Class that defines the likelihood function for multinomial logistic regression. More...

#include <MultiLogisticLikelihood.h>

Inheritance diagram for muq::Modeling::MultiLogisticLikelihood:

Detailed Description

Class that defines the likelihood function for multinomial logistic regression.

Consider a discrete random variable \(y\in\{1,2,\ldots, M\}\) that can take one of \(M\) values. Assume this random depends on another indpendent variable \(x\in\mathbb{R}^N\) and we are interested in modeling the probabilities \(p_i(x) = \mathbb{P}[y=i]\), which are functions of the independent varible \(x\). Logistic regression is the classic approach when \(M=2\) and Multinomial Logistic Regression is a natural way to extend logistic regression to the case where \(M>2\).

The basic idea is to model the log probabilities \(\log(p_i)\) through an expression of the form

\[ \log(p_i) = f_i(x) - \log(z(x)), \]

where \(\log(z(x))\) is a normalization term that ensure the sum of the probabilities is equal to \(1\). More precisely,

\[ z = \sum_{i=1}^M \exp(f_i(x)). \]

Typically, the functions \(f_i\) would also be represent through an expansion of the form

\[ \log(p_i) = -\log(z) + \sum_{j=1}^P \theta_j \phi_j(x), \]

for some basis functions \(\phi_j\).

This class evaluates \(\log(p_i)\) for each \(i\) given the values of \(f_i(x)\) and then computes the likelihood of \(K\) observations \(y_1,\ldots, y_K\). The data is passed to the constructor.

This piece assumes that each observation \(y_k\) corresponds to a condition \(x_k\). The input to this function is thus an unrolled vector containing \(f_i(x_k)\) for all \(i\in\left{1,\ldots,M\right}\) and \(k\in\{1,\ldots, K\}\). It is assumed that \(i\) is the faster index, so that the input vector would look like \([f_1(x_1),\ldots, f_M(x_1),f_1(x_2),\ldots]\).

This piece returns a scalar value, with the value of the loglikelihood

\[ \log \pi(y| x) = \sum_{k=1}^K \log(p_{y_k}(x_k)) \]

Definition at line 51 of file MultiLogisticLikelihood.h.

Public Member Functions
	MultiLogisticLikelihood (unsigned int numClasses, Eigen::VectorXi const &data)

Public Member Functions inherited from muq::Modeling::ModPiece
	ModPiece (std::vector< int > const &inputSizes, std::vector< int > const &outputSizes)

	ModPiece (Eigen::VectorXi const &inputSizes, Eigen::VectorXi const &outputSizes)

virtual	~ModPiece ()=default

virtual double	GetRunTime (const std::string &method="Evaluate") const override
	Get the average run time for one of the implemented methods. More...

virtual void	ResetCallTime () override
	Resets the number of call and times. More...

virtual unsigned long int	GetNumCalls (const std::string &method="Evaluate") const override
	get the number of times one of the implemented methods has been called. More...

virtual std::vector< Eigen::VectorXd > const &	Evaluate (std::vector< Eigen::VectorXd > const &input)
	Evaluate the ModPiece. More...

virtual std::vector< Eigen::VectorXd > const &	Evaluate (ref_vector< Eigen::VectorXd > const &input)

	VARIADIC_TO_REFVECTOR (Evaluate, Eigen::VectorXd, std::vector< Eigen::VectorXd > const &)

virtual Eigen::VectorXd const &	Gradient (unsigned int const outputDimWrt, unsigned int const inputDimWrt, std::vector< Eigen::VectorXd > const &input, Eigen::VectorXd const &sensitivity)
	Compute the Gradient \(J^Tv\). More...

virtual Eigen::VectorXd const &	Gradient (unsigned int const outputDimWrt, unsigned int const inputDimWrt, ref_vector< Eigen::VectorXd > const &input, Eigen::VectorXd const &sensitivity)

Eigen::VectorXd const &	Gradient (unsigned int outWrt, unsigned int inWrt, Eigen::VectorXd const &last, Eigen::VectorXd const &sens)

template<typename... Args>
Eigen::VectorXd const &	Gradient (unsigned int wrtOut, unsigned int wrtIn, Args const &... args)

Eigen::VectorXd const &	ApplyHessian (unsigned int outWrt, unsigned int inWrt1, unsigned int inWrt2, Eigen::VectorXd const &last, Eigen::VectorXd const &sens, Eigen::VectorXd const &vec)

template<typename... Args>
Eigen::VectorXd const &	ApplyHessian (unsigned int wrtOut, unsigned int wrtIn1, unsigned int wrtIn2, Args const &... args)

virtual Eigen::MatrixXd const &	Jacobian (unsigned int const outputDimWrt, unsigned int const inputDimWrt, std::vector< Eigen::VectorXd > const &input)
	Compute the Jacobian of this ModPiece. More...

virtual Eigen::MatrixXd const &	Jacobian (unsigned int const outputDimWrt, unsigned int const inputDimWrt, ref_vector< Eigen::VectorXd > const &input)

template<typename... Args>
Eigen::MatrixXd const &	Jacobian (unsigned int outWrt, unsigned int inWrt, Args const &... args)

template<typename... Args>
Eigen::MatrixXd	JacobianByFD (unsigned int outWrt, unsigned int inWrt, Args const &... args)

template<typename... Args>
Eigen::MatrixXd	ApplyJacobianByFD (unsigned int outWrt, unsigned int inWrt, Args const &... args)

virtual Eigen::VectorXd const &	ApplyJacobian (unsigned int const outputDimWrt, unsigned int const inputDimWrt, std::vector< Eigen::VectorXd > const &input, Eigen::VectorXd const &vec)
	Apply the Jacobian of this ModPiece to a vector. More...

virtual Eigen::VectorXd const &	ApplyJacobian (unsigned int const outputDimWrt, unsigned int const inputDimWrt, ref_vector< Eigen::VectorXd > const &input, Eigen::VectorXd const &vec)

Eigen::VectorXd const &	ApplyJacobian (unsigned int outWrt, unsigned int inWrt, Eigen::VectorXd const &last, Eigen::VectorXd const &sens)

template<typename... Args>
Eigen::VectorXd const &	ApplyJacobian (unsigned int wrtOut, unsigned int wrtIn, Args const &... args)

virtual Eigen::VectorXd	GradientByFD (unsigned int const outputDimWrt, unsigned int const inputDimWrt, std::vector< Eigen::VectorXd > const &input, Eigen::VectorXd const &sensitivity)

virtual Eigen::VectorXd	GradientByFD (unsigned int const outputDimWrt, unsigned int const inputDimWrt, ref_vector< Eigen::VectorXd > const &input, Eigen::VectorXd const &sensitivity)

virtual Eigen::MatrixXd	JacobianByFD (unsigned int const outputDimWrt, unsigned int const inputDimWrt, std::vector< Eigen::VectorXd > const &input)

virtual Eigen::MatrixXd	JacobianByFD (unsigned int const outputDimWrt, unsigned int const inputDimWrt, ref_vector< Eigen::VectorXd > const &input)

virtual Eigen::VectorXd	ApplyJacobianByFD (unsigned int const outputDimWrt, unsigned int const inputDimWrt, std::vector< Eigen::VectorXd > const &input, Eigen::VectorXd const &vec)

virtual Eigen::VectorXd	ApplyJacobianByFD (unsigned int const outputDimWrt, unsigned int const inputDimWrt, ref_vector< Eigen::VectorXd > const &input, Eigen::VectorXd const &vec)

virtual Eigen::VectorXd const &	ApplyHessian (unsigned int const outWrt, unsigned int const inWrt1, unsigned int const inWrt2, std::vector< Eigen::VectorXd > const &input, Eigen::VectorXd const &sens, Eigen::VectorXd const &vec)

virtual Eigen::VectorXd const &	ApplyHessian (unsigned int const outWrt, unsigned int const inWrt1, unsigned int const inWrt2, ref_vector< Eigen::VectorXd > const &input, Eigen::VectorXd const &sens, Eigen::VectorXd const &vec)

virtual Eigen::VectorXd	ApplyHessianByFD (unsigned int const outWrt, unsigned int const inWrt1, unsigned int const inWrt2, std::vector< Eigen::VectorXd > const &input, Eigen::VectorXd const &sens, Eigen::VectorXd const &vec)

virtual Eigen::VectorXd	ApplyHessianByFD (unsigned int const outWrt, unsigned int const inWrt1, unsigned int const inWrt2, ref_vector< Eigen::VectorXd > const &input, Eigen::VectorXd const &sens, Eigen::VectorXd const &vec)

void	EnableCache ()

void	DisableCache ()

bool	CacheStatus () const

virtual void	SetWarnLevel (unsigned int newLevel)

Public Member Functions inherited from muq::Modeling::WorkPiece
	WorkPiece ()
	Create a muq::Modeling::WorkPiece with no fixed number of inputs and outputs and variable input/output types. More...

	WorkPiece (int const num, WorkPiece::Fix const fix=WorkPiece::Fix::Inputs)
	Create a muq::Modeling::WorkPiece with either a fixed number of inputs or outputs and variable input/output types. More...

	WorkPiece (int const numIns, int const numOuts)
	Create a muq::Modeling::WorkPiece with a fixed number of inputs and outputs but variable input/output types. More...

	WorkPiece (std::vector< std::string > const &types, WorkPiece::Fix const fix=WorkPiece::Fix::Inputs)
	Create a muq::Modeling::WorkPiece with either a fixed number of inputs with specified types or a fixed number of outputs with specified types. More...

	WorkPiece (std::map< unsigned int, std::string > const &types, WorkPiece::Fix const fix=WorkPiece::Fix::Inputs)
	Create a muq::Modeling::WorkPiece where either some of the inputs have specified types or some of the outputs have specified types. More...

	WorkPiece (std::map< unsigned int, std::string > const &types, int const num, WorkPiece::Fix const fixTypes=WorkPiece::Fix::Inputs, WorkPiece::Fix const fixNum=WorkPiece::Fix::Inputs)
	Create a muq::Modeling::WorkPiece where either some of the inputs have specified types or some of the outputs have specified types and either the number of inputs or the number of outputs is fixed. More...

	WorkPiece (std::vector< std::string > const &types, int const num)
	Create a muq::Modeling::WorkPiece with a fixed number of inputs with specified types and a fixed number of outputs (of uknown type) More...

	WorkPiece (int const num, std::vector< std::string > const &types)
	Create a muq::Modeling::WorkPiece with a fixed number of outputs with specified types and a fixed number of inputs (of uknown type) More...

	WorkPiece (std::map< unsigned int, std::string > const &inTypes, int const numIns, int const numOuts)
	Create a muq::Modeling::WorkPiece where some of the inputs are known and we know the input and output numbers. More...

	WorkPiece (int const numIns, std::map< unsigned int, std::string > const &outTypes, int const numOuts)
	Create a muq::Modeling::WorkPiece where some of the outputs are known and we know the input and output numbers. More...

	WorkPiece (std::vector< std::string > const &inTypes, std::vector< std::string > const &outTypes)
	Create a muq::Modeling::WorkPiece with a fixed number of inputs and outputs with specified types. More...

	WorkPiece (std::map< unsigned int, std::string > const &inTypes, std::vector< std::string > const &outTypes)
	Create a muq::Modeling::WorkPiece where some of the inputs are known and all of the outputs have specified types. More...

	WorkPiece (std::map< unsigned int, std::string > const &inTypes, int const num, std::vector< std::string > const &outTypes)
	Create a muq::Modeling::WorkPiece where some of the inputs are known with a known number of inputs and all of the outputs have specified types. More...

	WorkPiece (std::vector< std::string > const &inTypes, std::map< unsigned int, std::string > const &outTypes)
	Create a muq::Modeling::WorkPiece where some of the outputs and all of the inputs have specified types. More...

	WorkPiece (std::vector< std::string > const &inTypes, std::map< unsigned int, std::string > const &outTypes, int const num)
	Create a muq::Modeling::WorkPiece where some of the outputs with a known number of outputs and all of the inputs have specified types. More...

	WorkPiece (std::map< unsigned int, std::string > const &inTypes, std::map< unsigned int, std::string > const &outTypes)
	Create a muq::Mdoeling::WorkPiece where some of the inputs and some of the outputs have specified types. More...

	WorkPiece (std::map< unsigned int, std::string > const &inTypes, int const numIn, std::map< unsigned int, std::string > const &outTypes)
	Create a muq::Mdoeling::WorkPiece where some of the inputs and some of the outputs have specified types with a fixed number of inputs. More...

	WorkPiece (std::map< unsigned int, std::string > const &inTypes, std::map< unsigned int, std::string > const &outTypes, int const numOut)
	Create a muq::Mdoeling::WorkPiece where some of the inputs and some of the outputs have specified types with a fixed number of outputs. More...

	WorkPiece (std::map< unsigned int, std::string > const &inTypes, int const numIn, std::map< unsigned int, std::string > const &outTypes, int const numOut)
	Create a muq::Mdoeling::WorkPiece where some of the inputs and some of the outputs have specified types with a fixed number of inputs and outputs. More...

virtual	~WorkPiece ()
	Default destructor. More...

std::vector< boost::any > const &	Evaluate (std::vector< boost::any > const &ins)
	Evaluate this muq::Modeling::WorkPiece. More...

std::vector< boost::any > const &	Evaluate (ref_vector< boost::any > const &ins)
	Evaluate this muq::Modeling::WorkPiece using references to the inputs. More...

std::vector< boost::any > const &	Evaluate ()
	Evaluate this muq::Modeling::WorkPiece in the case that there are no inputs. More...

template<typename... Args>
std::vector< boost::any > const &	Evaluate (Args... args)
	Evalaute this muq::Modeling::WorkPiece using multiple arguments. More...

std::string const &	Name ()
	Get the (unique) name of this work piece. More...

void	SetName (std::string const &newName)
	Set the name of this work piece. More...

std::string	InputType (unsigned int inputNum, bool const demangle=true) const
	Get the input type (if we know it) for a specific input. More...

int	InputSize (unsigned int inputNum) const
	Get the length of a vector valued input with fixed size. More...

void	SetInputSize (unsigned int inputNum, int newSize)

std::string	OutputType (unsigned int outputNum, bool const demangle=true) const
	Get the output type (if we know it) for a specific output. More...

std::map< unsigned int, std::string >	OutputTypes () const
	Get the output types. More...

std::map< unsigned int, std::string >	InputTypes () const
	Get the input types. More...

unsigned int	ID () const
	Get the unique ID number. More...

Additional Inherited Members
Static Public Member Functions inherited from muq::Modeling::WorkPiece
static ref_vector< const boost::any >	ToRefVector (std::vector< boost::any > const &anyVec)
	Create vector of references from a vector of boost::any's. More...

static ref_vector< const Eigen::VectorXd >	ToRefVector (std::vector< Eigen::VectorXd > const &anyVec)

Public Attributes inherited from muq::Modeling::ModPiece
const Eigen::VectorXi	inputSizes

const Eigen::VectorXi	outputSizes

Public Attributes inherited from muq::Modeling::WorkPiece
int	numInputs
	The number of inputs. More...

int	numOutputs
	The number of outputs. More...

Constructor & Destructor Documentation

◆ MultiLogisticLikelihood()

MultiLogisticLikelihood::MultiLogisticLikelihood	(	unsigned int	numClasses,
		Eigen::VectorXi const &	data
	)

Definition at line 5 of file MultiLogisticLikelihood.cpp.

Member Function Documentation

◆ ApplyJacobianImpl()

void MultiLogisticLikelihood::ApplyJacobianImpl	(	unsigned int const	outputDimWrt,
		unsigned int const	inputDimWrt,
		ref_vector< Eigen::VectorXd > const &	input,
		Eigen::VectorXd const &	vec
	)

overrideprivatevirtual

Reimplemented from muq::Modeling::ModPiece.

Definition at line 71 of file MultiLogisticLikelihood.cpp.

References muq::Modeling::ModPiece::Jacobian(), and muq::Modeling::ModPiece::jacobianAction.

◆ EvaluateImpl()

void MultiLogisticLikelihood::EvaluateImpl ( muq::Modeling::ref_vector< Eigen::VectorXd > const & inputs )

overrideprivatevirtual

Implements muq::Modeling::ModPiece.

Definition at line 14 of file MultiLogisticLikelihood.cpp.

References data, numClasses, and muq::Modeling::ModPiece::outputs.

◆ GradientImpl()

void MultiLogisticLikelihood::GradientImpl	(	unsigned int const	outputDimWrt,
		unsigned int const	inputDimWrt,
		ref_vector< Eigen::VectorXd > const &	input,
		Eigen::VectorXd const &	sensitivity
	)

overrideprivatevirtual

Reimplemented from muq::Modeling::ModPiece.

Definition at line 32 of file MultiLogisticLikelihood.cpp.

References data, muq::Modeling::ModPiece::gradient, muq::Modeling::ModPiece::inputSizes, and numClasses.

◆ JacobianImpl()

void MultiLogisticLikelihood::JacobianImpl	(	unsigned int const	outputDimWrt,
		unsigned int const	inputDimWrt,
		ref_vector< Eigen::VectorXd > const &	input
	)