Information Theory of Bayesian network

class pyagrum.InformationTheory(*args)

This class gathers information theory concepts for subsets named X,Y and Z computed with only one (optimized) inference.

it=pyagrum.InformationTheory(ie,X,Y,Z)

• Parameters:
  • ie (InferenceEngine) – the inference algorithme to use (for instance, pyagrum.LazyPropagation)
  • X (int or str or iterable *[*int or str ]) – a first nodeset
  • Y (int or str or iterable *[*int or str ]) – a second nodeset
  • Z ( : int or str or iterable *[*int or str ] *(*optional )) – a third (an optional) nodeset

Example——- : ```python import pyagrum as gum bn=pyagrum.fastBN(‘A->B<-C<-D->E<-F->G->A’) ie=pyagrum.LazyPropagation(bn) it=pyagrum.InformationTheory(ie,‘A’,[‘B’,‘G’],[‘C’]) print(f’Entropy(A)={it.entropyX()}”) print(f’MutualInformation(A;B,G)={it.mutualInformationXY()}’) print(f’MutualInformation(A;B,G| C)={it.mutualInformationXYgivenZ()}’) print(f’VariationOfInformation(A;B,G)={it.variationOfInformationXY()}’)

#### entropyX()

* **Returns:**
the entropy of nodeset X
* **Return type:**
`float`

#### entropyXY()

* **Return type:**
`float`
* **Returns:**
float
: The entropy of nodeset, union of X and Y.

#### entropyXYgivenZ()

* **Returns:**
the conditional entropy of nodeset (X ∪ Y) conditioned by nodeset Z
* **Return type:**
`float`

#### entropyXgivenY()

* **Return type:**
`float`
* **Returns:**
float
: The conditional entropy of nodeset X conditionned by nodeset Y

#### entropyY()

* **Return type:**
`float`
* **Returns:**
float
: The entropy of nodeset X.

#### entropyYgivenX()

* **Return type:**
`float`
* **Returns:**
float
: The conditional entropy of nodeset Y conditionned by nodeset X

#### mutualInformationXY()

* **Return type:**
`float`
* **Returns:**
float
: The mutual information between nodeset X and nodeset Y

#### mutualInformationXYgivenZ()

* **Return type:**
`float`
* **Returns:**
float
: The conditional mutual information between nodeset X and nodeset Y conditionned by nodeset Z

#### variationOfInformationXY()

* **Return type:**
`float`
* **Returns:**
float
: The variation of information between nodeset X and nodeset Y