Description of the class THSIC. More...

#include <THSIC.h>

Inheritance diagram for URANIE::Sensitivity::THSIC:

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Collaboration diagram for URANIE::Sensitivity::THSIC:

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Public Types
enum	EEstimatedVariance { kUnknown , kStdEmpirical , kMedianeDelta }

Public Types inherited from URANIE::Sensitivity::TSensitivity
enum	ELauncher { kCode , kCodeRemote , kFunction , kRun , kUnknown }

Public Member Functions
Constructor and Destructor
	THSIC ()
	Default constructor.

	THSIC (URANIE::DataServer::TDataServer tds, const char sInputs, const char sOutputs, Option_t option="")
	THSIC constructor with data contined in the TDS and the inputs and outputs attributes.

virtual	~THSIC ()
	Default destructor.

Overload Methods
virtual void	generateSample (Option_t *option="")
	The generate Sample method.

void	computeIndexes (Option_t *option="")
	computeIndexes

void	evaluateIndexes (Option_t *option="")
	evaluateIndexes

void	drawIndexes (TString sTitle, const char select="", Option_t option="")
	Draw the indexes computed by the method.

Setting and Getting attributs

EEstimatedVariance	getEstimatedVariance ()
	Which method used to estimate the variance of the gaussian kernel ( kUnknown \| kStdEmpirical \| kMedianeDelta )

void	setEstimatedVariance (EEstimatedVariance nMethod)
	Set the method used to estimate the variance of the gaussian kernel ( kUnknown \| kStdEmpirical \| kMedianeDelta )

Int_t	getNPermutationSample ()
	getNPermutationSample

void	setNPermutationSample (Int_t ns)
	Set the Permutation sample permutation Size (default NDefaultPermutation)

void	setThresholdPermutation (Int_t n)

Int_t	getThresholdPermutation ()
	Get the Threshold (nS/nX) to use the permutation permutation test to cumpute the p-value (default NDefaultThresholdPermutation)

void	setThresholdGamma (Int_t n)
	Set the Threshold (nS/nX) to use the Gamma approximation to cumpute the p-value (default NDefaultThresholdGamma)

Int_t	getThresholdGamma ()
	Get the Threshold (nS/nX) to use the Gamma approximation to cumpute the p-value (default NDefaultThresholdGamma)

General methods
void	generateHMatrix (Option_t *option="")
	generate the matrix

Double_t	computeTrace (TMatrixD mat, TMatrixD crtMatHLH)
	compute the trace of the product $\frac{1}{nS^2} \, K_{X} \times H \, K_{Y} \, H$ matrix

TMatrixDSym	doubleCentering (const TMatrixDSym &mat)
	compute the matrix $H \, K \, H$ matrix

TMatrixDSym	getMatrixKGaussian (const char *sAtt, Double_t dvariance)
	getMatrixKGaussian

Double_t	getSumOfMatrixBk (TMatrixD matHLkH, TMatrixD matHLH)
	getSumOfMatrixBk

Double_t	estimateSigma (const char sAtt, Option_t option="")
	estimateSigma

Double_t	unBiasedHSIC (TMatrixD matKx, TMatrixD matKy)
	Use the unbiased formula to compute .

void	permutedPermMatrix (TMatrixDSym &theMatK, TList tlstIndex, TList tlstMatrix)
	Create the list of permuted Permutation sample.

Parse the option
The options treated by the THSIC object were : "empiri" : Choose the Standard deviation of each attributes to compute the $\sigma$ parameter "median" : Choose the median distance between points of each attributes to compute the $\sigma$ parameter See also TSensitivity::parseOption()
virtual void	parseOption (Option_t *option="")
	Parse the option given by the user.

Printing Log
virtual void	printLog (Option_t *option="")
	Print the Log.

void	printSummary (Option_t *option="")
	Print the summary of the HSIC method.

Public Member Functions inherited from URANIE::Sensitivity::TSensitivityTest
	TSensitivityTest ()
	Default constructor.

	TSensitivityTest (URANIE::DataServer::TDataServer tds, const char varexpinput, const char varexpoutput, Option_t option="")
	Default constructor.

virtual	~TSensitivityTest ()
	Default destructor.

Public Member Functions inherited from URANIE::Sensitivity::TSensitivity
	TSensitivity ()
	Default constructor.

	TSensitivity (URANIE::DataServer::TDataServer tds, const char fcn, Int_t ns, const char varexpinput="", const char varexpoutput="", Option_t *option="")
	Default constructor with the name of a function.

	TSensitivity (URANIE::DataServer::TDataServer tds, void(fcn)(Double_t , Double_t ), const char varexpinput, const char varexpoutput, Int_t ns, Option_t *option="")

	TSensitivity (URANIE::DataServer::TDataServer tds, const char varexpinput, const char varexpoutput, Option_t option="")
	Default constructor.

	TSensitivity (URANIE::DataServer::TDataServer tds, URANIE::Launcher::TCode code, Int_t ns, Option_t *option="")
	Default constructor with TCode arg.

	TSensitivity (URANIE::DataServer::TDataServer tds, URANIE::Relauncher::TRun run, Int_t ns, Option_t *option="")
	Default constructor with TRun arg.

virtual	~TSensitivity ()
	Default destructor.

Int_t	getID ()

virtual TTree *	getResultTuple (bool commonresulttuple=true)
	Get the result ntuple (default parameter unused but for Morris method)

double	getValue (const char sorder="", const char sinputname="", const char *sselect="")

vector< int > *	getAttributeElements (string str)

void	setFunction (void(fct)(Double_t , Double_t *), Int_t nx=-1, Int_t ny=1)

TString	getFunctionName ()

void	setSeed (UInt_t nval)

UInt_t	getSeed ()

virtual void	setMethodName (const char *str)
	Set the Method name.

const char *	getMethodName ()
	Get the method name.

Bool_t	getNoIntermediateSaved ()
	Get the noIntermediateSaved flag.

const char *	getIteratorName ()
	Get the name of the iterator attribut of the method.

void	setSensitivityIteratorName (const char *str)
	Set the iterator name devoted to compute sensitivity indexes.

void	setTimeName (TString sname)
	Set the name of the time attribute (only one)

TString	getTimeName ()
	Get the name of the time attribute.

virtual void	setDrawProgressBar (Bool_t bbool=kTRUE)
	Set the "draw progress bar" flag.

void	setUsingErrors (bool thebool)
	Set the "using error results anyway" option.

Bool_t	getDrawProgressBar ()
	Get the clean flag.

Bool_t	isInputCorrelated ()

TMatrixD	getMatrixInputCorrelation ()

Int_t	getNInput ()
	Get the number of input attributes.

Int_t	getNOutput ()
	Get the number of output attributes.

void	setInputCorrelationMatrix (TMatrixD Corr)

void	checkOutputRequested (string attlist, bool fromoption=false)
	Check the output list requested by the user.

void	computeIndexes (Option_t *option="")
	Compute the Sensitivity Indexes.

void	fillIndex (const char sinputname, const char sorder, Double_t dval, const char *algo="", Double_t dvalCILower=-1.0, Double_t dvalCIUpper=-1.0)
	Method to fill in the tree the value of Sensitivity indexes for an input attribute.

virtual void	createTuple (Option_t *option="")

virtual void	setLog ()

void	unsetLog ()

void	changeLog ()

Bool_t	getLog ()

void	setNLauncher (ELauncher codeLauncher)

Private Attributes
Private and Public attributes
EEstimatedVariance	_nEstimatedVariance
	< The H matrix defined by H := ( Kronecker(i,j) - 1/nS)

Int_t	_nPermutationSample
	the method to compute the variance for the gaussian kernel

Int_t	_nThresholdPermutation
	The number of permutation sample ( permutation ) (default NDefaultPermutation)

Int_t	_nThresholdGamma
	The Threshold (nS/nX) to use the permutation permutation test to cumpute the p-value (default 5)

Additional Inherited Members
Public Attributes inherited from URANIE::Sensitivity::TSensitivity
URANIE::DataServer::TDataServer *	_tds
	Pointeur vers un TDS.

TList *	_listOfInputAttributes
	List of the input branches.

TList *	_listOfOutputAttributes
	List of the input branches.

TString	_sTimeAttribute
	The name of the Time attribute.

Int_t	_nS
	The number of simulation or other information depend on the used method.

Int_t	_nX
	Dimension of the input.

UInt_t	_nY
	Dimension of the target.

UInt_t	_nElY
	Number of element for one selected output.

Int_t	_nbOut
	Total number of Output to be considered.

Int_t	_iOut
	counter for output

unsigned int	_iy
	iterator over number of element

unsigned int	_iely
	iterator over number of element

ELauncher	_nLauncher
	The type of launcher.

TString	_sFunctionName
	The Name of the evaluatuor.

URANIE::Launcher::TCode *	_code
	The tcode.

URANIE::Relauncher::TRun *	_run

TObjArray *	_drawingGarbageCollector
	Garbage collector for prints.

Int_t	_nSeed
	The seed of the random generator.

Bool_t	_bChosenOutputs
	Fact that the input list is provided or not.

Bool_t	_blog
	Boolean for edit the log.

Bool_t	_bdrawProgressBar
	Boolean to know if the progress bar has to be drawn.

Bool_t	_bnoIntermediateSaved
	Boolean to know if the progress bar has to be drawn.

TString	_sIteratorName
	The specific iterator attribute for the method.

TString	_sMethodName
	The method name.

TString	_sSelectedOutput
	The output.

TString	_sSelectedInput
	The input.

map< string, unsigned int >	_mAttributeSize
	Map of size of element for attribute;.

map< string, vector< int > >	_mAttributeElements
	Map of Elements number to run (if vector subselection is requested)

vector< string >	_vOutputNames
	Name of the output.

TCanvas *	_canvas
	Canvas object to deal with.

void(*	_pFunction )(double , double )

TTree *	_ntresult
	The TTree of results.

Protected Member Functions inherited from URANIE::Sensitivity::TSensitivity
void	checkCanvasCreation (bool newcan)
	Create a canvas if needed.

void	drawIndexesHistogram (TString sTitre, const char select="", Option_t option="")
	Draws indexes with an histogram.

void	drawIndexesPie (TString sTitre, const char select="", Option_t option="")
	Draws indexes with an pie chart.

virtual void	preTreatment ()
	PreTreatment for every output.

virtual void	postTreatment ()
	PostTreatment for every output.

void	setNoIntermediateSaved (Bool_t bbool=kTRUE)
	Set the "only final file" flag.

Protected Attributes inherited from URANIE::Sensitivity::TSensitivity
Char_t	_sOutputAttribute [MAXLENGTHSTRING]
	The name of the output attribute.

Char_t	_sInputAttribute [MAXLENGTHSTRING]
	The name of the input attribute.

Char_t	_sOrder [MAXLENGTHSTRING]
	The order of sensitivity indexes.

Char_t	_sMethod [MAXLENGTHSTRING]
	The name of the method.

Char_t	_sAlgorithm [MAXLENGTHSTRING]
	The name of the algorithm to compute the index.

Double_t	_valSobolCrt
	The value of sensitivity indexes.

Double_t	_valSobolCILower
	The value of lower Condidence Interval (95)

Double_t	_valSobolCIUpper
	The value of upper Condidence Interval (95)

TMatrixD	_minputCorr
	Input correlation matrix if sample needs to be correlated.

Bool_t	_bisInputCorrelated
	State whether the input correlation matrix is set.

Bool_t	_bgoingThroughError
	State whether the error must not block the computation.

Detailed Description

Description of the class THSIC.

Introduction

The goal of this class is to find the list of input attributes which are dependent with the output attributes using the "HSIC" values (for "Hilbert-Schmidt Independence Criterion"). This approach was introduced by Gretton (2005, 2007).

Moreover, in the same time, we compute the $R^{2}_{HSIC}$ proposed by Da Veiga (2015) given by the formula

$R^{2}_{HSIC} ( X, Y) \; = \; \frac{ HSIC ( X, Y) }{\sqrt{ HSIC ( X, X) \, \times \, HSIC ( Y, Y)}}$

Draw Indexes

We use a "Pareto chart" to draw the "p-Values" and the $R^{2}_{HSIC}$ .

Bibliography

Da Veiga, S. " Global Sensitivity Analysis with Dependence Measures ", https://arxiv.org/abs/1311.2483, 2013
Zhang, Q., Filippi, S., Gretton, A., Sejdinovic, D., "Large-Scale Kernel Methods for Independence Testing", 2016
Gretton, A., Fukumizu, K., Teo, C.H., Song, L., Schoelkopf, B., et Smola, A., "A Kernel Statistical Test of Independence,", NIPS 2007
Gretton, A., Herbrich, R., Smola, A., Bousquet, O., et Schoelkopf, B., "Kernel Methods for Measuring Independence", Journal of Machine Learning Research, 6 , pp.2075–2129, 2005
The Pareto chart, https://en.wikipedia.org/wiki/Pareto_chart

Member Enumeration Documentation

◆ EEstimatedVariance

enum URANIE::Sensitivity::THSIC::EEstimatedVariance

Enumerator
kUnknown
kStdEmpirical
kMedianeDelta

Constructor & Destructor Documentation

◆ THSIC() [1/2]

URANIE::Sensitivity::THSIC::THSIC ( )

Default constructor.

Referenced by ClassImp().

◆ THSIC() [2/2]

URANIE::Sensitivity::THSIC::THSIC	(	URANIE::DataServer::TDataServer *	tds,
		const char *	sInputs,
		const char *	sOutputs,
		Option_t *	option = `""`
	)

THSIC constructor with data contined in the TDS and the inputs and outputs attributes.

Parameters

tds
sInputs
sOutputs
option	(Option_t *) option to pass [""]

◆ ~THSIC()

virtual URANIE::Sensitivity::THSIC::~THSIC ( )

virtual

Default destructor.

Referenced by ClassImp().

Member Function Documentation

◆ computeIndexes()

void URANIE::Sensitivity::THSIC::computeIndexes ( Option_t * option = "" )

computeIndexes

Parameters

option (Option_t *) option to pass [""]

Referenced by ClassImp().

◆ computeTrace()

Double_t URANIE::Sensitivity::THSIC::computeTrace	(	TMatrixD	mat,
		TMatrixD	crtMatHLH
	)

compute the trace of the product $\frac{1}{nS^2} \, K_{X} \times H \, K_{Y} \, H$ matrix

Parameters

mat	(TMatrixD) the $K_{X}$ matrix
crtMatHLH	(TMatrixD) the $H \, K_{Y} \, H$ matrix

Returns: (Double_t) the trace od the product matrix

Referenced by ClassImp().

◆ doubleCentering()

TMatrixDSym URANIE::Sensitivity::THSIC::doubleCentering ( const TMatrixDSym & mat )

compute the matrix $H \, K \, H$ matrix

Parameters

mat	(TMatrixD) the matrix

Returns: (TMatrixD) the $H \, K \, H$ matrix

Referenced by ClassImp().

◆ drawIndexes()

void URANIE::Sensitivity::THSIC::drawIndexes	(	TString	sTitle,
		const char *	select = `""`,
		Option_t *	option = `""`
	)

virtual

Draw the indexes computed by the method.

Parameters

sTitle	(TString) the title of the graph
select	(const char*) the select argument
option	(Option_t *) option to pass [""]

Reimplemented from URANIE::Sensitivity::TSensitivity.

Referenced by ClassImp().

◆ estimateSigma()

Double_t URANIE::Sensitivity::THSIC::estimateSigma	(	const char *	sAtt,
		Option_t *	option = `""`
	)

estimateSigma

Parameters

sAtt
option	(Option_t *) option to pass [""]

Returns

Referenced by ClassImp().

◆ evaluateIndexes()

void URANIE::Sensitivity::THSIC::evaluateIndexes ( Option_t * option = "" )

virtual

evaluateIndexes

Parameters

option (Option_t *) option to pass [""]

Implements URANIE::Sensitivity::TSensitivity.

Referenced by ClassImp().

◆ generateHMatrix()

void URANIE::Sensitivity::THSIC::generateHMatrix ( Option_t * option = "" )

generate the matrix

The matrix is defined by the formula

$H (i, j) \, = \, 1\!\!I_{nS, nS} \: - \: \frac{1}{nS} \: \delta_{i=j}$

Parameters

option (Option_t *) option to pass [""]

Referenced by ClassImp().

◆ generateSample()

virtual void URANIE::Sensitivity::THSIC::generateSample ( Option_t * option = "" )

virtual

The generate Sample method.

Nothing to do. Only the case where the TDS contains the data

Parameters

option (Option_t *) option to pass [""]

Implements URANIE::Sensitivity::TSensitivity.

Referenced by ClassImp().

◆ getEstimatedVariance()

EEstimatedVariance URANIE::Sensitivity::THSIC::getEstimatedVariance ( )

inline

Which method used to estimate the variance of the gaussian kernel ( kUnknown | kStdEmpirical | kMedianeDelta )

kStdEmpirical : the $\sigma$ parameters is estimated by the emperical standatd deviation of the attributes
kMedianeDelta : use the median distance between points
Returns
the method used to estimated the variance of the gaussian kernel ( kStdEmpirical | kMedianeDelta )

References _nEstimatedVariance.

◆ getMatrixKGaussian()

TMatrixDSym URANIE::Sensitivity::THSIC::getMatrixKGaussian	(	const char *	sAtt,
		Double_t	dvariance
	)

getMatrixKGaussian

Parameters

sAtt
dvariance

Returns

Referenced by ClassImp().

◆ getNPermutationSample()

Int_t URANIE::Sensitivity::THSIC::getNPermutationSample ( )

inline

getNPermutationSample

Returns: The number of Permutation sample (permutation zize) to estimate the pValues

References _nPermutationSample.

◆ getSumOfMatrixBk()

Double_t URANIE::Sensitivity::THSIC::getSumOfMatrixBk	(	TMatrixD	matHLkH,
		TMatrixD	matHLH
	)

getSumOfMatrixBk

Parameters

matHLkH
matHLH

Returns

Referenced by ClassImp().

◆ getThresholdGamma()

Int_t URANIE::Sensitivity::THSIC::getThresholdGamma ( )

inline

Get the Threshold (nS/nX) to use the Gamma approximation to cumpute the p-value (default NDefaultThresholdGamma)

Returns: The current Threshold (nS/nX) for using the Gamma approximation

References _nThresholdGamma.

◆ getThresholdPermutation()

Int_t URANIE::Sensitivity::THSIC::getThresholdPermutation ( )

inline

Get the Threshold (nS/nX) to use the permutation permutation test to cumpute the p-value (default NDefaultThresholdPermutation)

Returns: The current Threshold (nS/nX) for using the permutation permutation test

References _nThresholdPermutation.

◆ parseOption()

virtual void URANIE::Sensitivity::THSIC::parseOption ( Option_t * option = "" )

virtual

Parse the option given by the user.

Parameters

option (Option_t) the string of option

Reimplemented from URANIE::Sensitivity::TSensitivity.

Referenced by ClassImp().

◆ permutedPermMatrix()

void URANIE::Sensitivity::THSIC::permutedPermMatrix	(	TMatrixDSym &	theMatK,
		TList *	tlstIndex,
		TList *	tlstMatrix
	)

Create the list of permuted Permutation sample.

Parameters

theMatK
tlstIndex
tlstMatrix

Referenced by ClassImp().

◆ printLog()

virtual void URANIE::Sensitivity::THSIC::printLog ( Option_t * option = "" )

virtual

Print the Log.

Parameters

option (Option_t *) option to pass [""]

Reimplemented from URANIE::Sensitivity::TSensitivityTest.

Referenced by ClassImp().

◆ printSummary()

void URANIE::Sensitivity::THSIC::printSummary ( Option_t * option = "" )

Print the summary of the HSIC method.

Print just the results of the method NOT THE LOG Just a test to generalize

Parameters

option (Option_t *) option to pass [""]

Referenced by ClassImp().

◆ setEstimatedVariance()

void URANIE::Sensitivity::THSIC::setEstimatedVariance ( EEstimatedVariance nMethod )

Set the method used to estimate the variance of the gaussian kernel ( kUnknown | kStdEmpirical | kMedianeDelta )

Parameters

nMethod (EEstimatedVariance) One of the ( kStdEmpirical | kMedianeDelta ) choice

Exceptions

UErrorExceptions for the case (kUnknown)

Referenced by ClassImp().

◆ setNPermutationSample()

void URANIE::Sensitivity::THSIC::setNPermutationSample ( Int_t ns )

Set the Permutation sample permutation Size (default NDefaultPermutation)

Parameters

ns	size of the permutation permutation size

Referenced by ClassImp().

◆ setThresholdGamma()

void URANIE::Sensitivity::THSIC::setThresholdGamma ( Int_t n )

Set the Threshold (nS/nX) to use the Gamma approximation to cumpute the p-value (default NDefaultThresholdGamma)

Parameters

n	(Int_t) the Threshold (nS/nX) for using the Gamma approximation

Referenced by ClassImp().

◆ setThresholdPermutation()

void URANIE::Sensitivity::THSIC::setThresholdPermutation ( Int_t n )

Set the Threshold (nS/nX) to use the permutation permutation test to cumpute the p-value (default NDefaultThresholdPermutation)

Referenced by ClassImp().

◆ unBiasedHSIC()

Double_t URANIE::Sensitivity::THSIC::unBiasedHSIC	(	TMatrixD	matKx,
		TMatrixD	matKy
	)

Use the unbiased formula to compute .

The unbiased formula can be found in the article of Zhang (2016) (eq. 6 - page 8)

$HSIC(X, Y) \, = \, \frac{1}{nS-3} \, \left[ tr(\tilde{K_{X}} \tilde{K_{Y}}) + \frac{1^T \tilde{K_{X}} 1 \times 1^T \tilde{K_{Y}} 1 }{(nS-1)(nS-2)} - \frac{2}{nS-2} 1^T \tilde{K_{X}} \tilde{K_{Y}} 1 \right]$

where $\tilde{K_{X}} := K_{X} - diag(K_{X})$ ( i.e. the kernel matrix with diagonal elements set to zero) and similarly for $\tilde{K_{Y}}$ . is a vector of 1s of relevant dimension.

Parameters

matKx
matKy

Returns

Referenced by ClassImp().

Member Data Documentation

◆ _nEstimatedVariance

EEstimatedVariance URANIE::Sensitivity::THSIC::_nEstimatedVariance

private

< The H matrix defined by H := ( Kronecker(i,j) - 1/nS)

Referenced by ClassImp(), and getEstimatedVariance().

◆ _nPermutationSample

Int_t URANIE::Sensitivity::THSIC::_nPermutationSample

private

the method to compute the variance for the gaussian kernel

Referenced by ClassImp(), and getNPermutationSample().

◆ _nThresholdGamma

Int_t URANIE::Sensitivity::THSIC::_nThresholdGamma

private

The Threshold (nS/nX) to use the permutation permutation test to cumpute the p-value (default 5)

Referenced by ClassImp(), and getThresholdGamma().

◆ _nThresholdPermutation

Int_t URANIE::Sensitivity::THSIC::_nThresholdPermutation

private

The number of permutation sample ( permutation ) (default NDefaultPermutation)

Referenced by ClassImp(), and getThresholdPermutation().

Documentation / Developer's manual

Available modules

Public Types

Public Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Description of the class THSIC.

Introduction

Draw Indexes

Bibliography

Member Enumeration Documentation

◆ EEstimatedVariance

Constructor & Destructor Documentation

◆ THSIC() [1/2]

◆ THSIC() [2/2]

◆ ~THSIC()

Member Function Documentation

◆ computeIndexes()

◆ computeTrace()

◆ doubleCentering()

◆ drawIndexes()

◆ estimateSigma()

◆ evaluateIndexes()

◆ generateHMatrix()

◆ generateSample()

◆ getEstimatedVariance()

◆ getMatrixKGaussian()

◆ getNPermutationSample()

◆ getSumOfMatrixBk()

◆ getThresholdGamma()

◆ getThresholdPermutation()

◆ parseOption()

◆ permutedPermMatrix()

◆ printLog()

◆ printSummary()

◆ setEstimatedVariance()

◆ setNPermutationSample()

◆ setThresholdGamma()

◆ setThresholdPermutation()

◆ unBiasedHSIC()

Member Data Documentation

◆ _nEstimatedVariance

◆ _nPermutationSample

◆ _nThresholdGamma

◆ _nThresholdPermutation