Package edu.cmu.tetrad.search.test

Class IndTestHsic

java.lang.Object

edu.cmu.tetrad.search.test.IndTestHsic

All Implemented Interfaces:

IndependenceTest

public final class IndTestHsic
extends Object
implements IndependenceTest

Checks the conditional independence X _||_ Y | S, where S is a set of continuous variable, and X and Y are discrete variable not in S, using the Hilbert-Schmidth Independence Criterion (HSIC), a kernel based nonparametric test for conditional independence.

The Kpc algorithm by Tillman had run PC using this test; to run Kpc, simply select this test for PC.

Version:

$Id: $Id

Author:

Robert Tillman

See Also:

• Kpc

Constructor Summary

Constructors

Constructor	Description
IndTestHsic(DataSet dataSet, double alpha)	Constructs a new HSIC Independence test.
IndTestHsic(Matrix data, List<Node> variables, double alpha)	Constructs a new HSIC Independence test.

Method Summary

Modifier and Type	Method	Description
IndependenceResult	checkIndependence(Node y, Node x, Set<Node> _z)	Determines whether variable x is independent of variable y given a list of conditioning variables z.
boolean	determines(List<Node> z, Node x)	Determines whether variable x is independent of variable y given a list of conditioning variables z.
double	empiricalHSIC(Matrix Ky, Matrix Kx, int m)	Empirical unconditional Hilbert-Schmidt Dependence Measure for X and Y
double	empiricalHSICincompleteCholesky(Matrix Gy, Matrix Gx, int m)	Empirical unconditional Hilbert-Schmidt Dependence Measure for X and Y using incomplete Cholesky decomposition to approximate Gram matrices
double	empiricalHSICincompleteCholesky(Matrix Gy, Matrix Gx, Matrix Gz, int m)	Empirical unconditional Hilbert-Schmidt Dependence Measure for X and Y given Z using incomplete Cholesky decomposition to approximate Gram matrices
double	getAlpha()	Gets the getModel significance level.
DataSet	getData()	Returns the data set being analyzed.
Node	getVariable(String name)	Returns the variable with the given name.
List<Node>	getVariables()	Returns the list of variables over which this independence checker is capable of determinine independence relations-- that is, all the variables in the given graph or the given data set.
IndependenceTest	indTestSubset(List<Node> vars)	Subset of variables for independence testing.
boolean	isVerbose()	Determines if the verbose mode is enabled.
void	setAlpha(double alpha)	Sets the significance level.
void	setIncompleteCholesky(double precision)	Sets the precision for the Incomplete Choleksy factorization method for approximating Gram matrices.
void	setPerms(int numBootstraps)	Set the number of bootstrap samples to use
void	setRegularizer(double regularizer)	Sets the regularizer.
void	setVerbose(boolean verbose)	Sets the verbose mode for the IndTestHsic class.
String	toString()	Returns a string representation of this test.

Methods inherited from class java.lang.Object

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

Methods inherited from interface edu.cmu.tetrad.search.IndependenceTest

checkIndependence, determines, getCov, getDataSets, getSampleSize, getVariableNames

Constructor Details

IndTestHsic

public IndTestHsic(DataSet dataSet,
 double alpha)

Constructs a new HSIC Independence test. The given significance level is used.

Parameters:

dataSet - A data set containing only continuous columns.

alpha - The alpha level of the test.

IndTestHsic

public IndTestHsic(Matrix data,
 List<Node> variables,
 double alpha)

Constructs a new HSIC Independence test. The given significance level is used.

Parameters:

data - A matrix of continuous data.

variables - The list of variables for the data.

alpha - The alpha level of the test.

Method Details

indTestSubset

public IndependenceTest indTestSubset(List<Node> vars)

Subset of variables for independence testing.

Specified by:

indTestSubset in interface IndependenceTest

Parameters:

vars - The list of variables for the subset.

Returns:

An IndependenceTest object representing the subset for independence testing.

Throws:

IllegalArgumentException - If the subset is empty or contains variables not in the original set.

checkIndependence

public IndependenceResult checkIndependence(Node y,
 Node x,
 Set<Node> _z)

Determines whether variable x is independent of variable y given a list of conditioning variables z.

Specified by:

checkIndependence in interface IndependenceTest

Parameters:

y - a Node object

x - a Node object

_z - a Set object

Returns:

a IndependenceResult object

See Also:

• IndependenceResult

empiricalHSIC

public double empiricalHSIC(Matrix Ky,
 Matrix Kx,
 int m)

Empirical unconditional Hilbert-Schmidt Dependence Measure for X and Y

Parameters:

Ky - centralized Gram matrix for Y

Kx - centralized Gram matrix for X

m - sample size

Returns:

a double

empiricalHSICincompleteCholesky

public double empiricalHSICincompleteCholesky(Matrix Gy,
 Matrix Gx,
 int m)

Empirical unconditional Hilbert-Schmidt Dependence Measure for X and Y using incomplete Cholesky decomposition to approximate Gram matrices

Parameters:

Gy - Choleksy approximate Gram matrix for Y

Gx - Choleksy approximate Gram matrix for X

m - sample size

Returns:

a double

empiricalHSICincompleteCholesky

public double empiricalHSICincompleteCholesky(Matrix Gy,
 Matrix Gx,
 Matrix Gz,
 int m)

Empirical unconditional Hilbert-Schmidt Dependence Measure for X and Y given Z using incomplete Cholesky decomposition to approximate Gram matrices

Parameters:

Gy - Choleksy approximate Gram matrix for Y

Gx - Choleksy approximate Gram matrix for X

Gz - Choleksy approximate Gram matrix for Z

m - sample size

Returns:

a double

setIncompleteCholesky

public void setIncompleteCholesky(double precision)

Sets the precision for the Incomplete Choleksy factorization method for approximating Gram matrices. A value <= 0 indicates that the Incomplete Cholesky method should not be used and instead use the exact matrices.

Parameters:

precision - This precision.

setPerms

public void setPerms(int numBootstraps)

Set the number of bootstrap samples to use

Parameters:

numBootstraps - This number.

setRegularizer

public void setRegularizer(double regularizer)

Sets the regularizer.

Parameters:

regularizer - This value.

getAlpha

public double getAlpha()

Gets the getModel significance level.

Specified by:

getAlpha in interface IndependenceTest

Returns:

This alpha.

setAlpha

public void setAlpha(double alpha)

Sets the significance level.

Sets the significance level at which independence judgments should be made.

Specified by:

setAlpha in interface IndependenceTest

Parameters:

alpha - This level.

getVariables

public List<Node> getVariables()

Returns the list of variables over which this independence checker is capable of determinine independence relations-- that is, all the variables in the given graph or the given data set.

Specified by:

getVariables in interface IndependenceTest

Returns:

This list.

getVariable

public Node getVariable(String name)

Returns the variable with the given name.

Specified by:

getVariable in interface IndependenceTest

Parameters:

name - The name of the variable to retrieve.

Returns:

The variable with the given name, or null if no variable with that name is found.

getData

public DataSet getData()

Returns the data set being analyzed.

Specified by:

getData in interface IndependenceTest

Returns:

This data.

See Also:

• DataSet
• ICovarianceMatrix
• DataModel

toString

public String toString()

Returns a string representation of this test.

Specified by:

toString in interface IndependenceTest

Overrides:

toString in class Object

Returns:

This string.

determines

public boolean determines(List<Node> z,
 Node x)
                   throws UnsupportedOperationException

Determines whether variable x is independent of variable y given a list of conditioning variables z.

Parameters:

z - A list of conditioning variables.

x - The variable x to be tested.

Returns:

True if variable x is independent of variable y given the conditioning variables z, false otherwise.

Throws:

UnsupportedOperationException - This method is not implemented.

isVerbose

public boolean isVerbose()

Determines if the verbose mode is enabled.

Specified by:

isVerbose in interface IndependenceTest

Returns:

true if the verbose mode is enabled, false otherwise.

setVerbose

public void setVerbose(boolean verbose)

Sets the verbose mode for the IndTestHsic class.

Specified by:

setVerbose in interface IndependenceTest

Parameters:

verbose - true to enable verbose mode, false to disable it.