Package edu.cmu.tetrad.search.utils

Class GraphoidAxioms

java.lang.Object

edu.cmu.tetrad.search.utils.GraphoidAxioms

public class GraphoidAxioms
extends Object

Checks the graphoid axioms for a set of Independence Model statements.

Version:

$Id: $Id

Author:

josephramsey

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static class	GraphoidAxioms.GraphoidIndFact	Represents a graphoid independence fact--i.e., a fact in a general independence model (IM) X _||_Y | Z.

Constructor Summary

Constructors

Constructor	Description
GraphoidAxioms(Set<GraphoidAxioms.GraphoidIndFact> facts, List<Node> nodes)	Constructor.
GraphoidAxioms(Set<GraphoidAxioms.GraphoidIndFact> facts, List<Node> nodes, Map<GraphoidAxioms.GraphoidIndFact,String> textSpecs)	Constructor.

Method Summary

Modifier and Type	Method	Description
boolean	composition()	Checks if composition holds--e.g., (X ⊥⊥ Y | Z) ∧ (X ⊥⊥ W |Z) ==> X ⊥⊥ (Y ∪ W) |Z
boolean	compositionalGraphoid()	Checks whether the IM is a compositional graphoid.
boolean	contraction()	Checks if contraction holds--e.g., (X ⊥⊥ Y |Z) ∧ (X ⊥⊥ W |Z ∪ Y) ==> X ⊥⊥ (Y ∪ W) |Z
boolean	decomposition()	Checks if decomposition holds, e.g., X ⊥⊥ (Y ∪ W) |Z ==> (X ⊥⊥ Y |Z) ∧ (X ⊥⊥ W |Z)
void	ensureSymmetry()	Sets symmetry as assumed--i.e., ensures that X ⊥⊥ Y | Z ==> Y ⊥⊥ X | Z.
void	ensureTriviality()	Sets whether triviality as assumed.
IndependenceFacts	getIndependenceFacts()	Returns the independence facts in the form 1:2|3 for use in various Tetrad algorithms.
boolean	graphoid()	Checks whether teh IM is a semigraphoid.
boolean	intersection()	Checks if intersection holds--e.g., (X ⊥⊥ Y | (Z ∪ W)) ∧ (X ⊥⊥ W | (Z ∪ Y)) ==> X ⊥⊥ (Y ∪ W) |Z
static void	main(String... args)	The main methods.
boolean	semigraphoid()	Checked whether the IM is a semigraphoid.
boolean	symmetry()	Checks is symmetry holds--i.e., X ⊥⊥ Y | Z ==> Y ⊥⊥ X | Z
boolean	weakUnion()	Checks is weak union holds, e.g., X _||_ Y U W | Z ==> X _||_ Y | Z U W

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

GraphoidAxioms

public GraphoidAxioms(Set<GraphoidAxioms.GraphoidIndFact> facts,
 List<Node> nodes)

Constructor.

Parameters:

facts - A set of GraphoidIndFacts.

nodes - The list of nodes.

See Also:

• k

GraphoidAxioms

public GraphoidAxioms(Set<GraphoidAxioms.GraphoidIndFact> facts,
 List<Node> nodes,
 Map<GraphoidAxioms.GraphoidIndFact,String> textSpecs)

Constructor.

Parameters:

facts - A list of GraphoidIndFacts.

nodes - The list of nodes.

textSpecs - A map from GraphoidIndFacts to String text specs. The text specs are used for printing information to the user about which facts are found or are missing.

See Also:

• GraphoidAxioms.GraphoidIndFact

Method Details

main

public static void main(String... args)

The main methods.

Parameters:

args - E.g., "java -cp tetrad-gui-7.1.3-SNAPSHOT-launch.jar edu.cmu.tetrad.search.utils.GraphoidAxioms udags5.txt 5" Here, udgas5.txt is a file containing independence models, one per line, where each independence fast is specified by, e.g., "1:23|56", indicating that 1 is independence of 2 and 3 conditional on 5 and 6. No more than 9 variables can be handled this way. If you need more, let us know and we'll change the format.

semigraphoid

public boolean semigraphoid()

Checked whether the IM is a semigraphoid.

Returns:

True, if so.

graphoid

public boolean graphoid()

Checks whether teh IM is a semigraphoid.

Returns:

True, if so.

compositionalGraphoid

public boolean compositionalGraphoid()

Checks whether the IM is a compositional graphoid.

Returns:

True, if so.

getIndependenceFacts

public IndependenceFacts getIndependenceFacts()

Returns the independence facts in the form 1:2|3 for use in various Tetrad algorithms. Assumes decomposition and compositios, so that there are no complex independence facts.

Returns:

a IndependenceFacts object

symmetry

public boolean symmetry()

Checks is symmetry holds--i.e., X ⊥⊥ Y | Z ==> Y ⊥⊥ X | Z

Returns:

a boolean

decomposition

public boolean decomposition()

Checks if decomposition holds, e.g., X ⊥⊥ (Y ∪ W) |Z ==> (X ⊥⊥ Y |Z) ∧ (X ⊥⊥ W |Z)

Returns:

a boolean

weakUnion

public boolean weakUnion()

Checks is weak union holds, e.g., X _||_ Y U W | Z ==> X _||_ Y | Z U W

Returns:

a boolean

contraction

public boolean contraction()

Checks if contraction holds--e.g., (X ⊥⊥ Y |Z) ∧ (X ⊥⊥ W |Z ∪ Y) ==> X ⊥⊥ (Y ∪ W) |Z

Returns:

a boolean

intersection

public boolean intersection()

Checks if intersection holds--e.g., (X ⊥⊥ Y | (Z ∪ W)) ∧ (X ⊥⊥ W | (Z ∪ Y)) ==> X ⊥⊥ (Y ∪ W) |Z

Returns:

a boolean

composition

public boolean composition()

Checks if composition holds--e.g., (X ⊥⊥ Y | Z) ∧ (X ⊥⊥ W |Z) ==> X ⊥⊥ (Y ∪ W) |Z

Returns:

a boolean

ensureTriviality

public void ensureTriviality()

Sets whether triviality as assumed.

ensureSymmetry

public void ensureSymmetry()

Sets symmetry as assumed--i.e., ensures that X ⊥⊥ Y | Z ==> Y ⊥⊥ X | Z.