Poisson implements the multivariate homogeneous process. More...

#include "include/Poisson.h"

Inheritance diagram for Poisson:

Public Member Functions
	Poisson (const unsigned &n, const unsigned &num_dims)
	The constructor. More...

virtual void	NegLoglikelihood (double &objvalue, Eigen::VectorXd &Gradient)
	Negative loglikelihood of homogeneous Poisson process. More...

virtual double	Intensity (const double &t, const Sequence &data, Eigen::VectorXd &intensity_dim)
	The intensity of each dimension for a homogeneous Poisson process is a constant \(\lambda^0_n\). More...

virtual double	IntensityUpperBound (const double &t, const double &L, const Sequence &data, Eigen::VectorXd &intensity_upper_dim)
	Returns the upper bound of the summation of the intensity value on each dimension from time t to t + L given the history of past events in sequence data. Let \({\lambda_d^(t)}\) be the conditional intensity function on the d-th dimension where \(d=1\dotso D\), and num_dims_ = D. This function returns \begin{align} \lambda_0^D(t) \geq \sum_{d=1}^D\sup_{\tau\in[t, t + \tau(t)]}\lambda^_d(\tau), \end{align} where the returned value \(\lambda_0^D(t)\) will be used for Ogata's Thinning algorithm. More...

virtual double	IntensityIntegral (const double &lower, const double &upper, const Sequence &data)
	Returns the integral of the intensity function \(\int_{a}^b\lambda^*(\tau)d\tau\) where \(a = lower\) and \(b = upper\). More...

virtual void	Gradient (const unsigned &k, Eigen::VectorXd &gradient)
	Returns the gradient w.r.t. the model parameters on the k-th sequence. More...

virtual double	PredictNextEventTime (const Sequence &data, const unsigned &num_simulations)
	Predict the next event timing by the expectation \(\int_{t_n}^\infty tf^(t)dt\). Currently, we use the sample average by simulations to approximate the expectation since the conditional density \(f^(t)\) normally does not have an analytic form. More...

void	fit (const std::vector< Sequence > &data)
	Maximum likelihood estimation for the model parameters. More...

Public Member Functions inherited from IProcess
	IProcess (const unsigned &n, const unsigned &num_dims)
	The constructor. More...

const Eigen::VectorXd &	GetParameters ()
	Return the column vector of model parameters. More...

unsigned	GetNumDims ()
	Return the number of dimensions in the process. More...

void	SetParameters (const Eigen::VectorXd &v)
	Set the model parameters. More...

void	PlotIntensityFunction (const Sequence &data)
	Plots the intensity functions based on the given sequence. It plots the intensity function and the associated event points up of each dimension in the same figure. More...

void	PlotIntensityFunction (const Sequence &data, const unsigned &dim_id)
	Plots the intensity function and the associated event points of the dimension dim_id. More...

Protected Member Functions
void	Initialize (const std::vector< Sequence > &data)
	initialize the temporal features intensity_features_ and intensity_itegral_features_ from the input sequences. More...

Protected Member Functions inherited from IProcess
void	InitializeDimension (const std::vector< Sequence > &data)

Protected Attributes
Eigen::VectorXd	intensity_features_
	A column vector where each component is the average number of events on each dimension. More...

double	intensity_itegral_features_
	The average observation windown. More...

unsigned	num_sequences_
	total number of observed sequences More...

Eigen::VectorXd	observation_window_T_
	a column vector of length \(C\) which is the total number of sequences. Each component records the observation window in the respective sequence. More...

Protected Attributes inherited from IProcess
Eigen::VectorXd	parameters_
	A column vector represents all model parameters of the process. More...

unsigned	num_dims_
	The total number of dimensions of the process. More...

std::vector< std::vector< std::vector< double > > >	all_timestamp_per_dimension_
	all_timestamp_per_dimension_ is a 3-d array where all_timestamp_per_dimension_[c][n][i] records the i-th event on the n-th dimension in the c-th sequence. More...

Detailed Description

Poisson implements the multivariate homogeneous process.

Definition at line 17 of file Poisson.h.

Constructor & Destructor Documentation

Poisson::Poisson	(	const unsigned &	n,
		const unsigned &	num_dims
	)

inline

The constructor.

Parameters

[in]	n	the number of parameters in total.
[in]	num_dims	the number of dimensions in the process.

Definition at line 55 of file Poisson.h.

Member Function Documentation

void Poisson::fit ( const std::vector< Sequence > & data )

Maximum likelihood estimation for the model parameters.

Parameters

[in] data vectors of observed sequences.

Definition at line 92 of file Poisson.cc.

void Poisson::Gradient	(	const unsigned &	k,
		Eigen::VectorXd &	gradient
	)

virtual

Returns the gradient w.r.t. the model parameters on the k-th sequence.

Parameters

[in]	k	sequence index.
[out]	gradient	the gradient vector w.r.t. the model parameters.

Implements IProcess.

Definition at line 75 of file Poisson.cc.

void Poisson::Initialize ( const std::vector< Sequence > & data )

protected

initialize the temporal features intensity_features_ and intensity_itegral_features_ from the input sequences.

Parameters

[in] data input collection of sequences

Definition at line 24 of file Poisson.cc.

double Poisson::Intensity	(	const double &	t,
		const Sequence &	data,
		Eigen::VectorXd &	intensity_dim
	)

virtual

The intensity of each dimension for a homogeneous Poisson process is a constant \(\lambda^0_n\).

Parameters

[in]	t	the given time.
[in]	data	the given sequence of the past events until time t.
[out]	intensity_dim	a column vector of size num_dims_ where each component stores the intensity value of the respetive dimension at time t given the past sequence in data.

Returns: the summation of the intensity value from each dimension.

Implements IProcess.

Definition at line 10 of file Poisson.cc.

double Poisson::IntensityIntegral	(	const double &	lower,
		const double &	upper,
		const Sequence &	data
	)

virtual

Returns the integral of the intensity function \(\int_{a}^b\lambda^*(\tau)d\tau\) where \(a = lower\) and \(b = upper\).

Parameters

[in]	lower	starting point of the integral.
[in]	upper	ending point of the integral.
[in]	data	sequence of past events.

Returns: \(\int_{a}^b\lambda^*(\tau)d\tau\) where \(a = lower\) and \(b = upper\).

Implements IProcess.

Definition at line 99 of file Poisson.cc.

double Poisson::IntensityUpperBound	(	const double &	t,
		const double &	L,
		const Sequence &	data,
		Eigen::VectorXd &	intensity_upper_dim
	)

virtual

Returns the upper bound of the summation of the intensity value on each dimension from time t to t + L given the history of past events in sequence data. Let \({\lambda_d^*(t)}\) be the conditional intensity function on the d-th dimension where \(d=1\dotso D\), and num_dims_ = D. This function returns

\begin{align} \lambda_0^D(t) \geq \sum_{d=1}^D\sup_{\tau\in[t, t + \tau(t)]}\lambda^*_d(\tau), \end{align}

where the returned value \(\lambda_0^D(t)\) will be used for Ogata's Thinning algorithm.

Parameters

t	the starting time.
L	the duration.
data	the given sequence of the past events until time t.
intensity_upper_dim	a column vector of size num_dims_ storing the upper bound of the intensity function on each dimension from time t to t + L.

Returns: the summation of the upper-bound of each intensity function from the respetive dimension within the interval [t, t + L].

Implements IProcess.

Definition at line 19 of file Poisson.cc.

void Poisson::NegLoglikelihood	(	double &	objvalue,
		Eigen::VectorXd &	Gradient
	)

virtual

Negative loglikelihood of homogeneous Poisson process.

\begin{align} -\frac{1}{C}\sum_{c=1}^C\bigg\{\sum_{n=1}^D (\sum_{i=1}^{n_c}\log\lambda^0_n - T_c\lambda^0_n) \bigg\} \end{align}

Parameters

objvalue	negative loglikelihood.
gradient	gradient of the parameters.

Implements IProcess.

Definition at line 60 of file Poisson.cc.

double Poisson::PredictNextEventTime	(	const Sequence &	data,
		const unsigned &	num_simulations
	)

virtual

Predict the next event timing by the expectation \(\int_{t_n}^\infty tf^*(t)dt\). Currently, we use the sample average by simulations to approximate the expectation since the conditional density \(f^*(t)\) normally does not have an analytic form.

Parameters

[in]	data	the sequence of past events.
[in]	num_simulations	number of simulations we use to calculate the sample average.

Returns: the prediction of the next event timing.

Implements IProcess.

Definition at line 105 of file Poisson.cc.

Member Data Documentation

Eigen::VectorXd Poisson::intensity_features_

protected

A column vector where each component is the average number of events on each dimension.

Definition at line 25 of file Poisson.h.

double Poisson::intensity_itegral_features_

protected

The average observation windown.

Definition at line 30 of file Poisson.h.

unsigned Poisson::num_sequences_

protected

total number of observed sequences

Definition at line 35 of file Poisson.h.

Eigen::VectorXd Poisson::observation_window_T_

protected

a column vector of length \(C\) which is the total number of sequences. Each component records the observation window in the respective sequence.

Definition at line 46 of file Poisson.h.

The documentation for this class was generated from the following files:

/Users/nandu/Development/MultiVariatePointProcess/include/Poisson.h
/Users/nandu/Development/MultiVariatePointProcess/src/Poisson.cc

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation