a BayesNet object
for exact maximum a posteriori inference.
This has been validated w/ and w/out evidence
"""
_phi = Factorization(bn)
order = copy(list(bn.nodes()))
#### EVIDENCE PROCESSING ####
for E, e in evidence.items():
_phi -= (E,e)
order.remove(E)
#### MAX-PRODUCT ELIMINATE VAR ####
for var in order:
_phi //= var
#### TRACEBACK MAP ASSIGNMENT ####
max_assignment = _phi.traceback_map()
#### RETURN ####
if prob:
# multiply phi's together if there is evidence
final_phi = _phi.consolidate()
max_prob = round(final_phi.cpt[0],5)
if target is not None:
return max_prob, max_assignment[target]
else:
return max_prob, max_assignment
else:
if target is not None:
return max_assignment[target]
else:
return max_assignment
def initialize_tree(self):
"""
Initialize the structure of a clique tree, using
the following steps:
- Moralize graph (i.e. marry parents)
- Triangulate graph (i.e. make graph chordal)
- Get max cliques (i.e. community/clique detection)
- Max spanning tree over sepset cardinality (i.e. create tree)
"""
### MORALIZE GRAPH & MAKE IT CHORDAL ###
chordal_G = make_chordal(self.bn) # must return a networkx object
V = chordal_G.nodes()
### GET MAX CLIQUES FROM CHORDAL GRAPH ###
C = {} # key = vertex, value = clique object
max_cliques = reversed(list(nx.chordal_graph_cliques(chordal_G)))
for v_idx,clique in enumerate(max_cliques):
C[v_idx] = Clique(set(clique))
### MAXIMUM SPANNING TREE OVER COMPLETE GRAPH TO MAKE A TREE ###
weighted_edge_dict = dict([(c_idx,{}) for c_idx in xrange(len(C))])
for i in range(len(C)):
for j in range(len(C)):
if i!=j:
intersect_cardinality = len(C[i].sepset(C[j]))
weighted_edge_dict[i][j] = -1*intersect_cardinality
mst_G = mst(weighted_edge_dict)
### SET V,E,C ###
self.E = mst_G # dictionary
self.V = mst_G.keys() # list
self.C = C
### ASSIGN EACH FACTOR TO ONE CLIQUE ONLY ###
v_a = dict([(rv, False) for rv in self.bn.nodes()])
for clique in self.C.values():
temp_scope = []
for var in v_a:
if v_a[var] == False and set(self.bn.scope(var)).issubset(clique.scope):
temp_scope.append(var)
v_a[var] = True
clique._F = Factorization(self.bn, temp_scope)
### COMPUTE INITIAL POTENTIAL FOR EACH FACTOR ###
# - i.e. multiply all of its assigned factors together
for i, clique in self.C.items():
if len(self.parents(i)) == 0:
clique.is_ready = True
clique.initialize_psi()
def __init__(self, bn):
"""
Instantiate a CliqueTree object.
Arguments
---------
*bn*: a BayesNet object
Notes
-----
Ideally, the Factor class should be used as the
cliques instead of the Clique class (because it's
just a watered down version of the Factor class)
"""
####
self.V = None
self.E = None
self.C = None
###
self.bn = bn
self._F = Factorization(bn)
self.initialize_tree()