def inferenceByVariableElimination(bayesNet, queryVariables, evidenceDict, eliminationOrder):
"""
Question 6: Your inference by variable elimination implementation
This function should perform a probabilistic inference query that
returns the factor:
P(queryVariables | evidenceDict)
It should perform inference by interleaving joining on a variable
and eliminating that variable, in the order of variables according
to eliminationOrder. See inferenceByEnumeration for an example on
how to use these functions.
You need to use joinFactorsByVariable to join all of the factors
that contain a variable in order for the autograder to
recognize that you performed the correct interleaving of
joins and eliminates.
If a factor that you are about to eliminate a variable from has
only one unconditioned variable, you should not eliminate it
and instead just discard the factor. This is since the
result of the eliminate would be 1 (you marginalize
all of the unconditioned variables), but it is not a
valid factor. So this simplifies using the result of eliminate.
The sum of the probabilities should sum to one (so that it is a true
conditional probability, conditioned on the evidence).
bayesNet: The Bayes Net on which we are making a query.
queryVariables: A list of the variables which are unconditioned
in the inference query.
evidenceDict: An assignment dict {variable : value} for the
variables which are presented as evidence
(conditioned) in the inference query.
eliminationOrder: The order to eliminate the variables in.
Hint: BayesNet.getAllCPTsWithEvidence will return all the Conditional
Probability Tables even if an empty dict (or None) is passed in for
evidenceDict. In this case it will not specialize any variable domains
in the CPTs.
Useful functions:
BayesNet.getAllCPTsWithEvidence
normalize
eliminate
joinFactorsByVariable
joinFactors
"""
# this is for autograding -- don't modify
joinFactorsByVariable = joinFactorsByVariableWithCallTracking(callTrackingList)
eliminate = eliminateWithCallTracking(callTrackingList)
if eliminationOrder is None: # set an arbitrary elimination order if None given
eliminationVariables = bayesNet.variablesSet() - set(queryVariables) -\
set(evidenceDict.keys())
eliminationOrder = sorted(list(eliminationVariables))
"*** YOUR CODE HERE ***"
# grab all factors where we know the evidence variables (to reduce the size of the tables)
currentFactorsList = bayesNet.getAllCPTsWithEvidence(evidenceDict)
# join all factors by variable
for joinVariable in eliminationOrder:
currentFactorsList, joinedFactor = joinFactorsByVariable(currentFactorsList, joinVariable)
if len(joinedFactor.unconditionedVariables()) > 1:
eliminateFactor = eliminate(joinedFactor, joinVariable)
currentFactorsList.append(eliminateFactor)
fullJoint = joinFactors(currentFactorsList)
return normalize(fullJoint)
def inferenceByEnumeration(bayesNet, queryVariables, evidenceDict):
"""
An inference by enumeration implementation provided as reference.
This function performs a probabilistic inference query that
returns the factor:
P(queryVariables | evidenceDict)
bayesNet: The Bayes Net on which we are making a query.
queryVariables: A list of the variables which are unconditioned in
the inference query.
evidenceDict: An assignment dict {variable : value} for the
variables which are presented as evidence
(conditioned) in the inference query.
"""
callTrackingList = []
joinFactorsByVariable = joinFactorsByVariableWithCallTracking(
callTrackingList)
eliminate = eliminateWithCallTracking(callTrackingList)
# initialize return variables and the variables to eliminate
evidenceVariablesSet = set(evidenceDict.keys())
queryVariablesSet = set(queryVariables)
eliminationVariables = (bayesNet.variablesSet() -
evidenceVariablesSet) - queryVariablesSet
# grab all factors where we know the evidence variables (to reduce the size of the tables)
currentFactorsList = bayesNet.getAllCPTsWithEvidence(evidenceDict)
# join all factors by variable
for joinVariable in bayesNet.variablesSet():
currentFactorsList, joinedFactor = joinFactorsByVariable(
currentFactorsList, joinVariable)
currentFactorsList.append(joinedFactor)
# currentFactorsList should contain the connected components of the graph now as factors, must join the connected components
fullJoint = joinFactors(currentFactorsList)
# marginalize all variables that aren't query or evidence
incrementallyMarginalizedJoint = fullJoint
for eliminationVariable in eliminationVariables:
incrementallyMarginalizedJoint = eliminate(
incrementallyMarginalizedJoint, eliminationVariable)
fullJointOverQueryAndEvidence = incrementallyMarginalizedJoint
# normalize so that the probability sums to one
# the input factor contains only the query variables and the evidence variables,
# both as unconditioned variables
queryConditionedOnEvidence = normalize(fullJointOverQueryAndEvidence)
# now the factor is conditioned on the evidence variables
# the order is join on all variables, then eliminate on all elimination variables
#print "callTrackingList: ", callTrackingList
return queryConditionedOnEvidence
def inferenceByEnumeration(bayesNet, queryVariables, evidenceDict):
"""
An inference by enumeration implementation provided as reference.
This function performs a probabilistic inference query that
returns the factor:
P(queryVariables | evidenceDict)
bayesNet: The Bayes Net on which we are making a query.
queryVariables: A list of the variables which are unconditioned in
the inference query.
evidenceDict: An assignment dict {variable : value} for the
variables which are presented as evidence
(conditioned) in the inference query.
"""
callTrackingList = []
joinFactorsByVariable = joinFactorsByVariableWithCallTracking(callTrackingList)
eliminate = eliminateWithCallTracking(callTrackingList)
# initialize return variables and the variables to eliminate
evidenceVariablesSet = set(evidenceDict.keys())
queryVariablesSet = set(queryVariables)
eliminationVariables = (bayesNet.variablesSet() - evidenceVariablesSet) - queryVariablesSet
# grab all factors where we know the evidence variables (to reduce the size of the tables)
currentFactorsList = bayesNet.getAllCPTsWithEvidence(evidenceDict)
# join all factors by variable
for joinVariable in bayesNet.variablesSet():
currentFactorsList, joinedFactor = joinFactorsByVariable(currentFactorsList, joinVariable)
currentFactorsList.append(joinedFactor)
# currentFactorsList should contain the connected components of the graph now as factors, must join the connected components
fullJoint = joinFactors(currentFactorsList)
# marginalize all variables that aren't query or evidence
incrementallyMarginalizedJoint = fullJoint
for eliminationVariable in eliminationVariables:
incrementallyMarginalizedJoint = eliminate(incrementallyMarginalizedJoint, eliminationVariable)
fullJointOverQueryAndEvidence = incrementallyMarginalizedJoint
# normalize so that the probability sums to one
# the input factor contains only the query variables and the evidence variables,
# both as unconditioned variables
queryConditionedOnEvidence = normalize(fullJointOverQueryAndEvidence)
# now the factor is conditioned on the evidence variables
# the order is join on all variables, then eliminate on all elimination variables
#print "callTrackingList: ", callTrackingList
return queryConditionedOnEvidence
def inferenceByVariableElimination(bayesNet, queryVariables, evidenceDict,
eliminationOrder):
"""
Question 6: Your inference by variable elimination implementation
This function should perform a probabilistic inference query that
returns the factor:
P(queryVariables | evidenceDict)
It should perform inference by interleaving joining on a variable
and eliminating that variable, in the order of variables according
to eliminationOrder. See inferenceByEnumeration for an example on
how to use these functions.
You need to use joinFactorsByVariable to join all of the factors
that contain a variable in order for the autograder to
recognize that you performed the correct interleaving of
joins and eliminates.
If a factor that you are about to eliminate a variable from has
only one unconditioned variable, you should not eliminate it
and instead just discard the factor. This is since the
result of the eliminate would be 1 (you marginalize
all of the unconditioned variables), but it is not a
valid factor. So this simplifies using the result of eliminate.
The sum of the probabilities should sum to one (so that it is a true
conditional probability, conditioned on the evidence).
bayesNet: The Bayes Net on which we are making a query.
queryVariables: A list of the variables which are unconditioned
in the inference query.
evidenceDict: An assignment dict {variable : value} for the
variables which are presented as evidence
(conditioned) in the inference query.
eliminationOrder: The order to eliminate the variables in.
Hint: BayesNet.getAllCPTsWithEvidence will return all the Conditional
Probability Tables even if an empty dict (or None) is passed in for
evidenceDict. In this case it will not specialize any variable domains
in the CPTs.
Useful functions:
BayesNet.getAllCPTsWithEvidence
normalize
eliminate
joinFactorsByVariable
joinFactors
"""
# this is for autograding -- don't modify
joinFactorsByVariable = joinFactorsByVariableWithCallTracking(
callTrackingList)
eliminate = eliminateWithCallTracking(callTrackingList)
if eliminationOrder is None: # set an arbitrary elimination order if None given
eliminationVariables = bayesNet.variablesSet() - set(queryVariables) -\
set(evidenceDict.keys())
eliminationOrder = sorted(list(eliminationVariables))
"*** YOUR CODE HERE ***"
evidenceVariablesSet = set(evidenceDict.keys())
queryVariablesSet = set(queryVariables)
eliminationVariables = (bayesNet.variablesSet() -
evidenceVariablesSet) - queryVariablesSet
# grab all factors where we know the evidence variables (to reduce the size of the tables)
newfactor = None
currentFactorsList = bayesNet.getAllCPTsWithEvidence(evidenceDict)
for var in eliminationOrder:
currentFactorsList, newfactor = joinFactorsByVariable(
currentFactorsList, var)
if len(newfactor.unconditionedVariables()) == 1:
pass
else:
newfactor = eliminate(newfactor, var)
currentFactorsList.append(newfactor)
retfactor = joinFactors(currentFactorsList)
retfactor = normalize(retfactor)
return retfactor
def inferenceByVariableElimination(bayesNet, queryVariables, evidenceDict,
eliminationOrder):
"""
Question 6: Your inference by variable elimination implementation
This function should perform a probabilistic inference query that
returns the factor:
P(queryVariables | evidenceDict)
It should perform inference by interleaving joining on a variable
and eliminating that variable, in the order of variables according
to eliminationOrder. See inferenceByEnumeration for an example on
how to use these functions.
You need to use joinFactorsByVariable to join all of the factors
that contain a variable in order for the autograder to
recognize that you performed the correct interleaving of
joins and eliminates.
If a factor that you are about to eliminate a variable from has
only one unconditioned variable, you should not eliminate it
and instead just discard the factor. This is since the
result of the eliminate would be 1 (you marginalize
all of the unconditioned variables), but it is not a
valid factor. So this simplifies using the result of eliminate.
The sum of the probabilities should sum to one (so that it is a true
conditional probability, conditioned on the evidence).
bayesNet: The Bayes Net on which we are making a query.
queryVariables: A list of the variables which are unconditioned
in the inference query.
evidenceDict: An assignment dict {variable : value} for the
variables which are presented as evidence
(conditioned) in the inference query.
eliminationOrder: The order to eliminate the variables in.
Hint: BayesNet.getAllCPTsWithEvidence will return all the Conditional
Probability Tables even if an empty dict (or None) is passed in for
evidenceDict. In this case it will not specialize any variable domains
in the CPTs.
Useful functions:
BayesNet.getAllCPTsWithEvidence
normalize
eliminate
joinFactorsByVariable
joinFactors
Query: ['D']
eliminateOrder: ['T']
evidenceDict : W {'W': 'sun'}
Variables: D, W, T
Edges: W -> D, W -> T
cpt [Factor(set(['D']), set(['W']), {'D': ['dry', 'wet'], 'W': ['sun'],
'T': ['hot', 'cold']}), Factor(set(['W']), set([]),
{'D': ['dry', 'wet'], 'W': ['sun'], 'T': ['hot', 'cold']}),
Factor(set(['T']), set(['W']), {'D': ['dry', 'wet'],
'W': ['sun'], 'T': ['hot', 'cold']})]
join -> eliminate -> join -> eliminate
###
"""
# this is for autograding -- don't modify
joinFactorsByVariable = joinFactorsByVariableWithCallTracking(
callTrackingList)
eliminate = eliminateWithCallTracking(callTrackingList)
if eliminationOrder is None: # set an arbitrary elimination order if None given
eliminationVariables = bayesNet.variablesSet() - set(queryVariables) -\
set(evidenceDict.keys())
eliminationOrder = sorted(list(eliminationVariables))
"*** YOUR CODE HERE ***"
cpts = bayesNet.getAllCPTsWithEvidence(evidenceDict)
for join in eliminationOrder:
cpts, joinedFactor = joinFactorsByVariable(cpts, join)
if (len(joinedFactor.unconditionedVariables()) == 1):
continue
else:
#eliminate
eliminateVariable = join
eliminatedFactor = eliminate(joinedFactor, eliminateVariable)
cpts.append(eliminatedFactor)
factor = joinFactors(cpts)
normalizeFactor = normalize(factor)
return normalizeFactor
def inferenceByVariableElimination(bayesNet, queryVariables, evidenceDict, eliminationOrder):
"""
Question 4: Your inference by variable elimination implementation
This function should perform a probabilistic inference query that
returns the factor:
P(queryVariables | evidenceDict)
It should perform inference by interleaving joining on a variable
and eliminating that variable, in the order of variables according
to eliminationOrder. See inferenceByEnumeration for an example on
how to use these functions.
You need to use joinFactorsByVariable to join all of the factors
that contain a variable in order for the autograder to
recognize that you performed the correct interleaving of
joins and eliminates.
If a factor that you are about to eliminate a variable from has
only one unconditioned variable, you should not eliminate it
and instead just discard the factor. This is since the
result of the eliminate would be 1 (you marginalize
all of the unconditioned variables), but it is not a
valid factor. So this simplifies using the result of eliminate.
The sum of the probabilities should sum to one (so that it is a true
conditional probability, conditioned on the evidence).
bayesNet: The Bayes Net on which we are making a query.
queryVariables: A list of the variables which are unconditioned
in the inference query.
evidenceDict: An assignment dict {variable : value} for the
variables which are presented as evidence
(conditioned) in the inference query.
eliminationOrder: The order to eliminate the variables in.
Hint: BayesNet.getAllCPTsWithEvidence will return all the Conditional
Probability Tables even if an empty dict (or None) is passed in for
evidenceDict. In this case it will not specialize any variable domains
in the CPTs.
Useful functions:
BayesNet.getAllCPTsWithEvidence
normalize
eliminate
joinFactorsByVariable
joinFactors
"""
# this is for autograding -- don't modify
joinFactorsByVariable = joinFactorsByVariableWithCallTracking(callTrackingList)
eliminate = eliminateWithCallTracking(callTrackingList)
if eliminationOrder is None: # set an arbitrary elimination order if None given
eliminationVariables = bayesNet.variablesSet() - set(queryVariables) -\
set(evidenceDict.keys())
eliminationOrder = sorted(list(eliminationVariables))
"*** YOUR CODE HERE ***"
evidenceVariablesSet = set(evidenceDict.keys())
queryVariablesSet = set(queryVariables)
eliminationVariables = set(eliminationOrder)
currentFactorsList = bayesNet.getAllCPTsWithEvidence(evidenceDict)
for i in range(len(eliminationOrder)):
'''eviDict = {eliminationOrder[i]:evidenceDict[eliminationOrder[i]]}
currentFactorsList = bayesNet.getAllCPTsWithEvidence(eviDict)'''
# join factors by variable
joinVariable = eliminationOrder[i]
currentFactorsList, joinedFactor = joinFactorsByVariable(currentFactorsList, joinVariable)
# marginalize the variable
if joinedFactor.unconditionedVariables() != set(joinVariable):
joinedFactor = eliminate(joinedFactor, joinVariable)
currentFactorsList.append(joinedFactor)
# currentFactorsList should contain the connected components of the graph now as factors, must join the connected components
fullJointOverQueryAndEvidence = joinFactors(currentFactorsList)
queryConditionedOnEvidence = normalize(fullJointOverQueryAndEvidence)
return queryConditionedOnEvidence
'pdb.set_trace()'
util.raiseNotDefined()
def inferenceByVariableElimination(bayesNet, queryVariables, evidenceDict,
eliminationOrder):
"""
Question 6: Your inference by variable elimination implementation
This function should perform a probabilistic inference query that
returns the factor:
P(queryVariables | evidenceDict)
It should perform inference by interleaving joining on a variable
and eliminating that variable, in the order of variables according
to eliminationOrder. See inferenceByEnumeration for an example on
how to use these functions.
You need to use joinFactorsByVariable to join all of the factors
that contain a variable in order for the autograder to
recognize that you performed the correct interleaving of
joins and eliminates.
If a factor that you are about to eliminate a variable from has
only one unconditioned variable, you should not eliminate it
and instead just discard the factor. This is since the
result of the eliminate would be 1 (you marginalize
all of the unconditioned variables), but it is not a
valid factor. So this simplifies using the result of eliminate.
The sum of the probabilities should sum to one (so that it is a true
conditional probability, conditioned on the evidence).
bayesNet: The Bayes Net on which we are making a query.
queryVariables: A list of the variables which are unconditioned
in the inference query.
evidenceDict: An assignment dict {variable : value} for the
variables which are presented as evidence
(conditioned) in the inference query.
eliminationOrder: The order to eliminate the variables in.
Hint: BayesNet.getAllCPTsWithEvidence will return all the Conditional
Probability Tables even if an empty dict (or None) is passed in for
evidenceDict. In this case it will not specialize any variable domains
in the CPTs.
Useful functions:
BayesNet.getAllCPTsWithEvidence
normalize
eliminate
joinFactorsByVariable
joinFactors
"""
# this is for autograding -- don't modify
joinFactorsByVariable = joinFactorsByVariableWithCallTracking(
callTrackingList)
eliminate = eliminateWithCallTracking(callTrackingList)
if eliminationOrder is None: # set an arbitrary elimination order if None given
eliminationVariables = bayesNet.variablesSet() - set(queryVariables) -\
set(evidenceDict.keys())
eliminationOrder = sorted(list(eliminationVariables))
"*** YOUR CODE HERE ***"
#util.raiseNotDefined()
"""
# print "@@@@@queryVariables ", queryVariables
# print "@@@@@evidenceDict ", evidenceDict
# print "@@@@@eliminationOrder ", eliminationOrder
# print "@@@@@bayesNet ", bayesNet
# currentFactorsList = bayesNet.getAllCPTsWithEvidence(evidenceDict)
currentFactorsList = bayesNet.getAllCPTsWithEvidence(evidenceDict)
# print "@@@@@currentFactorsList ", currentFactorsList
for joinVariable in eliminationOrder:
# print "@@@@@joinVariable ", joinVariable
currentFactorsList, joinedFactor = joinFactorsByVariable(currentFactorsList, joinVariable)
# print "@@@@@currentFactorsList ", currentFactorsList
# print "@@@@@joinedFactor ", joinedFactor
if len(joinedFactor.unconditionedVariables()) > 1:
eliminatedFactor = eliminate(joinedFactor, joinVariable)
currentFactorsList.append(eliminatedFactor)
# print "@@@@@currentFactorsList ", currentFactorsList
joinedFactor = joinFactors(currentFactorsList)
normalizedFactor = normalize(joinedFactor)
return normalizedFactor
"""
# grab all factors where we know the evidence variables (to reduce the size of the tables)
# pass by evidenceDict through BayesNet.getAllCPTsWithEvidence
factors = bayesNet.getAllCPTsWithEvidence(evidenceDict)
# join all factors by eliminationOrder
for join_Factor in eliminationOrder:
not_joined_Factor, joined = joinFactorsByVariable(
factors, join_Factor)
factors = not_joined_Factor
# currentFactorsList should contain the connected components of the graph now as factors, must join the connected components
joined_unconditioned = joined.unconditionedVariables()
if len(joined_unconditioned) > 1:
temp_factor = eliminate(joined, join_Factor) # eliminate
not_joined_Factor.append(temp_factor)
joinedFactors = joinFactors(not_joined_Factor)
return normalize(joinedFactors) # normalize the joinedFactors
def inferenceByVariableElimination(bayesNet, queryVariables, evidenceDict,
eliminationOrder):
"""
Question 6: Your inference by variable elimination implementation
This function should perform a probabilistic inference query that
returns the factor:
P(queryVariables | evidenceDict)
It should perform inference by interleaving joining on a variable
and eliminating that variable, in the order of variables according
to eliminationOrder. See inferenceByEnumeration for an example on
how to use these functions.
You need to use joinFactorsByVariable to join all of the factors
that contain a variable in order for the autograder to
recognize that you performed the correct interleaving of
joins and eliminates.
If a factor that you are about to eliminate a variable from has
only one unconditioned variable, you should not eliminate it
and instead just discard the factor. This is since the
result of the eliminate would be 1 (you marginalize
all of the unconditioned variables), but it is not a
valid factor. So this simplifies using the result of eliminate.
The sum of the probabilities should sum to one (so that it is a true
conditional probability, conditioned on the evidence).
bayesNet: The Bayes Net on which we are making a query.
queryVariables: A list of the variables which are unconditioned
in the inference query.
evidenceDict: An assignment dict {variable : value} for the
variables which are presented as evidence
(conditioned) in the inference query.
eliminationOrder: The order to eliminate the variables in.
Hint: BayesNet.getAllCPTsWithEvidence will return all the Conditional
Probability Tables even if an empty dict (or None) is passed in for
evidenceDict. In this case it will not specialize any variable domains
in the CPTs.
Useful functions:
BayesNet.getAllCPTsWithEvidence
normalize
eliminate
joinFactorsByVariable
joinFactors
"""
# this is for autograding -- don't modify
joinFactorsByVariable = joinFactorsByVariableWithCallTracking(
callTrackingList)
eliminate = eliminateWithCallTracking(callTrackingList)
if eliminationOrder is None: # set an arbitrary elimination order if None given
eliminationVariables = bayesNet.variablesSet() - set(queryVariables) -\
set(evidenceDict.keys())
eliminationOrder = sorted(list(eliminationVariables))
"*** YOUR CODE HERE ***"
"""
this section is heavily based on the "inferenceByEnumeration" section.
In "inferenceByEnumeration" section we would join all "joinVariable"
to the "currentFactorsList" according to:
for joinVariable in bayesNet.variablesSet():
currentFactorsList, joinedFactor = joinFactorsByVariable(currentFactorsList, joinVariable)
currentFactorsList.append(joinedFactor)
and then eliminate by:
for eliminationVariable in eliminationVariables:
incrementallyMarginalizedJoint = eliminate(incrementallyMarginalizedJoint, eliminationVariable)
fullJointOverQueryAndEvidence = incrementallyMarginalizedJoint
and then normalize so that the probability sums to one
queryConditionedOnEvidence = normalize(fullJointOverQueryAndEvidence)
and then return "queryConditionedOnEvidence"
NOW, for "inferenceByVariableElimination" we would heavily use the same
method but instead of adding all of them together and then removing
all together, we would add one and then remove the same:
to achieve this task we would loop through all the "eliminationOrder"
and form a "currentFactorsList" with the "joinedFactor" and "elimVariable"
currentFactorsList, joinedFactor = joinFactorsByVariable(currentFactorsList, elimVariable)
then I would eliminate "elimVariable" from "joinedFactor" as long as
there is at least more than 1 variable in the unconditioned in the
"joinedFactor". I am not fully sure why I have to do it but the comments
above say:
If a factor that you are about to eliminate a variable from has
only one unconditioned variable, you should not eliminate it
and instead just discard the factor. This is since the
result of the eliminate would be 1 (you marginalize
all of the unconditioned variables), but it is not a
valid factor. So this simplifies using the result of eliminate.
I guess the reason is that if there is only one unconditioned in the
joint and we remove them there would be no unconditioned left in joint.
if there is only 1 unconditioned this is what happens:
P(A|B).P(B) = P(A,B) --> end of it --> cant eliminate B from P(A,B)
once the currentfactorList is updated a new factors list is generated
and the normalized result is returned.
finalFactorsList = joinFactors(currentFactorsList)
finalFactorsListNormalized = normalize(finalFactorsList)
"""
#util.raiseNotDefined()
"generate the current factor list. this list will be updated on the road"
currentFactorsList = bayesNet.getAllCPTsWithEvidence(evidenceDict)
"loop through the elimination parameters and thenjoin and remove"
for elimVariable in eliminationOrder:
#print currentFactorsList
"add the elimVariable and generate join"
currentFactorsList, joinedFactor = joinFactorsByVariable(
currentFactorsList, elimVariable)
#print joinedFactor
#print currentFactorsList
"if unconditioned are larger or equal to 2 then remove from joinedFactor"
numUncontiotioned = len(joinedFactor.unconditionedVariables())
if numUncontiotioned >= 2:
incrementallyMarginalizedJoint = eliminate(
joinedFactor, elimVariable)
currentFactorsList.append(incrementallyMarginalizedJoint)
#print "incrementallyMarginalizedJoint", incrementallyMarginalizedJoint
#print currentFactorsList
"otherwise this is the end of the add and remove --> do nothing"
"generate final factor list join out of the updated currentFactorsList"
finalFactorsList = joinFactors(currentFactorsList)
#print finalFactorsList
"normalize"
finalFactorsListNormalized = normalize(finalFactorsList)
return finalFactorsListNormalized
