SelfInhibitingProcess implements the standard multivariate Self-inhibiting (or self-correcting) process. More...

#include "include/SelfInhibitingProcess.h"

Inheritance diagram for SelfInhibitingProcess:

Classes
struct	OPTION
	Options used to configure the fitting of the terminating point process. More...

Public Types
enum	Regularizer { L1, L22, NONE }
	Supported regularizations used to fit the standard Hawkes Process. More...

enum	RegCoef { LAMBDA0, LAMBDA }
	Regularization coefficients. More...

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

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

virtual void	NegLoglikelihood (double &objvalue, Eigen::VectorXd &gradient)
	Negative loglikelihood of self-inhibiting point process. 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	Intensity (const double &t, const Sequence &data, Eigen::VectorXd &intensity_dim)
	Intensity function of self-inhibiting point process. 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 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...

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 arrayK and arrayG from the input sequences. More...

void	RestoreOptionToDefault ()
	restore to the default optimization configuration More...

void	GetNegLoglikelihood (double &objvalue, Eigen::VectorXd &gradient)
	Negative loglikelihood of self-inhibiting point process. More...

void	PostProcessing ()
	Post process the learned dependency structure. More...

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

Protected Attributes
std::vector< std::vector< Eigen::MatrixXd > >	arrayK_
	Temporal features associated with the intensity function. More...

std::vector< std::vector< std::vector< std::vector< std::pair< double, unsigned > > > > >	arrayG_
	Temporal features associated with the integral of the intensity function. 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...

OPTION	options_

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

SelfInhibitingProcess implements the standard multivariate Self-inhibiting (or self-correcting) process.

In a multivariate Self-inhibiting process, the intensity of each dimension $n$ is defined as:

\begin{align} \lambda^*_n(t) = exp\bigg(\lambda^n_0t - \sum_{m=1}^D\sum_{t^m_j < t}\beta_{mn}\bigg), \end{align}

where $\{\lambda^n_0\}$ and $\{\beta_{mn}\}$ are the model parameters. In contrast to the Hawkes process, the intuition here is that while the intensity increases steadily with the rate $\lambda^n_0$, every time when a new event appears, it is decreased by multiplying a constant $e^{-{mn}} < 1$, so the chance of new points decreases after an event has occurred recently.

Definition at line 23 of file SelfInhibitingProcess.h.

Member Enumeration Documentation

enum SelfInhibitingProcess::RegCoef

Regularization coefficients.

Enumerator
LAMBDA0	Regularization coefficient for $\\|\boldsymbol{\lambda}_0\\|$
LAMBDA	Regularization coefficient for $\\|\boldsymbol{\beta}\\|$

Definition at line 99 of file SelfInhibitingProcess.h.

enum SelfInhibitingProcess::Regularizer

Supported regularizations used to fit the standard Hawkes Process.

Enumerator
L1	Sparse L1 norm $\\|\cdot\\|_1$
L22	L22 norm $\\|\cdot\\|_2^2$
NONE	No regularization

Definition at line 82 of file SelfInhibitingProcess.h.

Constructor & Destructor Documentation

SelfInhibitingProcess::SelfInhibitingProcess	(	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 141 of file SelfInhibitingProcess.h.

Member Function Documentation

void SelfInhibitingProcess::fit	(	const std::vector< Sequence > &	data,
		const OPTION &	options
	)

Maximum likelihood estimation for the model parameters.

Parameters

[in]	data	vectors of observed sequences.
[in]	options	data structure sotring different configuration for the optimization algorithm and the respective regularizations.

Definition at line 340 of file SelfInhibitingProcess.cc.

void SelfInhibitingProcess::GetNegLoglikelihood	(	double &	objvalue,
		Eigen::VectorXd &	gradient
	)

protected

Negative loglikelihood of self-inhibiting point process.

\begin{align} -\frac{1}{C}\sum_{c=1}^C\bigg\{\sum_{n = 1}^D\bigg(\sum_{i=1}^{n_c}\bigg(\lambda^n_0t^n_{i,c} - \sum_{m=1}^D\sum_{t^m_{j,c} < t^n_{i,c}}\beta_{mn} - \int_{t^n_{i-1,c}}^{t^n_{i,c}}\exp(\lambda^n_0t - \sum_{m=1}^D\sum_{t^m_{j,c} < t}\beta_{mn})dt\bigg) - \int_{t^n_{n_c,c}}^{T_c}\exp(\lambda^n_0t - \sum_{m=1}^D\sum_{t^m_{j,c} < t}\beta_{mn})dt\bigg)\bigg\} \end{align}

Parameters

[out]	objvalue	negative loglikelihood.
[out]	gradient	gradient of the parameters.

Definition at line 185 of file SelfInhibitingProcess.cc.

void SelfInhibitingProcess::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 335 of file SelfInhibitingProcess.cc.

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

protected

Initialize the temporal features arrayK and arrayG from the input sequences.

Parameters

[in] data input collection of sequences

Definition at line 17 of file SelfInhibitingProcess.cc.

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

virtual

Intensity function of self-inhibiting point process.

In a multivariate Self-inhibiting process, the intensity of each dimension $n$ is defined as:

\begin{align} \lambda^*_n(t) = exp\bigg(\lambda^n_0t - \sum_{m=1}^D\sum_{t^m_j < t}\beta_{mn}\bigg), \end{align}

where $\{\lambda^n_0\}$ and $\{\beta_{mn}\}$ are the model parameters. In contrast to the Hawkes process, the intuition here is that while the intensity increases steadily with the rate $\lambda^n_0$, every time when a new event appears, it is decreased by multiplying a constant $e^{-{mn}} < 1$, so the chance of new points decreases after an event has occurred recently.

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 sequence of past events in data.

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

Implements IProcess.

Definition at line 123 of file SelfInhibitingProcess.cc.

double SelfInhibitingProcess::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 406 of file SelfInhibitingProcess.cc.

double SelfInhibitingProcess::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 154 of file SelfInhibitingProcess.cc.

void SelfInhibitingProcess::NegLoglikelihood	(	double &	objvalue,
		Eigen::VectorXd &	gradient
	)

virtual

Negative loglikelihood of self-inhibiting point process.

Call GetNegLoglikelihood with different types of regularization.

Parameters

[out]	objvalue	negative loglikelihood.
[out]	gradient	gradient of the parameters.

Implements IProcess.

Definition at line 272 of file SelfInhibitingProcess.cc.

void SelfInhibitingProcess::PostProcessing ( )

protected

Post process the learned dependency structure.

Definition at line 381 of file SelfInhibitingProcess.cc.

double SelfInhibitingProcess::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 401 of file SelfInhibitingProcess.cc.

void SelfInhibitingProcess::RestoreOptionToDefault ( )

protected

restore to the default optimization configuration

Definition at line 411 of file SelfInhibitingProcess.cc.

Member Data Documentation

std::vector<std::vector<std::vector<std::vector<std::pair<double, unsigned> > > > > SelfInhibitingProcess::arrayG_

protected

Temporal features associated with the integral of the intensity function.

arrayG_[c][n][i] is a vector of pairs. Each pair records how many events have occurred on each dimension between the $(i-1)$-th event and the $i$-th event on the dimension $n$.

Definition at line 40 of file SelfInhibitingProcess.h.

std::vector<std::vector<Eigen::MatrixXd > > SelfInhibitingProcess::arrayK_

protected

Temporal features associated with the intensity function.

arrayK_[c][n] is an $n_c$ by $D$ matrix where arrayK_[c][n][i][m] records how many events have occurred on dimension $m$ before the $i$-th event on dimension $n$ in the given sequence $c$.

Definition at line 33 of file SelfInhibitingProcess.h.

unsigned SelfInhibitingProcess::num_sequences_

protected

Total number of observed sequences.

Definition at line 45 of file SelfInhibitingProcess.h.

Eigen::VectorXd SelfInhibitingProcess::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 50 of file SelfInhibitingProcess.h.

OPTION SelfInhibitingProcess::options_

protected

Definition at line 132 of file SelfInhibitingProcess.h.

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

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

Enumerator
LAMBDA0	Regularization coefficient for \(\\|\boldsymbol{\lambda}_0\\|\)
LAMBDA	Regularization coefficient for \(\\|\boldsymbol{\beta}\\|\)

Enumerator
L1	Sparse L1 norm \(\\|\cdot\\|_1\)
L22	L22 norm \(\\|\cdot\\|_2^2\)
NONE	No regularization

Classes

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation