gum::EssentialGraph Class Reference

Class building the essential graph from a BN. More...

#include <agrum/BN/algorithms/essentialGraph.h>

Collaboration diagram for gum::EssentialGraph:

Public Member Functions
	EssentialGraph ()=default
	EssentialGraph (const DAGmodel &m)
	EssentialGraph (const DAGmodel &m, const MixedGraph &mg)
	EssentialGraph (const EssentialGraph &g)
EssentialGraph &	operator= (const EssentialGraph &g)
	~EssentialGraph ()
MixedGraph	mixedGraph ()
std::string	toDot () const
const NodeSet &	parents (NodeId id) const
	wrapping MixedGraph::parents(id) More...
const NodeSet &	children (NodeId id) const
	wrapping MixedGraph::parents(id) More...
NodeSet	parents (const NodeSet &ids) const
	wrapping MixedGraph::parents(ids) More...
NodeSet	children (const NodeSet &ids) const
	wrapping MixedGraph::parents(ids) More...
const NodeSet &	neighbours (NodeId id) const
	wrapping MixedGraph::parents(id) More...
Size	sizeArcs () const
	wrapping MixedGraph::sizeArcs() More...
const ArcSet &	arcs () const
	wrapping MixedGraph::arcs() More...
Size	sizeEdges () const
	wrapping MixedGraph::sizeEdges() More...
const EdgeSet &	edges () const
	wrapping MixedGraph::edges() More...
Size	sizeNodes () const
	wrapping MixedGraph::sizeNodes() More...
Size	size () const
	wrapping MixedGraph::size() More...
UndiGraph	skeleton () const
const NodeGraphPart &	nodes () const
	wrapping MixedGraph::nodes() More...

Detailed Description

Class building the essential graph from a BN.

Essential graph is a mixed graph (Chain Graph) that represents the class of markov equivalent Bayesian networks (with the same independence model).

The main goal of this class is to nest the algorithm to build the essential graph from a BN and to encapsulate the representation (as a MixedGraph) of the essential graph.

gum::operator<<(std::ostream&, const BayesNet<GUM_SCALAR>&).

Definition at line 54 of file essentialGraph.h.

Constructor & Destructor Documentation

EssentialGraph() [1/4]

gum::EssentialGraph::EssentialGraph ( )

default

EssentialGraph() [2/4]

gum::EssentialGraph::EssentialGraph ( const DAGmodel &  m )

explicit

Definition at line 36 of file essentialGraph.cpp.

References gum::Set< Key, Alloc >::emplace().

: _dagmodel_(&m) { _buildEssentialGraph_(); }

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EssentialGraph() [3/4]

gum::EssentialGraph::EssentialGraph	(	const DAGmodel &	m,
		const MixedGraph &	mg
	)

Definition at line 38 of file essentialGraph.cpp.

References gum::Set< Key, Alloc >::emplace().

                                                                        :
      _dagmodel_(&m), _mg_(mg) {}

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EssentialGraph() [4/4]

gum::EssentialGraph::EssentialGraph

(

const EssentialGraph &

g

)

Definition at line 40 of file essentialGraph.cpp.

References gum::Set< Key, Alloc >::emplace().

                                                        {
    _dagmodel_ = g._dagmodel_;
    _buildEssentialGraph_();
  }

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~EssentialGraph()

gum::EssentialGraph::~EssentialGraph ( )

default

Member Function Documentation

_buildEssentialGraph_()

void gum::EssentialGraph::_buildEssentialGraph_ ( )

private

Definition at line 54 of file essentialGraph.cpp.

References gum::Set< Key, Alloc >::emplace().

                                             {
    _mg_.clear();
    if (_dagmodel_ == nullptr) return;

    for (const auto& node: _dagmodel_->nodes()) {
      _mg_.addNodeWithId(node);
    }
    for (const auto& arc: _dagmodel_->arcs()) {
      _mg_.addArc(arc.tail(), arc.head());
    }

    std::vector< Arc > v;
    do {
      v.clear();
      for (const auto x: _dagmodel_->topologicalOrder())
        for (const auto y: _mg_.children(x))
          if (!_strongly_protected_(x, y)) v.emplace_back(x, y);

      for (const auto& arc: v) {
        _mg_.eraseArc(arc);
        _mg_.addEdge(arc.tail(), arc.head());
      }
    } while (!v.empty());
  }

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_strongly_protected_()

bool gum::EssentialGraph::_strongly_protected_ ( NodeId  a, NodeId  b  )

private

Definition at line 79 of file essentialGraph.cpp.

References gum::Set< Key, Alloc >::emplace().

                                                              {
    // testing a->b from
    // A Characterization of Markov Equivalence Classes for Acyclic Digraphs (2001)
    //  Steen A. Andersson, David Madigan, and Michael D. Perlman*

    // condition (a)
    for (const auto& c: _mg_.parents(a)) {
      if (!_mg_.existsArc(c, b)) { return true; }
    }


    for (const auto& c: _mg_.parents(b)) {
      if (c == a) { continue; }
      // condition (c)
      if (_mg_.existsArc(a, c)) { return true; }

      // condition (b) knowing that a can not be a parent of c (condition below)
      if (!_mg_.existsEdge(a, c) && !_mg_.existsArc(c, a)) { return true; }
    }

    // condition (d)
    bool oneFound = false;
    for (const auto& c: _mg_.parents(b)) {
      if (c == a) { continue; }
      // condition (d)
      if (_mg_.existsEdge(c, a)) {
        if (oneFound) {   // this is the second found
          return true;
        }
        oneFound = true;
      }
    }

    return false;
  }

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arcs()

INLINE const ArcSet & gum::EssentialGraph::arcs

(

)

const

wrapping MixedGraph::arcs()

Definition at line 49 of file essentialGraph_inl.h.

References gum::Set< Key, Alloc >::emplace().

{ return _mg_.arcs(); }

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children() [1/2]

INLINE const NodeSet & gum::EssentialGraph::children

(

NodeId

id

)

const

wrapping MixedGraph::parents(id)

Definition at line 38 of file essentialGraph_inl.h.

References gum::Set< Key, Alloc >::emplace().

{ return _mg_.children(id); }

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children() [2/2]

INLINE NodeSet gum::EssentialGraph::children

(

const NodeSet &

ids

)

const

wrapping MixedGraph::parents(ids)

Definition at line 42 of file essentialGraph_inl.h.

References gum::Set< Key, Alloc >::emplace().

{ return _mg_.children(ids); }

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edges()

INLINE const EdgeSet & gum::EssentialGraph::edges

(

)

const

wrapping MixedGraph::edges()

Definition at line 53 of file essentialGraph_inl.h.

References gum::Set< Key, Alloc >::emplace().

{ return _mg_.edges(); }

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mixedGraph()

INLINE MixedGraph gum::EssentialGraph::mixedGraph

(

)

Returns

a copy of the mixed graph

Definition at line 34 of file essentialGraph_inl.h.

References gum::Set< Key, Alloc >::emplace().

{ return _mg_; }

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neighbours()

INLINE const NodeSet & gum::EssentialGraph::neighbours

(

NodeId

id

)

const

wrapping MixedGraph::parents(id)

Definition at line 44 of file essentialGraph_inl.h.

References gum::Set< Key, Alloc >::emplace().

{ return _mg_.neighbours(id); }

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nodes()

INLINE const NodeGraphPart & gum::EssentialGraph::nodes

(

)

const

wrapping MixedGraph::nodes()

Definition at line 59 of file essentialGraph_inl.h.

References gum::Set< Key, Alloc >::emplace().

{ return _mg_.nodes(); }

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operator=()

EssentialGraph & gum::EssentialGraph::operator=

(

const EssentialGraph &

g

)

Definition at line 44 of file essentialGraph.cpp.

References gum::Set< Key, Alloc >::emplace().

                                                                   {
    if (&g != this) {
      _dagmodel_ = g._dagmodel_;
      _buildEssentialGraph_();
    }
    return *this;
  }

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parents() [1/2]

INLINE const NodeSet & gum::EssentialGraph::parents

(

NodeId

id

)

const

wrapping MixedGraph::parents(id)

Definition at line 36 of file essentialGraph_inl.h.

References gum::Set< Key, Alloc >::emplace().

{ return _mg_.parents(id); }

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parents() [2/2]

INLINE NodeSet gum::EssentialGraph::parents

(

const NodeSet &

ids

)

const

wrapping MixedGraph::parents(ids)

Definition at line 40 of file essentialGraph_inl.h.

References gum::Set< Key, Alloc >::emplace().

{ return _mg_.parents(ids); }

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size()

INLINE Size gum::EssentialGraph::size

(

)

const

wrapping MixedGraph::size()

Definition at line 57 of file essentialGraph_inl.h.

References gum::Set< Key, Alloc >::emplace().

{ return _mg_.size(); }

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sizeArcs()

INLINE Size gum::EssentialGraph::sizeArcs

(

)

const

wrapping MixedGraph::sizeArcs()

Definition at line 47 of file essentialGraph_inl.h.

References gum::Set< Key, Alloc >::emplace().

{ return _mg_.sizeArcs(); }

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sizeEdges()

INLINE Size gum::EssentialGraph::sizeEdges

(

)

const

wrapping MixedGraph::sizeEdges()

Definition at line 51 of file essentialGraph_inl.h.

References gum::Set< Key, Alloc >::emplace().

{ return _mg_.sizeEdges(); }

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sizeNodes()

INLINE Size gum::EssentialGraph::sizeNodes

(

)

const

wrapping MixedGraph::sizeNodes()

Definition at line 55 of file essentialGraph_inl.h.

References gum::Set< Key, Alloc >::emplace().

{ return _mg_.sizeNodes(); }

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skeleton()

UndiGraph gum::EssentialGraph::skeleton

(

)

const

Definition at line 143 of file essentialGraph.cpp.

References gum::Set< Key, Alloc >::emplace().

                                           {
    UndiGraph skel;
    for (const auto& n: nodes())
      skel.addNodeWithId(n);
    for (const auto& edge: edges())
      skel.addEdge(edge.first(), edge.second());
    for (const auto& arc: arcs())
      skel.addEdge(arc.tail(), arc.head());
    return skel;
  }

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toDot()

std::string gum::EssentialGraph::toDot

(

)

const

Returns

a dot representation of this essentialGraph

Definition at line 115 of file essentialGraph.cpp.

References gum::Set< Key, Alloc >::emplace().

                                        {
    std::stringstream output;
    std::stringstream nodeStream;
    std::stringstream edgeStream;
    List< NodeId >    treatedNodes;
    output << "digraph \""
           << "no_name\" {" << std::endl;
    nodeStream << "node [shape = ellipse];" << std::endl;
    std::string tab = "  ";
    if (_dagmodel_ != nullptr) {
      for (const auto node: _mg_.nodes()) {
        nodeStream << tab << node << "[label=\"" << _dagmodel_->variable(node).name() << "\"];";

        for (const auto nei: _mg_.neighbours(node))
          if (!treatedNodes.exists(nei))
            edgeStream << tab << node << " -> " << nei << " [dir=none];" << std::endl;

        for (const auto chi: _mg_.children(node))
          edgeStream << tab << node << " -> " << chi << " [color=red];" << std::endl;

        treatedNodes.insert(node);
      }
    }
    output << nodeStream.str() << std::endl << edgeStream.str() << std::endl << "}" << std::endl;

    return output.str();
  }

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Member Data Documentation

_dagmodel_

const DAGmodel* gum::EssentialGraph::_dagmodel_

private

Definition at line 112 of file essentialGraph.h.

_mg_

MixedGraph gum::EssentialGraph::_mg_

private

Definition at line 113 of file essentialGraph.h.

---

The documentation for this class was generated from the following files:

• agrum/BN/algorithms/essentialGraph.h
• agrum/BN/algorithms/essentialGraph.cpp
• agrum/BN/algorithms/essentialGraph_inl.h