def timer(inputfile, trials, datalength):
# load nodedata and graphskeleton
nd = NodeData()
skel = GraphSkeleton()
#print "bp1"
nd.load(inputfile)
#print "bp2"
skel.load(inputfile)
#print "bp3"
# msg = "%d, %d" % (asizeof(nd), asizeof(skel))
# print >>op, msg
# topologically order graphskeleton
skel.toporder()
# load bayesian network
bn = DiscreteBayesianNetwork(skel, nd)
# instantiate pgm learner
l = PGMLearner()
# free unused memory
del nd
#sum1 = summary.summarize(muppy.get_objects())
#summary.print_(sum1)
# TIME
totaltime = 0
for _ in range(trials):
data = bn.randomsample(datalength)
start = time.clock()
ret = l.discrete_mle_estimateparams(skel, data)
elapsed = time.clock() - start
totaltime += elapsed
totaltime /= trials
print json.dumps(ret.Vdata, indent=1)
return totaltime
def timer(inputfile, trials):
# load nodedata and graphskeleton
nd = NodeData()
skel = GraphSkeleton()
nd.load(inputfile)
skel.load(inputfile)
# topologically order graphskeleton
skel.toporder()
# load bayesian network
bn = DiscreteBayesianNetwork(skel, nd)
# TIME
totaltime = 0
for _ in range(trials):
start = time.clock()
ret = bn.randomsample(100)
elapsed = time.clock() - start
totaltime += elapsed
totaltime /= trials
return totaltime
def discrete_constraint_estimatestruct(self, data, pvalparam=0.05, indegree=1):
'''
Learn a Bayesian network structure from discrete data given by *data*, using constraint-based approaches. This function first calculates all the independencies and conditional independencies present between variables in the data. To calculate dependencies, it uses the *discrete_condind* method on each pair of variables, conditioned on other sets of variables of size *indegree* or smaller, to generate a chi-squared result and a p-value. If this p-value is less than *pvalparam*, the pair of variables are considered dependent conditioned on the variable set. Once all true dependencies -- pairs of variables that are dependent no matter what they are conditioned by -- are found, the algorithm uses these dependencies to construct a directed acyclic graph. It returns this DAG in the form of a :doc:`GraphSkeleton <graphskeleton>` class.
Arguments:
1. *data* -- An array of dicts containing samples from the network in {vertex: value} format. Example::
[
{
'Grade': 'B',
'SAT': 'lowscore',
...
},
...
]
2. *pvalparam* -- (Optional, default is 0.05) The p-value below which to consider something significantly unlikely. A common number used is 0.05. This is passed to *discrete_condind* when it is called.
3. *indegree* -- (Optional, default is 1) The upper bound on the size of a witness set (see Koller et al. 85). If this is larger than 1, a huge amount of samples in *data* are required to avoid a divide-by-zero error.
Usage example: this would learn structure from a set of 8000 discrete samples::
import json
from libpgm.nodedata import NodeData
from libpgm.graphskeleton import GraphSkeleton
from libpgm.discretebayesiannetwork import DiscreteBayesianNetwork
from libpgm.pgmlearner import PGMLearner
# generate some data to use
nd = NodeData()
nd.load("../tests/unittestdict.txt") # an input file
skel = GraphSkeleton()
skel.load("../tests/unittestdict.txt")
skel.toporder()
bn = DiscreteBayesianNetwork(skel, nd)
data = bn.randomsample(8000)
# instantiate my learner
learner = PGMLearner()
# estimate structure
result = learner.discrete_constraint_estimatestruct(data)
# output
print json.dumps(result.E, indent=2)
'''
assert (isinstance(data, list) and data and isinstance(data[0], dict)), "Arg must be a list of dicts."
# instantiate array of variables and array of potential dependencies
variables = data[0].keys()
ovariables = variables[:]
dependencies = []
for x in variables:
ovariables.remove(x)
for y in ovariables:
if (x != y):
dependencies.append([x, y])
# define helper function to find subsets
def subsets(array):
result = []
for i in range(indegree + 1):
comb = itertools.combinations(array, i)
for c in comb:
result.append(list(c))
return result
witnesses = []
othervariables = variables[:]
# for each pair of variables X, Y:
for X in variables:
othervariables.remove(X)
for Y in othervariables:
# consider all sets of witnesses that do not have X or Y in
# them, and are less than or equal to the size specified by
# the "indegree" argument
for U in subsets(variables):
if (X not in U) and (Y not in U) and len(U) <= indegree:
# determine conditional independence
chi, pv, witness = self.discrete_condind(data, X, Y, U)
if pv > pvalparam:
msg = "***%s and %s are found independent (chi = %f, pv = %f) with witness %s***" % (X, Y, chi, pv, U)
try:
dependencies.remove([X, Y])
dependencies.remove([Y, X])
except:
pass
witnesses.append([X, Y, witness])
break
# now that we have found our dependencies, run build PDAG (cf. Koller p. 89)
# with the stored set of independencies:
# assemble undirected graph skeleton
pdag = GraphSkeleton()
pdag.E = dependencies
pdag.V = variables
# adjust for immoralities (cf. Koller 86)
dedges = [x[:] for x in pdag.E]
for edge in dedges:
edge.append('u')
# define helper method "exists_undirected_edge"
def exists_undirected_edge(one_end, the_other_end):
for edge in dedges:
if len(edge) == 3:
if (edge[0] == one_end and edge[1] == the_other_end):
return True
elif (edge[1] == one_end and edge[0] == the_other_end):
return True
return False
# define helper method "exists_edge"
def exists_edge(one_end, the_other_end):
if exists_undirected_edge(one_end, the_other_end):
return True
elif [one_end, the_other_end] in dedges:
return True
elif [the_other_end, one_end] in dedges:
return True
return False
for edge1 in reversed(dedges):
for edge2 in reversed(dedges):
if (edge1 in dedges) and (edge2 in dedges):
if edge1[0] == edge2[1] and not exists_edge(edge1[1], edge2[0]):
if (([edge1[1], edge2[0], [edge1[0]]] not in witnesses) and ([edge2[0], edge1[1], [edge1[0]]] not in witnesses)):
dedges.append([edge1[1], edge1[0]])
dedges.append([edge2[0], edge2[1]])
dedges.remove(edge1)
dedges.remove(edge2)
elif edge1[1] == edge2[0] and not exists_edge(edge1[0], edge2[1]):
if (([edge1[0], edge2[1], [edge1[1]]] not in witnesses) and ([edge2[1], edge1[0], [edge1[1]]] not in witnesses)):
dedges.append([edge1[0], edge1[1]])
dedges.append([edge2[1], edge2[0]])
dedges.remove(edge1)
dedges.remove(edge2)
elif edge1[1] == edge2[1] and edge1[0] != edge2[0] and not exists_edge(edge1[0], edge2[0]):
if (([edge1[0], edge2[0], [edge1[1]]] not in witnesses) and ([edge2[0], edge1[0], [edge1[1]]] not in witnesses)):
dedges.append([edge1[0], edge1[1]])
dedges.append([edge2[0], edge2[1]])
dedges.remove(edge1)
dedges.remove(edge2)
elif edge1[0] == edge2[0] and edge1[1] != edge2[1] and not exists_edge(edge1[1], edge2[1]):
if (([edge1[1], edge2[1], [edge1[0]]] not in witnesses) and ([edge2[1], edge1[1], [edge1[0]]] not in witnesses)):
dedges.append([edge1[1], edge1[0]])
dedges.append([edge2[1], edge2[0]])
dedges.remove(edge1)
dedges.remove(edge2)
# use right hand rules to improve graph until convergence (Koller 89)
olddedges = []
while (olddedges != dedges):
olddedges = [x[:] for x in dedges]
for edge1 in reversed(dedges):
for edge2 in reversed(dedges):
# rule 1
inverted = False
check1, check2 = False, True
if (edge1[1] == edge2[0] and len(edge1) == 2 and len(edge2) == 3):
check1 = True
elif (edge1[1] == edge2[1] and len(edge1) == 2 and len(edge2) == 3):
check = True
inverted = True
for edge3 in dedges:
if edge3 != edge1 and ((edge3[0] == edge1[0] and edge3[1]
== edge2[1]) or (edge3[1] == edge1[0] and edge3[0]
== edge2[1])):
check2 = False
if check1 == True and check2 == True:
if inverted:
dedges.append([edge1[1], edge2[0]])
else:
dedges.append([edge1[1], edge2[1]])
dedges.remove(edge2)
# rule 2
check1, check2 = False, False
if (edge1[1] == edge2[0] and len(edge1) == 2 and len(edge2) == 2):
check1 = True
for edge3 in dedges:
if ((edge3[0] == edge1[0] and edge3[1]
== edge2[1]) or (edge3[1] == edge1[0] and edge3[0]
== edge2[1]) and len(edge3) == 3):
check2 = True
if check1 == True and check2 == True:
if edge3[0] == edge1[0]:
dedges.append([edge3[0], edge3[1]])
elif edge3[1] == edge1[0]:
dedges.append([edge3[1], edge3[0]])
dedges.remove(edge3)
# rule 3
check1, check2 = False, False
if len(edge1) == 2 and len(edge2) == 2:
if (edge1[1] == edge2[1] and edge1[0] != edge2[0]):
check1 = True
for v in variables:
if (exists_undirected_edge(v, edge1[0]) and
exists_undirected_edge(v, edge1[1]) and
exists_undirected_edge(v, edge2[0])):
check2 = True
if check1 == True and check2 == True:
dedges.append([v, edge1[1]])
for edge3 in dedges:
if (len(edge3) == 3 and ((edge3[0] == v and edge3[1]
== edge1[1]) or (edge3[1] == v and edge3[0] ==
edge1[1]))):
dedges.remove(edge3)
# return one possible graph skeleton from the pdag class found
for x in range(len(dedges)):
if len(dedges[x]) == 3:
dedges[x] = dedges[x][:2]
pdag.E = dedges
pdag.toporder()
return pdag
