def enumerate_joint(vars, values, P):
"As in Fig 13.4, except x and e are already incorporated in values."
if not vars:
return P[values]
Y = vars[0]; rest = vars[1:]
return sum([enumerate_joint(rest, extend(values, Y, y), P)
for y in P.values(Y)])
def enumerate_all(vars, e, bn):
"""Returns the probability that X = xi given e.
vars is a list of variables, the parents of X in bn.
e is a dictionary of variable-name: value pairs
bn is an instance of BayesNet.
Precondition: no variable in vars precedes its parents."""
if vars == []:
return 1.0
else:
Y = vars[0]
rest = vars[1:]
Ynode = bn.variable_node(Y)
parents = Ynode.parents
cpt = Ynode.cpt
if e.has_key(Y):
y = e[Y]
cp = cpt.p(y, parents, e) # P(y | parents(Y))
result = cp * enumerate_all(rest, e, bn)
else:
result = 0
for y in bn.variable_values(Y):
cp = cpt.p(y, parents, e) # P(y | parents(Y))
result += cp * enumerate_all(rest, extend(e, Y, y), bn)
return result
def enumerate_all (vars, e, bn):
"""Returns the probability that X = xi given e.
vars is a list of variables, the parents of X in bn.
e is a dictionary of variable-name: value pairs
bn is an instance of BayesNet.
Precondition: no variable in vars precedes its parents."""
if vars == []:
return 1.0
else:
Y = vars[0]
rest = vars[1:]
Ynode = bn.variable_node(Y)
parents = Ynode.parents
cpt = Ynode.cpt
if e.has_key(Y):
y = e[Y]
cp = cpt.p(y, parents, e) # P(y | parents(Y))
result = cp * enumerate_all(rest, e, bn)
else:
result = 0
for y in bn.variable_values(Y):
cp = cpt.p(y, parents, e) # P(y | parents(Y))
result += cp * enumerate_all(rest, extend(e, Y, y), bn)
return result
def sum_out(self, var, bn):
"""Make a factor eliminating var by summing over its values."""
variables = [X for X in self.variables if X != var]
cpt = {event_values(e, variables): sum(self.p(extend(e, var, val))
for val in bn.variable_values(var))
for e in all_events(variables, bn, {})}
return Factor(variables, cpt)
def sum_out(self, var, bn):
"""Make a factor eliminating var by summing over its values."""
variables = [X for X in self.variables if X != var]
cpt = {event_values(e, variables): sum(self.p(extend(e, var, val))
for val in bn.variable_values(var))
for e in all_events(variables, bn, {})}
return Factor(variables, cpt)
def enumerate_joint(vars, values, P):
"As in Fig 13.4, except x and e are already incorporated in values."
if not vars:
return P[values]
Y = vars[0]; rest = vars[1:]
return sum([enumerate_joint(rest, extend(values, Y, y), P)
for y in P.values(Y)])
def enumerate_joint(variables, e, P):
"""Return the sum of those entries in P consistent with e,
provided variables is P's remaining variables (the ones not in e)."""
if not variables:
return P[e]
Y, rest = variables[0], variables[1:]
return sum([enumerate_joint(rest, extend(e, Y, y), P)
for y in P.values(Y)])
def enumerate_joint(variables, e, P):
"""Return the sum of those entries in P consistent with e,
provided variables is P's remaining variables (the ones not in e)."""
if not variables:
return P[e]
Y, rest = variables[0], variables[1:]
return sum(
[enumerate_joint(rest, extend(e, Y, y), P) for y in P.values(Y)])
def all_events(variables, bn, e):
"""Yield every way of extending e with values for all variables."""
if not variables:
yield e
else:
X, rest = variables[0], variables[1:]
for e1 in all_events(rest, bn, e):
for x in bn.variable_values(X):
yield extend(e1, X, x)
def all_events(variables, bn, e):
"Yield every way of extending e with values for all variables."
if not variables:
yield e
else:
X, rest = variables[0], variables[1:]
for e1 in all_events(rest, bn, e):
for x in bn.variable_values(X):
yield extend(e1, X, x)
def enumerate_joint_ask(X, e, P):
"""Return a probability distribution over the values of the variable X,
given the {var:val} observations e, in the JointProbDist P.
Works for Boolean variables only. [Fig. 13.4]"""
Q = ProbDist(X) ## A probability distribution for X, initially empty
Y = [v for v in P.variables if v != X and v not in e]
for xi in P.values(X):
Q[xi] = enumerate_joint(Y, extend(e, X, xi), P)
return Q.normalize()
def enumeration_ask(X, e, bn):
"""Return the conditional probability distribution of variable X
given evidence e, from BayesNet bn. [Fig. 14.9]
>>> enumeration_ask('Burglary', dict(JohnCalls=T, MaryCalls=T), burglary
... ).show_approx()
'False: 0.716, True: 0.284'"""
assert X not in e, "Query variable must be distinct from evidence"
Q = ProbDist(X)
for xi in bn.variable_values(X):
Q[xi] = enumerate_all(bn.variables, extend(e, X, xi), bn)
return Q.normalize()
def enumeration_ask(X, e, bn):
"""Return the conditional probability distribution of variable X
given evidence e, from BayesNet bn. [Figure 14.9]
>>> enumeration_ask('Burglary', dict(JohnCalls=T, MaryCalls=T), burglary
... ).show_approx()
'False: 0.716, True: 0.284'"""
assert X not in e, "Query variable must be distinct from evidence"
Q = ProbDist(X)
for xi in bn.variable_values(X):
Q[xi] = enumerate_all(bn.variables, extend(e, X, xi), bn)
return Q.normalize()
def markov_blanket_sample(X, e, bn):
"""Return a sample from P(X | mb) where mb denotes that the
variables in the Markov blanket of X take their values from event
e (which must assign a value to each). The Markov blanket of X is
X's parents, children, and children's parents."""
Xnode = bn.variable_node(X)
Q = ProbDist(X)
for xi in bn.variable_values(X):
ei = extend(e, X, xi)
# [Equation 14.12:]
Q[xi] = Xnode.p(xi, e) * product(Yj.p(ei[Yj.variable], ei)
for Yj in Xnode.children)
return probability(Q.normalize()[True]) # (assuming a Boolean variable here)
def enumerate_all(vars, e, bn):
"""Return the sum of those entries in P(vars | e{others})
consistent with e, where P is the joint distribution represented
by bn, and e{others} means e restricted to bn's other variables
(the ones other than vars). Parents must precede children in vars."""
if not vars:
return 1.0
Y, rest = vars[0], vars[1:]
Ynode = bn.variable_node(Y)
if Y in e:
return Ynode.p(e[Y], e) * enumerate_all(rest, e, bn)
else:
return sum(Ynode.p(y, e) * enumerate_all(rest, extend(e, Y, y), bn)
for y in bn.variable_values(Y))
def enumerate_joint_ask(X, e, P):
"""Return a probability distribution over the values of the variable X,
given the {var:val} observations e, in the JointProbDist P. [Section 13.3]
>>> P = JointProbDist(['X', 'Y'])
>>> P[0,0] = 0.25; P[0,1] = 0.5; P[1,1] = P[2,1] = 0.125
>>> enumerate_joint_ask('X', dict(Y=1), P).show_approx()
'0: 0.667, 1: 0.167, 2: 0.167'
"""
assert X not in e, "Query variable must be distinct from evidence"
Q = ProbDist(X) # probability distribution for X, initially empty
Y = [v for v in P.variables if v != X and v not in e] # hidden variables.
for xi in P.values(X):
Q[xi] = enumerate_joint(Y, extend(e, X, xi), P)
return Q.normalize()
def markov_blanket_sample(X, e, bn):
"""Return a sample from P(X | mb) where mb denotes that the
variables in the Markov blanket of X take their values from event
e (which must assign a value to each). The Markov blanket of X is
X's parents, children, and children's parents."""
Xnode = bn.variable_node(X)
Q = ProbDist(X)
for xi in bn.variable_values(X):
ei = extend(e, X, xi)
# [Equation 14.12:]
Q[xi] = Xnode.p(xi, e) * product(
Yj.p(ei[Yj.variable], ei) for Yj in Xnode.children)
# (assuming a Boolean variable here)
return probability(Q.normalize()[True])
def enumerate_joint_ask(X, e, P):
"""Return a probability distribution over the values of the variable X,
given the {var:val} observations e, in the JointProbDist P. [Section 13.3]
>>> P = JointProbDist(['X', 'Y'])
>>> P[0,0] = 0.25; P[0,1] = 0.5; P[1,1] = P[2,1] = 0.125
>>> enumerate_joint_ask('X', dict(Y=1), P).show_approx()
'0: 0.667, 1: 0.167, 2: 0.167'
"""
assert X not in e, "Query variable must be distinct from evidence"
Q = ProbDist(X) # probability distribution for X, initially empty
Y = [v for v in P.variables if v != X and v not in e] # hidden variables.
for xi in P.values(X):
Q[xi] = enumerate_joint(Y, extend(e, X, xi), P)
return Q.normalize()
def enumerate_all(variables, e, bn):
"""Return the sum of those entries in P(variables | e{others})
consistent with e, where P is the joint distribution represented
by bn, and e{others} means e restricted to bn's other variables
(the ones other than variables). Parents must precede children in variables."""
if not variables:
return 1.0
Y, rest = variables[0], variables[1:]
Ynode = bn.variable_node(Y)
if Y in e:
return Ynode.p(e[Y], e) * enumerate_all(rest, e, bn)
else:
return sum(Ynode.p(y, e) * enumerate_all(rest, extend(e, Y, y), bn)
for y in bn.variable_values(Y))
def enumerate_joint_ask(X, e, P):
"""Return a probability distribution over the values of the variable X,
given the {var:val} observations e, in the JointProbDist P.
Works for Boolean variables only. [Fig. 13.4].
X is a string (variable name).
e is a dictionary of variable-name value pairs.
P is an instance of JointProbDist."""
Q = ProbDist(X) # probability distribution for X, initially empty
Y = [v for v in P.variables if v != X and v not in e] # hidden vars.
for xi in P.values(X):
ext = extend(e, X, xi) # copies e and adds X: xi
Q[xi] = enumerate_joint(Y, ext, P)
return Q.normalize()
def enumerate_joint_ask(X, e, P):
"""Return a probability distribution over the values of the variable X,
given the {var:val} observations e, in the JointProbDist P.
Works for Boolean variables only. [Fig. 13.4].
X is a string (variable name).
e is a dictionary of variable-name value pairs.
P is an instance of JointProbDist."""
Q = ProbDist(X) # probability distribution for X, initially empty
Y = [v for v in P.variables if v != X and v not in e] # hidden vars.
for xi in P.values(X):
ext = extend(e, X, xi) # copies e and adds X: xi
Q[xi] = enumerate_joint(Y, ext, P)
return Q.normalize()
def max_out(self, var, bn):
"""
Make a factor eliminating var by summing over its values.
:param var:
:param bn:
:return:
"""
variables = [X for X in self.variables if X != var]
cpt_with_assignement = {event_values(e, variables): max((self.p(extend(e, var, val)), val)
for val in bn.variable_values(var))
for e in all_events(variables, bn, {})}
assignement = {}
cpt = {}
for key, (value, assgn) in cpt_with_assignement.items():
cpt[key] = value
assignement[key] = assgn
factor = Factor(variables, cpt, assignement, self)
factor.last_max_out = bn.last_max_out
bn.last_max_out = factor
return factor
def enumeration_ask (X, e, bn):
"""Returns a distribution of X given e from bayes net bn. [Fig. 14.9]
X is a string (variable name).
e is a dictionary of variablename: value pairs.
bn is an instance of BayesNet.
>>> p = enumeration_ask('Earthquake', {}, burglary)
>>> [p[True], p[False]]
[0.002, 0.998]
>>> p = enumeration_ask('Burglary',
... {'JohnCalls': True, 'MaryCalls': True}, burglary)
>>> p.show_approx()
'False: 0.716, True: 0.284'"""
Q = ProbDist(X) # empty probability distribution for X
for xi in bn.variable_values(X):
Q[xi] = enumerate_all(bn.variables(), extend(e, X, xi), bn)
# Assume that parents precede children in bn.variables.
# Otherwise, in enumerate_all, the values of Y's parents
# may be unspecified.
return Q.normalize()
def all_events_jpd(vars, jpd, e):
"""
e is evidence, it is a dict containing 'variable:value' pairs
vars is a list of variables
jpd is an object of JointProbDist
The function generates all events of variables in vars with all possible value assignments and variables in e with fixed values
>>>P = JointProbDist(['X', 'Y', 'Z'], {'X':[1,2], 'Y': [True, False], 'Z' : ['a', 'b']})
>>>events = all_events_jpd(['X', 'Y'], P, {'Z':'a'})
>>>for each in events: print each
{'Y': True, 'X': 1, 'Z': 'a'}
{'Y': True, 'X': 2, 'Z': 'a'}
{'Y': False, 'X': 1, 'Z': 'a'}
{'Y': False, 'X': 2, 'Z': 'a'}
"""
if not vars: ## if vars is empty
yield e
else:
X, rest = vars[0], vars[1:]
for e1 in all_events_jpd(rest, jpd, e):
for x in jpd.values(X):
yield extend(e1, X, x)
def all_events_jpd(vars, jpd, e):
"""
e is evidence, it is a dict containing 'variable:value' pairs
vars is a list of variables
jpd is an object of JointProbDist
The function generates all events of variables in vars with all possible value assignments and variables in e with fixed values
>>>P = JointProbDist(['X', 'Y', 'Z'], {'X':[1,2], 'Y': [True, False], 'Z' : ['a', 'b']})
>>>events = all_events_jpd(['X', 'Y'], P, {'Z':'a'})
>>>for each in events: print each
{'Y': True, 'X': 1, 'Z': 'a'}
{'Y': True, 'X': 2, 'Z': 'a'}
{'Y': False, 'X': 1, 'Z': 'a'}
{'Y': False, 'X': 2, 'Z': 'a'}
"""
if not vars: ## if vars is empty
yield e
else:
X, rest = vars[0], vars[1:]
for e1 in all_events_jpd(rest, jpd,e):
for x in jpd.values(X):
yield extend(e1, X,x)
def enumeration_ask(X, e, bn):
"""Returns a distribution of X given e from bayes net bn. [Fig. 14.9]
X is a string (variable name).
e is a dictionary of variablename: value pairs.
bn is an instance of BayesNet.
>>> p = enumeration_ask('Earthquake', {}, burglary)
>>> [p[True], p[False]]
[0.002, 0.998]
>>> p = enumeration_ask('Burglary',
... {'JohnCalls': True, 'MaryCalls': True}, burglary)
>>> p.show_approx()
'False: 0.716, True: 0.284'
"""
Q = ProbDist(X) # empty probability distribution for X
for xi in bn.variable_values(X):
Q[xi] = enumerate_all(bn.variables(), extend(e, X, xi), bn)
# Assume that parents precede children in bn.variables.
# Otherwise, in enumerate_all, the values of Y's parents
# may be unspecified.
return Q.normalize()