Markov Network

A Markov network is a undirected probabilistic graphical model. It represents a joint distribution over a set of random variables. In pyAgrum, the variables are (for now) only discrete.

A Markov network uses a undirected graph to represent conditional independence in the joint distribution. These conditional independence allow to factorize the joint distribution, thereby allowing to compactly represent very large ones.

\[P(X_1,\cdots,X_n)\propto\prod_{i=1}^{n_c} \phi_i(C_i)\]

Where the \(\phi_i\) are potentials over the \(n_c\) cliques of the undirected graph.

Moreover, inference algorithms can also use this graph to speed up the computations.

Tutorial

• Tutorial on Markov Network

Reference

• Undirected Graphical Model
  • MarkovNet
    • MarkovNet.add()
    • MarkovNet.addFactor()
    • MarkovNet.addStructureListener()
    • MarkovNet.addVariables()
    • MarkovNet.beginTopologyTransformation()
    • MarkovNet.changeVariableLabel()
    • MarkovNet.changeVariableName()
    • MarkovNet.clear()
    • MarkovNet.completeInstantiation()
    • MarkovNet.connectedComponents()
    • MarkovNet.dim()
    • MarkovNet.edges()
    • MarkovNet.empty()
    • MarkovNet.endTopologyTransformation()
    • MarkovNet.erase()
    • MarkovNet.eraseFactor()
    • MarkovNet.exists()
    • MarkovNet.existsEdge()
    • MarkovNet.factor()
    • MarkovNet.factors()
    • MarkovNet.fastPrototype()
    • MarkovNet.fromBN()
    • MarkovNet.generateFactor()
    • MarkovNet.generateFactors()
    • MarkovNet.graph()
    • MarkovNet.hasSameStructure()
    • MarkovNet.idFromName()
    • MarkovNet.ids()
    • MarkovNet.isIndependent()
    • MarkovNet.loadUAI()
    • MarkovNet.log10DomainSize()
    • MarkovNet.maxNonOneParam()
    • MarkovNet.maxParam()
    • MarkovNet.maxVarDomainSize()
    • MarkovNet.minNonZeroParam()
    • MarkovNet.minParam()
    • MarkovNet.minimalCondSet()
    • MarkovNet.names()
    • MarkovNet.neighbours()
    • MarkovNet.nodeId()
    • MarkovNet.nodes()
    • MarkovNet.nodeset()
    • MarkovNet.saveUAI()
    • MarkovNet.size()
    • MarkovNet.sizeEdges()
    • MarkovNet.smallestFactorFromNode()
    • MarkovNet.thisown
    • MarkovNet.toDot()
    • MarkovNet.toDotAsFactorGraph()
    • MarkovNet.variable()
    • MarkovNet.variableFromName()
    • MarkovNet.variableNodeMap()
• Inference in Markov Networks
  • Shafer Shenoy Inference in Markov Network
    • ShaferShenoyMNInference