def factor_product(*args):
"""
Returns factor product over `args`.
Parameters
----------
args: `BaseFactor` instances.
factors to be multiplied
Returns
-------
BaseFactor: `BaseFactor` representing factor product over all the `BaseFactor` instances in args.
Examples
--------
>>> from pgmpy.factors.discrete import DiscreteFactor
>>> from pgmpy.factors import factor_product
>>> phi1 = DiscreteFactor(['x1', 'x2', 'x3'], [2, 3, 2], range(12))
>>> phi2 = DiscreteFactor(['x3', 'x4', 'x1'], [2, 2, 2], range(8))
>>> phi = factor_product(phi1, phi2)
>>> phi.variables
['x1', 'x2', 'x3', 'x4']
>>> phi.cardinality
array([2, 3, 2, 2])
>>> phi.values
array([[[[ 0, 0],
[ 4, 6]],
[[ 0, 4],
[12, 18]],
[[ 0, 8],
[20, 30]]],
[[[ 6, 18],
[35, 49]],
[[ 8, 24],
[45, 63]],
[[10, 30],
[55, 77]]]])
"""
if not all(isinstance(phi, BaseFactor) for phi in args):
raise TypeError("Arguments must be factors")
# Check if all of the arguments are of the same type
elif len(set(map(type, args))) != 1:
raise NotImplementedError("All the args are expected to ",
"be instances of the same factor class.")
for arg in args:
for i in range(len(arg.values)):
replace_absolute_values(arg.values, i)
return reduce(lambda phi1, phi2: phi1 * phi2, args)
def factor_product(*args):
"""
Returns factor product over `args`.
Parameters
----------
args: `BaseFactor` instances.
factors to be multiplied
Returns
-------
BaseFactor: `BaseFactor` representing factor product over all the `BaseFactor` instances in args.
Examples
--------
>>> from pgmpy.factors.discrete import DiscreteFactor
>>> from pgmpy.factors import factor_product
>>> phi1 = DiscreteFactor(['x1', 'x2', 'x3'], [2, 3, 2], range(12))
>>> phi2 = DiscreteFactor(['x3', 'x4', 'x1'], [2, 2, 2], range(8))
>>> phi = factor_product(phi1, phi2)
>>> phi.variables
['x1', 'x2', 'x3', 'x4']
>>> phi.cardinality
array([2, 3, 2, 2])
>>> phi.values
array([[[[ 0, 0],
[ 4, 6]],
[[ 0, 4],
[12, 18]],
[[ 0, 8],
[20, 30]]],
[[[ 6, 18],
[35, 49]],
[[ 8, 24],
[45, 63]],
[[10, 30],
[55, 77]]]])
"""
if not all(isinstance(phi, BaseFactor) for phi in args):
raise TypeError("Arguments must be factors")
# Check if all of the arguments are of the same type
elif len(set(map(type, args))) != 1:
raise NotImplementedError("All the args are expected to ",
"be instances of the same factor class.")
return reduce(lambda phi1, phi2: phi1 * phi2, args)
def factor_product(*args):
"""
Returns factor product over `args`.
Parameters
----------
args: `Factor` instances.
factors to be multiplied
Returns
-------
Factor: `Factor` representing factor product over all the `Factor` instances in args.
Examples
--------
>>> from pgmpy.factors import Factor, factor_product
>>> phi1 = Factor(['x1', 'x2', 'x3'], [2, 3, 2], range(12))
>>> phi2 = Factor(['x3', 'x4', 'x1'], [2, 2, 2], range(8))
>>> phi = factor_product(phi1, phi2)
>>> phi.variables
['x1', 'x2', 'x3', 'x4']
>>> phi.cardinality
array([2, 3, 2, 2])
>>> phi.values
array([[[[ 0, 0],
[ 4, 6]],
[[ 0, 4],
[12, 18]],
[[ 0, 8],
[20, 30]]],
[[[ 6, 18],
[35, 49]],
[[ 8, 24],
[45, 63]],
[[10, 30],
[55, 77]]]])
"""
if not all(isinstance(phi, Factor) for phi in args):
raise TypeError("Arguments must be factors")
return reduce(lambda phi1, phi2: phi1 * phi2, args)
def is_imap(self, JPD):
"""
Checks whether the bayesian model is Imap of given JointProbabilityDistribution
Parameters
----------
JPD : An instance of JointProbabilityDistribution Class, for which you want to
check the Imap
Returns
-------
boolean : True if bayesian model is Imap for given Joint Probability Distribution
False otherwise
Examples
--------
>>> from pgmpy.models import BayesianModel
>>> from pgmpy.factors.discrete import TabularCPD
>>> from pgmpy.factors.discrete import JointProbabilityDistribution
>>> G = BayesianModel([('diff', 'grade'), ('intel', 'grade')])
>>> diff_cpd = TabularCPD('diff', 2, [[0.2], [0.8]])
>>> intel_cpd = TabularCPD('intel', 3, [[0.5], [0.3], [0.2]])
>>> grade_cpd = TabularCPD('grade', 3,
... [[0.1,0.1,0.1,0.1,0.1,0.1],
... [0.1,0.1,0.1,0.1,0.1,0.1],
... [0.8,0.8,0.8,0.8,0.8,0.8]],
... evidence=['diff', 'intel'],
... evidence_card=[2, 3])
>>> G.add_cpds(diff_cpd, intel_cpd, grade_cpd)
>>> val = [0.01, 0.01, 0.08, 0.006, 0.006, 0.048, 0.004, 0.004, 0.032,
0.04, 0.04, 0.32, 0.024, 0.024, 0.192, 0.016, 0.016, 0.128]
>>> JPD = JointProbabilityDistribution(['diff', 'intel', 'grade'], [2, 3, 3], val)
>>> G.is_imap(JPD)
True
"""
if not isinstance(JPD, JointProbabilityDistribution):
raise TypeError(
"JPD must be an instance of JointProbabilityDistribution")
factors = [cpd.to_factor() for cpd in self.get_cpds()]
factor_prod = reduce(mul, factors)
JPD_fact = DiscreteFactor(JPD.variables, JPD.cardinality, JPD.values)
if JPD_fact == factor_prod:
return True
else:
return False
def is_imap(self, JPD):
"""
Checks whether the bayesian model is Imap of given JointProbabilityDistribution
Parameters
-----------
JPD : An instance of JointProbabilityDistribution Class, for which you want to
check the Imap
Returns
--------
boolean : True if bayesian model is Imap for given Joint Probability Distribution
False otherwise
Examples
--------
>>> from pgmpy.models import BayesianModel
>>> from pgmpy.factors.discrete import TabularCPD
>>> from pgmpy.factors.discrete import JointProbabilityDistribution
>>> G = BayesianModel([('diff', 'grade'), ('intel', 'grade')])
>>> diff_cpd = TabularCPD('diff', 2, [[0.2], [0.8]])
>>> intel_cpd = TabularCPD('intel', 3, [[0.5], [0.3], [0.2]])
>>> grade_cpd = TabularCPD('grade', 3,
... [[0.1,0.1,0.1,0.1,0.1,0.1],
... [0.1,0.1,0.1,0.1,0.1,0.1],
... [0.8,0.8,0.8,0.8,0.8,0.8]],
... evidence=['diff', 'intel'],
... evidence_card=[2, 3])
>>> G.add_cpds(diff_cpd, intel_cpd, grade_cpd)
>>> val = [0.01, 0.01, 0.08, 0.006, 0.006, 0.048, 0.004, 0.004, 0.032,
0.04, 0.04, 0.32, 0.024, 0.024, 0.192, 0.016, 0.016, 0.128]
>>> JPD = JointProbabilityDistribution(['diff', 'intel', 'grade'], [2, 3, 3], val)
>>> G.is_imap(JPD)
True
"""
if not isinstance(JPD, JointProbabilityDistribution):
raise TypeError("JPD must be an instance of JointProbabilityDistribution")
factors = [cpd.to_factor() for cpd in self.get_cpds()]
factor_prod = reduce(mul, factors)
JPD_fact = DiscreteFactor(JPD.variables, JPD.cardinality, JPD.values)
if JPD_fact == factor_prod:
return True
else:
return False
def factorset_product(*factorsets_list):
r"""
Base method used for product of factor sets.
Suppose :math:`\vec\phi_1` and :math:`\vec\phi_2` are two factor sets then their product is a another factors set
:math:`\vec\phi_3 = \vec\phi_1 \cup \vec\phi_2`.
Parameters
----------
factorsets_list: FactorSet1, FactorSet2, ..., FactorSetn
All the factor sets to be multiplied
Returns
-------
Product of factorset in factorsets_list
Examples
--------
>>> from pgmpy.factors import FactorSet
>>> from pgmpy.factors.discrete import DiscreteFactor
>>> from pgmpy.factors import factorset_product
>>> phi1 = DiscreteFactor(['x1', 'x2', 'x3'], [2, 3, 2], range(12))
>>> phi2 = DiscreteFactor(['x3', 'x4', 'x1'], [2, 2, 2], range(8))
>>> factor_set1 = FactorSet(phi1, phi2)
>>> phi3 = DiscreteFactor(['x5', 'x6', 'x7'], [2, 2, 2], range(8))
>>> phi4 = DiscreteFactor(['x5', 'x7', 'x8'], [2, 2, 2], range(8))
>>> factor_set2 = FactorSet(phi3, phi4)
>>> factor_set3 = factorset_product(factor_set1, factor_set2)
>>> print(factor_set3)
set([<DiscreteFactor representing phi(x1:2, x2:3, x3:2) at 0x7fb3a1933e90>,
<DiscreteFactor representing phi(x5:2, x7:2, x8:2) at 0x7fb3a1933f10>,
<DiscreteFactor representing phi(x5:2, x6:2, x7:2) at 0x7fb3a1933f90>,
<DiscreteFactor representing phi(x3:2, x4:2, x1:2) at 0x7fb3a1933e10>])
"""
if not all(
isinstance(factorset, FactorSet) for factorset in factorsets_list):
raise TypeError("Input parameters must be FactorSet instances")
return reduce(lambda x, y: x.product(y, inplace=False), factorsets_list)
def factorset_product(*factorsets_list):
r"""
Base method used for product of factor sets.
Suppose :math:`\vec\phi_1` and :math:`\vec\phi_2` are two factor sets then their product is a another factors set
:math:`\vec\phi_3 = \vec\phi_1 \cup \vec\phi_2`.
Parameters
----------
factorsets_list: FactorSet1, FactorSet2, ..., FactorSetn
All the factor sets to be multiplied
Returns
-------
Product of factorset in factorsets_list
Examples
--------
>>> from pgmpy.factors import FactorSet
>>> from pgmpy.factors.discrete import DiscreteFactor
>>> from pgmpy.factors import factorset_product
>>> phi1 = DiscreteFactor(['x1', 'x2', 'x3'], [2, 3, 2], range(12))
>>> phi2 = DiscreteFactor(['x3', 'x4', 'x1'], [2, 2, 2], range(8))
>>> factor_set1 = FactorSet(phi1, phi2)
>>> phi3 = DiscreteFactor(['x5', 'x6', 'x7'], [2, 2, 2], range(8))
>>> phi4 = DiscreteFactor(['x5', 'x7', 'x8'], [2, 2, 2], range(8))
>>> factor_set2 = FactorSet(phi3, phi4)
>>> factor_set3 = factorset_product(factor_set1, factor_set2)
>>> print(factor_set3)
set([<DiscreteFactor representing phi(x1:2, x2:3, x3:2) at 0x7fb3a1933e90>,
<DiscreteFactor representing phi(x5:2, x7:2, x8:2) at 0x7fb3a1933f10>,
<DiscreteFactor representing phi(x5:2, x6:2, x7:2) at 0x7fb3a1933f90>,
<DiscreteFactor representing phi(x3:2, x4:2, x1:2) at 0x7fb3a1933e10>])
"""
if not all(isinstance(factorset, FactorSet) for factorset in factorsets_list):
raise TypeError("Input parameters must be FactorSet instances")
return reduce(lambda x, y: x.product(y, inplace=False), factorsets_list)
# * KLD solution
# A natural choice of objective function will be the Kullback-Leibler (KL) divergence of two probability distribution $p(\mathbf{x})$ and $q(\mathbf{x})$, i.e., $KL(p(\mathbf{x})||q(\mathbf{x}))$.
# This should be straightforward using the standard Boltzmann machine training since the
# Bayesian network also allows us to evaluate the expected $\phi(\mathbf{x})$ under $p(\mathbf{x})$ tractably.
# The only issue left is the negative phase in training Boltzmann machine, which requires evaluation of partition function.
# We can circumvent this requirement by using either Monte-Carlo Markov Chain (MCMC) method like contrastive divergence (CD) or persistent CD (PCD),
# or quantum hardware to draw samples with quantum mechanics.
# We can also find the optimal solution by minimizing the KL-divergence.
# Obtain the joint probability distribution (JPD) from conditional probability distributiom.
# calculate the true JPD fron CPDs
factors = [cpd.to_factor() for cpd in grass_model.get_cpds()]
factor_prod = reduce(mul, factors)
p_true = factor_prod.values.flatten().astype('float32')
print(factor_prod)
#------------------------------------
# Method (1) Least-squares solution
#------------------------------------
#optimization function
def optimize_lsq(p, nodes):
# Define phi
x1, x2, x3, x4 = symbols('x1, x2, x3, x4')
h1, h2, h3, h4, J12, J13, J23, J24, J34, a, b = symbols(