Inference

Inference is the process that consists in computing new probabilistc information from a Markov network and some evidence. aGrUM/pyAgrum mainly focus and the computation of (joint) posterior for some variables of the Markov networks given soft or hard evidence that are the form of likelihoods on some variables. Inference is a hard task (NP-complete). For now, aGrUM/pyAgrum implements only one exact inference for Markov Network.

Shafer Shenoy Inference

class pyAgrum.ShaferShenoyMNInference(MN: pyAgrum.IMarkovNet, use_binary_join_tree: bool = True)

Class used for Shafer-Shenoy inferences for Markov network.

ShaferShenoyInference(bn) -> ShaferShenoyInference

Parameters:

• mn (pyAgrum.MarkovNet) – a Markov network

H(self, X)

H(self, nodeName) -> double

Parameters:

• X (int) – a node Id
• nodeName (str) – a node name

Returns:

the Shanon’s entropy of a node given the observation

Return type:

double

I(self, X, Y)

Parameters:

• X (int or str) – a node Id or a node name
• Y (int or str) – another node Id or node name

Returns:

the Mutual Information of X and Y given the observation

Return type:

double

MN(self)

VI(self, X, Y)

Parameters:

• X (int or str) – a node Id or a node name
• Y (int or str) – another node Id or node name

Returns:

variation of information between X and Y

Return type:

double

addAllTargets(self)

Add all the nodes as targets.

addEvidence(self, id, val)

addEvidence(self, nodeName, val) addEvidence(self, id, val) addEvidence(self, nodeName, val) addEvidence(self, id, vals) addEvidence(self, nodeName, vals)

Adds a new evidence on a node (might be soft or hard).

Parameters:

• id (int) – a node Id
• nodeName (int) – a node name
• val – (int) a node value
• val – (str) the label of the node value
• vals (list) – a list of values

Raises:

• gum.InvalidArgument – If the node already has an evidence
• gum.InvalidArgument – If val is not a value for the node
• gum.InvalidArgument – If the size of vals is different from the domain side of the node
• gum.FatalError – If vals is a vector of 0s
• gum.UndefinedElement – If the node does not belong to the Bayesian network

addJointTarget(self, targets)

Add a list of nodes as a new joint target. As a collateral effect, every node is added as a marginal target.

Parameters:list – a list of names of nodes Raises:gum.UndefinedElement – If some node(s) do not belong to the Bayesian network

addTarget(self, target)

addTarget(self, nodeName)

Add a marginal target to the list of targets.

Parameters:

• target (int) – a node Id
• nodeName (str) – a node name

Raises:

gum.UndefinedElement – If target is not a NodeId in the Bayes net

chgEvidence(self, id, val)

chgEvidence(self, nodeName, val) chgEvidence(self, id, val) chgEvidence(self, nodeName, val) chgEvidence(self, id, vals) chgEvidence(self, nodeName, vals)

Change the value of an already existing evidence on a node (might be soft or hard).

Parameters:

• id (int) – a node Id
• nodeName (int) – a node name
• val – (int) a node value
• val – (str) the label of the node value
• vals (list) – a list of values

Raises:

• gum.InvalidArgument – If the node does not already have an evidence
• gum.InvalidArgument – If val is not a value for the node
• gum.InvalidArgument – If the size of vals is different from the domain side of the node
• gum.FatalError – If vals is a vector of 0s
• gum.UndefinedElement – If the node does not belong to the Bayesian network

eraseAllEvidence(self)

Removes all the evidence entered into the network.

eraseAllJointTargets(self)

Clear all previously defined joint targets.

eraseAllMarginalTargets(self)

Clear all the previously defined marginal targets.

eraseAllTargets(self)

Clear all previously defined targets (marginal and joint targets).

As a result, no posterior can be computed (since we can only compute the posteriors of the marginal or joint targets that have been added by the user).

eraseEvidence(self, id)

eraseEvidence(self, nodeName)

Remove the evidence, if any, corresponding to the node Id or name.

Parameters:

• id (int) – a node Id
• nodeName (int) – a node name

Raises:

gum.IndexError – If the node does not belong to the Bayesian network

eraseJointTarget(self, targets)

Remove, if existing, the joint target.

Parameters:

list – a list of names or Ids of nodes

Raises:

• gum.IndexError – If one of the node does not belong to the Bayesian network
• gum.UndefinedElement – If node Id is not in the Bayesian network

eraseTarget(self, target)

eraseTarget(self, nodeName)

Remove, if existing, the marginal target.

Parameters:

• target (int) – a node Id
• nodeName (int) – a node name

Raises:

• gum.IndexError – If one of the node does not belong to the Bayesian network
• gum.UndefinedElement – If node Id is not in the Bayesian network

evidenceImpact(self, target, evs)

Create a pyAgrum.Potential for P(target|evs) (for all instanciation of target and evs)

Parameters:

• target (set) – a set of targets ids or names.
• evs (set) – a set of nodes ids or names.

Warning

if some evs are d-separated, they are not included in the Potential.

Returns:a Potential for P(targets|evs) Return type:pyAgrum.Potential

evidenceJointImpact(self, targets, evs)

evidenceJointImpact(self, targets, evs) -> Potential

Create a pyAgrum.Potential for P(joint targets|evs) (for all instanciation of targets and evs)

Parameters:

• targets – (int) a node Id
• targets – (str) a node name
• evs (set) – a set of nodes ids or names.

Returns:

a Potential for P(target|evs)

Return type:

pyAgrum.Potential

Raises:

gum.Exception – If some evidene entered into the Bayes net are incompatible (their joint proba = 0)

evidenceProbability(self)

Returns:the probability of evidence Return type:double

hardEvidenceNodes(self)

Returns:the set of nodes with hard evidence Return type:set

hasEvidence(self, id)

hasEvidence(self, nodeName) -> bool

Parameters:

• id (int) – a node Id
• nodeName (str) – a node name

Returns:

True if some node(s) (or the one in parameters) have received evidence

Return type:

bool

Raises:

gum.IndexError – If the node does not belong to the Bayesian network

hasHardEvidence(self, nodeName)

Parameters:

• id (int) – a node Id
• nodeName (str) – a node name

Returns:

True if node has received a hard evidence

Return type:

bool

Raises:

gum.IndexError – If the node does not belong to the Bayesian network

hasSoftEvidence(self, id)

hasSoftEvidence(self, nodeName) -> bool

Parameters:

• id (int) – a node Id
• nodeName (str) – a node name

Returns:

True if node has received a soft evidence

Return type:

bool

Raises:

gum.IndexError – If the node does not belong to the Bayesian network

isJointTarget(self, targets)

Parameters:

list – a list of nodes ids or names.

Returns:

True if target is a joint target.

Return type:

bool

Raises:

• gum.IndexError – If the node does not belong to the Bayesian network
• gum.UndefinedElement – If node Id is not in the Bayesian network

isTarget(self, variable)

isTarget(self, nodeName) -> bool

Parameters:

• variable (int) – a node Id
• nodeName (str) – a node name

Returns:

True if variable is a (marginal) target

Return type:

bool

Raises:

• gum.IndexError – If the node does not belong to the Bayesian network
• gum.UndefinedElement – If node Id is not in the Bayesian network

joinTree(self)

Returns:the current join tree used Return type:pyAgrum.CliqueGraph

jointMutualInformation(self, targets)

jointPosterior(self, targets)

Compute the joint posterior of a set of nodes.

Parameters:list – the list of nodes whose posterior joint probability is wanted

Warning

The order of the variables given by the list here or when the jointTarget is declared can not be assumed to be used bu the Potential.

Returns:a ref to the posterior joint probability of the set of nodes. Return type:pyAgrum.Potential Raises:gum.UndefinedElement – If an element of nodes is not in targets

jointTargets(self)

Returns:the list of target sets Return type:list

junctionTree(self)

Returns:the current junction tree Return type:pyAgrum.CliqueGraph

makeInference(self)

Perform the heavy computations needed to compute the targets’ posteriors

In a Junction tree propagation scheme, for instance, the heavy computations are those of the messages sent in the JT. This is precisely what makeInference should compute. Later, the computations of the posteriors can be done ‘lightly’ by multiplying and projecting those messages.

nbrEvidence(self)

Returns:the number of evidence entered into the Bayesian network Return type:int

nbrHardEvidence(self)

Returns:the number of hard evidence entered into the Bayesian network Return type:int

nbrJointTargets(self)

Returns:the number of joint targets Return type:int

nbrSoftEvidence(self)

Returns:the number of soft evidence entered into the Bayesian network Return type:int

nbrTargets(self)

Returns:the number of marginal targets Return type:int

posterior(self, var)

posterior(self, nodeName) -> Potential posterior(self, nodeName) -> Potential

Computes and returns the posterior of a node.

Parameters:

• var (int) – the node Id of the node for which we need a posterior probability
• nodeName (str) – the node name of the node for which we need a posterior probability

Returns:

a ref to the posterior probability of the node

Return type:

pyAgrum.Potential

Raises:

gum.UndefinedElement – If an element of nodes is not in targets

setEvidence(evidces)

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

Parameters:

evidces (dict) – a dict of evidences

Raises:

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

setTargets(targets)

Remove all the targets and add the ones in parameter.

Parameters:targets (set) – a set of targets Raises:gum.UndefinedElement – If one target is not in the Bayes net

setTriangulation(self, new_triangulation)

softEvidenceNodes(self)

Returns:the set of nodes with soft evidence Return type:set

targets(self)

Returns:the list of marginal targets Return type:list

updateEvidence(evidces)

Apply chgEvidence(key,value) for every pairs in evidces (or addEvidence).

Parameters:

evidces (dict) – a dict of evidences

Raises:

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