Credal Network

Credal networks are probabilistic graphical models based on imprecise probability. Credal networks can be regarded as an extension of Bayesian networks, where credal sets replace probability mass functions in the specification of the local models for the network variables given their parents. As a Bayesian network defines a joint probability mass function over its variables, a credal network defines a joint credal set (from Wikipedia).

Tutorial

Reference

CN Model

class pyAgrum.CredalNet(*args)

Constructor used to create a CredalNet (step by step or with two BayesNet)

CredalNet() -> CredalNet

default constructor

CredalNet(src_min_num,src_max_den) -> CredalNet

Parameters:

  • src_min_num (str or pyAgrum.BayesNet) – The path to a BayesNet or the BN itself which contains lower probabilities.

  • src_max_den (str or pyAgrum.BayesNet) – The (optional) path to a BayesNet or the BN itself which contains upper probabilities.

NodeType_Credal = 1
NodeType_Indic = 3
NodeType_Precise = 0
NodeType_Vacuous = 2
addArc(tail, head)

Adds an arc between two nodes

Parameters:

  • tail (int) – the id of the tail node

  • head (int) – the id of the head node

Raises:

  • pyAgrum.InvalidDirectedCircle – If any (directed) cycle is created by this arc

  • pyAgrum.InvalidNode – If head or tail does not belong to the graph nodes

  • pyAgrum.DuplicateElement – If one of the arc already exists

Return type:

None

addVariable(name, card)
Parameters:

  • name (str) – the name of the new variable

  • card (int) – the domainSize of the new variable

Returns:

the id of the new node

Return type:

int

approximatedBinarization()

Approximate binarization.

Each bit has a lower and upper probability which is the lowest - resp. highest - over all vertices of the credal set. Enlarge the orignal credal sets and may induce huge imprecision. :rtype: None

Warning

Enlarge the orignal credal sets and therefor induce huge imprecision by propagation. Not recommended, use MCSampling or something else instead

bnToCredal(beta, oneNet, keepZeroes=False)

Perturbates the BayesNet provided as input for this CredalNet by generating intervals instead of point probabilities and then computes each vertex of each credal set.

Parameters:

  • beta (float) – The beta used to perturbate the network

  • oneNet (bool) – used as a flag. Set to True if one BayesNet if provided with counts, to False if two BayesNet are provided; one with probabilities (the lower net) and one with denominators over the first modalities (the upper net)

  • keepZeroes (bool) – used as a flag as whether or not - respectively True or False - we keep zeroes as zeroes. Default is False, i.e. zeroes are not kept

Return type:

None

computeBinaryCPTMinMax()
Return type:

None

credalNet_currentCpt()

Warning

Experimental function - Return type to be wrapped

Returns:

a constant reference to the (up-to-date) CredalNet CPTs.

Return type:

tbw

credalNet_srcCpt()

Warning

Experimental function - Return type to be wrapped

Returns:

a constant reference to the (up-to-date) CredalNet CPTs.

Return type:

tbw

currentNodeType(id)
Parameters:

id (int) – The constant reference to the choosen NodeId

Returns:

the type of the choosen node in the (up-to-date) CredalNet __current_bn if any, __src_bn otherwise.

Return type:

pyAgrum.CredalNet

current_bn()
Returns:

Returs a constant reference to the actual BayesNet (used as a DAG, it’s CPTs does not matter).

Return type:

pyAgrum.BayesNet

domainSize(id)
Parameters:

id (int) – The id of the node

Returns:

The cardinality of the node

Return type:

int

epsilonMax()
Returns:

a constant reference to the highest perturbation of the BayesNet provided as input for this CredalNet.

Return type:

float

epsilonMean()
Returns:

a constant reference to the average perturbation of the BayesNet provided as input for this CredalNet.

Return type:

float

epsilonMin()
Returns:

a constant reference to the lowest perturbation of the BayesNet provided as input for this CredalNet.

Return type:

float

fillConstraint(*args)

Set the interval constraints of a credal set of a given node (from an instantiation index)

Parameters:

  • id (int) – The id of the node

  • entry (int) – The index of the instantiation excluding the given node (only the parents are used to compute the index of the credal set)

  • ins (pyAgrum.Instantiation) – The Instantiation

  • lower (list) – The lower value for each probability in correct order

  • upper (list) – The upper value for each probability in correct order

Return type:

None

Warning

You need to call intervalToCredal when done filling all constraints.

Warning

DOES change the BayesNet (s) associated to this credal net !

fillConstraints(id, lower, upper)

Set the interval constraints of the credal sets of a given node (all instantiations)

Parameters:

  • id (int) – The id of the node

  • lower (list) – The lower value for each probability in correct order

  • upper (list) – The upper value for each probability in correct order

Return type:

None

Warning

You need to call intervalToCredal when done filling all constraints.

Warning

DOES change the BayesNet (s) associated to this credal net !

get_binaryCPT_max()

Warning

Experimental function - Return type to be wrapped

Returns:

a constant reference to the upper probabilities of each node X over the ‘True’ modality

Return type:

tbw

get_binaryCPT_min()

Warning

Experimental function - Return type to be wrapped

Returns:

a constant reference to the lower probabilities of each node X over the ‘True’ modality

Return type:

tbw

hasComputedBinaryCPTMinMax()
Return type:

bool

idmLearning(s=0, keepZeroes=False)

Learns parameters from a BayesNet storing counts of events.

Use this method when using a single BayesNet storing counts of events. IDM model if s > 0, standard point probability if s = 0 (default value if none precised).

Parameters:

  • s (int) – the IDM parameter.

  • keepZeroes (bool) – used as a flag as whether or not - respectively True or False - we keep zeroes as zeroes. Default is False, i.e. zeroes are not kept.

Return type:

None

instantiation(id)

Get an Instantiation from a node id, usefull to fill the constraints of the network.

bnet accessors / shortcuts.

Parameters:

id (int) – the id of the node we want an instantiation from

Returns:

the instantiation

Return type:

pyAgrum.Instantiation

intervalToCredal()

Computes the vertices of each credal set according to their interval definition (uses lrs).

Use this method when using two BayesNet, one with lower probabilities and one with upper probabilities.

Return type:

None

intervalToCredalWithFiles()
Return type:

None

Warning

Deprecated : use intervalToCredal (lrsWrapper with no input / output files needed).

Computes the vertices of each credal set according to their interval definition (uses lrs).

Use this method when using a single BayesNet storing counts of events.

isSeparatelySpecified()
Returns:

True if this CredalNet is separately and interval specified, False otherwise.

Return type:

bool

lagrangeNormalization()

Normalize counts of a BayesNet storing counts of each events such that no probability is 0.

Use this method when using a single BayesNet storing counts of events. Lagrange normalization. This call is irreversible and modify counts stored by __src_bn.

Doest not performs computations of the parameters but keeps normalized counts of events only. Call idmLearning to compute the probabilities (with any parameter value).

Return type:

None

nodeType(id)
Parameters:

id (int) – the constant reference to the choosen NodeId

Returns:

the type of the choosen node in the (up-to-date) CredalNet in __src_bn.

Return type:

pyAgrum.CredalNet

saveBNsMinMax(min_path, max_path)

If this CredalNet was built over a perturbed BayesNet, one can save the intervals as two BayesNet.

to call after bnToCredal(GUM_SCALAR beta) save a BN with lower probabilities and a BN with upper ones

Parameters:

  • min_path (str) – the path to save the BayesNet which contains the lower probabilities of each node X.

  • max_path (str) – the path to save the BayesNet which contains the upper probabilities of each node X.

Return type:

None

setCPT(*args)

Warning

(experimental function) - Parameters to be wrapped

Set the vertices of one credal set of a given node (any instantiation index)

Parameters:

  • id (int) – the Id of the node

  • entry (int) – the index of the instantiation (from 0 to K - 1) excluding the given node (only the parents are used to compute the index of the credal set)

  • ins (pyAgrum.Instantiation) – the Instantiation (only the parents matter to find the credal set index)

  • cpt (tbw) – the vertices of every credal set (for each instantiation of the parents)

Return type:

None

Warning

DOES not change the BayesNet(s) associated to this credal net !

setCPTs(id, cpt)

Warning

(experimental function) - Parameters to be wrapped

Set the vertices of the credal sets (all of the conditionals) of a given node

Parameters:

  • id (int) – the NodeId of the node

  • cpt (tbw) – the vertices of every credal set (for each instantiation of the parents)

Warning

DOES not change the BayesNet (s) associated to this credal net !

src_bn()
Returns:

Returns a constant reference to the original BayesNet (used as a DAG, it’s CPTs does not matter).

Return type:

pyAgrum.BayesNet

CN Inference

class pyAgrum.CNMonteCarloSampling(credalNet)

Class used for inferences in credal networks with Monte Carlo sampling algorithm.

CNMonteCarloSampling(cn) -> CNMonteCarloSampling
Parameters:

  • cn (pyAgrum.CredalNet) – a credal network

Parameters:

credalNet (CredalNet)

CN()
Return type:

CredalNet

addEvidence(*args)
Return type:

None

currentTime()
Returns:

get the current running time in second (float)

Return type:

float

dynamicExpMax(varName)

Get the upper dynamic expectation of a given variable prefix.

Parameters:

varName (str) – the variable name prefix which upper expectation we want.

Returns:

a constant reference to the variable upper expectation over all time steps.

Return type:

float

dynamicExpMin(varName)

Get the lower dynamic expectation of a given variable prefix.

Parameters:

varName (str) – the variable name prefix which lower expectation we want.

Returns:

a constant reference to the variable lower expectation over all time steps.

Return type:

float

epsilon()
Returns:

the value of epsilon

Return type:

float

eraseAllEvidence()

Erase all inference related data to perform another one.

You need to insert evidence again if needed but modalities are kept. You can insert new ones by using the appropriate method which will delete the old ones.

Return type:

None

history()
Returns:

the scheme history

Return type:

tuple

Raises:

pyAgrum.OperationNotAllowed – If the scheme did not performed or if verbosity is set to false

insertEvidenceFile(path)

Insert evidence from file.

Parameters:

path (str) – the path to the evidence file.

Return type:

None

insertModalsFile(path)

Insert variables modalities from file to compute expectations.

Parameters:

path (str) – The path to the modalities file.

Return type:

None

makeInference()

Starts the inference.

Return type:

None

marginalMax(*args)

Get the upper marginals of a given node id.

Parameters:

  • id (int) – the node id which upper marginals we want.

  • varName (str) – the variable name which upper marginals we want.

Returns:

a constant reference to this node upper marginals.

Return type:

list

Raises:

pyAgrum.IndexError – If the node does not belong to the Credal network

marginalMin(*args)

Get the lower marginals of a given node id.

Parameters:

  • id (int) – the node id which lower marginals we want.

  • varName (str) – the variable name which lower marginals we want.

Returns:

a constant reference to this node lower marginals.

Return type:

list

Raises:

pyAgrum.IndexError – If the node does not belong to the Credal network

maxIter()
Returns:

the criterion on number of iterations

Return type:

int

maxTime()
Returns:

the timeout(in seconds)

Return type:

float

messageApproximationScheme()
Returns:

the approximation scheme message

Return type:

str

minEpsilonRate()
Returns:

the value of the minimal epsilon rate

Return type:

float

nbrIterations()
Returns:

the number of iterations

Return type:

int

periodSize()
Returns:

the number of samples between 2 stopping

Return type:

int

Raises:

pyAgrum.OutOfBounds – If p<1

setEpsilon(eps)
Parameters:

eps (float) – the epsilon we want to use

Raises:

pyAgrum.OutOfBounds – If eps<0

Return type:

None

setEvidence(evidces)

Erase all the evidences and apply addEvidence(key,value) for every pairs in evidces.

Parameters:

evidces (Dict[str,Union[int,str,List[float]]] or List[pyAgrum.Potential]) – a dict of “name:evidence” where name is a string (the name of the variable) and evidence is an integer (an index) or a string (a label) or a list of float (a likelihood).

Raises:

pyAgrum.InvalidArgument – If one value is not a value for the node pyAgrum.InvalidArgument If the size of a value is different from the domain side of the node pyAgrum.FatalError If one value is a vector of 0s pyAgrum.UndefinedElement If one node does not belong to the Bayesian network

setMaxIter(max)
Parameters:

max (int) – the maximum number of iteration

Raises:

pyAgrum.OutOfBounds – If max <= 1

Return type:

None

setMaxTime(timeout)
Parameters:

  • tiemout (float) – stopping criterion on timeout (in seconds)

  • timeout (float)

Raises:

pyAgrum.OutOfBounds – If timeout<=0.0

Return type:

None

setMinEpsilonRate(rate)
Parameters:

rate (float) – the minimal epsilon rate

Return type:

None

setPeriodSize(p)
Parameters:

p (int) – number of samples between 2 stopping

Raises:

pyAgrum.OutOfBounds – If p<1

Return type:

None

setRepetitiveInd(flag)
Parameters:

flag (bool) – True if repetitive independence is to be used, false otherwise. Only usefull with dynamic networks.

Return type:

None

setVerbosity(v)
Parameters:

v (bool) – verbosity

Return type:

None

verbosity()
Returns:

True if the verbosity is enabled

Return type:

bool

class pyAgrum.CNLoopyPropagation(credalNet)

Class used for inferences in credal networks with Loopy Propagation algorithm.

CNLoopyPropagation(cn) -> CNLoopyPropagation
Parameters:

  • cn (pyAgrum.CredalNet) – a Credal network

Parameters:

credalNet (CredalNet)

CN()
Return type:

CredalNet

InferenceType_nodeToNeighbours = 0
InferenceType_ordered = 1
InferenceType_randomOrder = 2
addEvidence(*args)
Return type:

None

currentTime()
Returns:

get the current running time in second (float)

Return type:

float

dynamicExpMax(varName)

Get the upper dynamic expectation of a given variable prefix.

Parameters:

varName (str) – the variable name prefix which upper expectation we want.

Returns:

a constant reference to the variable upper expectation over all time steps.

Return type:

float

dynamicExpMin(varName)

Get the lower dynamic expectation of a given variable prefix.

Parameters:

varName (str) – the variable name prefix which lower expectation we want.

Returns:

a constant reference to the variable lower expectation over all time steps.

Return type:

float

epsilon()
Returns:

the value of epsilon

Return type:

float

eraseAllEvidence()

Erase all inference related data to perform another one.

You need to insert evidence again if needed but modalities are kept. You can insert new ones by using the appropriate method which will delete the old ones.

Return type:

None

history()
Returns:

the scheme history

Return type:

tuple

Raises:

pyAgrum.OperationNotAllowed – If the scheme did not performed or if verbosity is set to false

inferenceType(*args)
Returns:

the inference type

Return type:

int

insertEvidenceFile(path)

Insert evidence from file.

Parameters:

path (str) – the path to the evidence file.

Return type:

None

insertModalsFile(path)

Insert variables modalities from file to compute expectations.

Parameters:

path (str) – The path to the modalities file.

Return type:

None

makeInference()

Starts the inference.

Return type:

None

marginalMax(*args)

Get the upper marginals of a given node id.

Parameters:

  • id (int) – the node id which upper marginals we want.

  • varName (str) – the variable name which upper marginals we want.

Returns:

a constant reference to this node upper marginals.

Return type:

list

Raises:

pyAgrum.IndexError – If the node does not belong to the Credal network

marginalMin(*args)

Get the lower marginals of a given node id.

Parameters:

  • id (int) – the node id which lower marginals we want.

  • varName (str) – the variable name which lower marginals we want.

Returns:

a constant reference to this node lower marginals.

Return type:

list

Raises:

pyAgrum.IndexError – If the node does not belong to the Credal network

maxIter()
Returns:

the criterion on number of iterations

Return type:

int

maxTime()
Returns:

the timeout(in seconds)

Return type:

float

messageApproximationScheme()
Returns:

the approximation scheme message

Return type:

str

minEpsilonRate()
Returns:

the value of the minimal epsilon rate

Return type:

float

nbrIterations()
Returns:

the number of iterations

Return type:

int

periodSize()
Returns:

the number of samples between 2 stopping

Return type:

int

Raises:

pyAgrum.OutOfBounds – If p<1

saveInference(path)

Saves marginals.

Parameters:

path (str) – The path to the file to save marginals.

Return type:

None

setEpsilon(eps)
Parameters:

eps (float) – the epsilon we want to use

Raises:

pyAgrum.OutOfBounds – If eps<0

Return type:

None

setEvidence(evidces)

Erase all the evidences and apply addEvidence(key,value) for every pairs in evidces.

Parameters:

evidces (Dict[str,Union[int,str,List[float]]] or List[pyAgrum.Potential]) – a dict of “name:evidence” where name is a string (the name of the variable) and evidence is an integer (an index) or a string (a label) or a list of float (a likelihood).

Raises:

pyAgrum.InvalidArgument – If one value is not a value for the node pyAgrum.InvalidArgument If the size of a value is different from the domain side of the node pyAgrum.FatalError If one value is a vector of 0s pyAgrum.UndefinedElement If one node does not belong to the Bayesian network

setMaxIter(max)
Parameters:

max (int) – the maximum number of iteration

Raises:

pyAgrum.OutOfBounds – If max <= 1

Return type:

None

setMaxTime(timeout)
Parameters:

  • tiemout (float) – stopping criterion on timeout (in seconds)

  • timeout (float)

Raises:

pyAgrum.OutOfBounds – If timeout<=0.0

Return type:

None

setMinEpsilonRate(rate)
Parameters:

rate (float) – the minimal epsilon rate

Return type:

None

setPeriodSize(p)
Parameters:

p (int) – number of samples between 2 stopping

Raises:

pyAgrum.OutOfBounds – If p<1

Return type:

None

setRepetitiveInd(flag)
Parameters:

flag (bool) – True if repetitive independence is to be used, false otherwise. Only usefull with dynamic networks.

Return type:

None

setVerbosity(v)
Parameters:

v (bool) – verbosity

Return type:

None

property thisown

The membership flag

verbosity()
Returns:

True if the verbosity is enabled

Return type:

bool