Package edu.cmu.tetrad.search.test

Class ConditionalCorrelationIndependence

java.lang.Object

edu.cmu.tetrad.search.test.ConditionalCorrelationIndependence

public final class ConditionalCorrelationIndependence
extends Object

Checks conditional independence of variable in a continuous data set using Daudin's method. See

Ramsey, J. D. (2014). A scalable conditional independence test for nonlinear, non-Gaussian data. arXiv preprint arXiv:1401.5031.

This is corrected using Lemma 2, condition 4 of

Zhang, K., Peters, J., Janzing, D., and Schölkopf, B. (2012). Kernel-based conditional independence test and application in causal discovery. arXiv preprint arXiv:1202.3775.

This all follows the original Daudin paper, which is this:

Daudin, J. J. (1980). Partial association measures and ann application to qualitative regression. Biometrika, 67(3), 581-590.

We use Nadaraya-Watson kernel regression, though we further restrict the sample size to nearby points.

Author:

josephramsey

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static enum	ConditionalCorrelationIndependence.Basis	Gives a choice of basis functions to use for judgments of independence for conditional correlation independence.
static enum	ConditionalCorrelationIndependence.Kernel	Gives a choice of kernels to use for the independence judgments for conditional correlation independence.

Constructor Summary

Constructors

Constructor	Description
ConditionalCorrelationIndependence(DataSet dataSet)	Constructs a new Independence test which checks independence facts based on the correlation data implied by the given data set (must be continuous).

Method Summary

Modifier and Type	Method	Description
double	getPValue(double score)	Returns the p-value of the score.
double	getScore()	Returns the minimal scores value calculated by the method for the most recent independence check, less the cutoff so that negative scores correspond to independence.
double	getWidth()	Returns the kernel width.
double	isIndependent(Node x, Node y, Set<Node> _z)	Returns the p-value of the test, x _||_ y | z.
double[]	residuals(Node x, List<Node> z, List<Integer> rows)	Calculates the residuals of x regressed nonparametrically onto z.
void	setAlpha(double alpha)	Sets the alpha cutoff.
void	setBasis(ConditionalCorrelationIndependence.Basis basis)	Sets the basis.
void	setKernelMultiplier(ConditionalCorrelationIndependence.Kernel kernelMultiplier)	Sets the kernel multiplier.
void	setKernelRegressionSampleSize(int kernelRegressionSapleSize)	Sets the kernel regression sample size.
void	setNumFunctions(int numFunctions)	Sets the number of functions to use in (truncated) basis
void	setWidth(double width)	Sets the kernel width.

Methods inherited from class java.lang.Object

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

Constructor Details

ConditionalCorrelationIndependence

public ConditionalCorrelationIndependence(DataSet dataSet)

Constructs a new Independence test which checks independence facts based on the correlation data implied by the given data set (must be continuous). The given significance level is used.

Parameters:

dataSet - A data set containing only continuous columns.

Method Details

isIndependent

public double isIndependent(Node x,
 Node y,
 Set<Node> _z)

Returns the p-value of the test, x _||_ y | z. Can be compared to alpha.

Returns:

This p-value.

residuals

public double[] residuals(Node x,
 List<Node> z,
 List<Integer> rows)

Calculates the residuals of x regressed nonparametrically onto z. Left public so it can be accessed separately.

Returns:

a double[2][] array. The first double[] array contains the residuals for x, and the second double[] array contains the residuals for y.

setNumFunctions

public void setNumFunctions(int numFunctions)

Sets the number of functions to use in (truncated) basis

Parameters:

numFunctions - This number.

setKernelMultiplier

public void setKernelMultiplier(ConditionalCorrelationIndependence.Kernel kernelMultiplier)

Sets the kernel multiplier.

Parameters:

kernelMultiplier - This multiplier.

setBasis

public void setBasis(ConditionalCorrelationIndependence.Basis basis)

Sets the basis.

Parameters:

basis - This basis.

See Also:

• ConditionalCorrelationIndependence.Basis

getWidth

public double getWidth()

Returns the kernel width.

Returns:

This width.

setWidth

public void setWidth(double width)

Sets the kernel width.

Parameters:

width - This width.

getPValue

public double getPValue(double score)

Returns the p-value of the score.

Parameters:

score - The score.

Returns:

This p-value.

getScore

public double getScore()

Returns the minimal scores value calculated by the method for the most recent independence check, less the cutoff so that negative scores correspond to independence.

Returns:

This minimal score.

setAlpha

public void setAlpha(double alpha)

Sets the alpha cutoff.

Parameters:

alpha - This cutoff.

setKernelRegressionSampleSize

public void setKernelRegressionSampleSize(int kernelRegressionSapleSize)

Sets the kernel regression sample size.

Parameters:

kernelRegressionSapleSize - This sample size