BIE::DifferentialEvolution Class Reference

Implements the Differential Evolution (DE) algorithm following the manuscript of Cajo J. More...

#include <DifferentialEvolution.h>

Inheritance diagram for BIE::DifferentialEvolution:

Collaboration diagram for BIE::DifferentialEvolution:

List of all members.

Global variables

enum Control { parallel, serial }

Parallelization type. More...

enum Distrib { uniform, gaussian, cauchy }

Symmetric distribution. More...

static Control cntrl

Current control.

static int minmc

Minimum number of chains.

static int state_iter

Number of iterations allowed for finding a good initial state.

static double tiny

Small pos double "machine" constant (default: double=1.0e-12).

static unsigned jfreq

Frequency in steps for setting $gamma=1$ (default: 10).

static bool linear

Use linear or logit mapping for variables (default: false).

static unsigned nfifo

Number of states for acceptance rate queue.

Public Member Functions

DifferentialEvolution (int max, int ndim, int number, string deinit, BaseDataTree *d, Model *m, Integration *i, Converge *c, MixturePrior *mp, LikelihoodComputation *l, MCAlgorithm *mca, Simulation *last=0)

Constructor for top level invocation.

virtual ~DifferentialEvolution ()

Destructor.

virtual void Initialize ()

Initialize all the chains.

virtual void Reinitialize (MHWidth *width, MixturePrior *mp)

Reinitialize with new class instances.

void PrintState ()

Print current state (override).

virtual void PrintStepDiagnostic ()

override of Simulation method to provide diagnostics specific to DifferentialEvolution

virtual void PrintStateDiagnostic ()

override of Simulation method to provide state specific diagnostics.

vector< double > GetStat (void)

Return vector with fraction of acceptances for each chain.

void NewNumber (int)

Specify the number of desired chains.

void NewGamma (double p)

Change the shift length from the default.

void EnableLogging ()

Enable caching per chain.

void SetLinearMapping (bool b)

Change mapping from logit to linear (or vice versa).

void SetJumpFreq (int n)

Change jump frequency for multimodel mixing (default: 10).

void AdditionalInfo ()

Print out simulation specific diagnostics.

void NewState (int Mcur, vector< double > &w, vector< vector< double > > &p)

Initialize new state (override from Simulation).

void NewState (Chain &ch)

Compute the state from the Chain value.

void NewState (State &s)

Compute the state from the State value.

void SetControl (int)

Set global parameters.

Members which report and diagnose current state

double GetValue ()

Return current posterior probability value (override).

double GetPrior ()

Return current prior value (override).

double GetLikelihood ()

Return current likelihood probability value.

State GetState ()

Return current state (override).

virtual void ReportState ()

Print passed state in ascii with labels (override).

virtual void LogState (string &logfile)

Add state to log file.

virtual void LogState (int level, int iterno, string &outfile)

Protected Member Functions

virtual void MCMethod ()

The Markov Chain implementation.

void CreateChains ()

Create the chain structures.

void SampleNewState (int k)

Attempt to find a good state from the prior distribution for chain k.

void SampleNewStateParallel (int k)

Use the parallel version (called by SampleNewState()).

void NewStateSerialInit ()

Serial sampling init.

void SampleNewStateSerial (int k)

Use the serial version (called by SampleNewState()).

void NewStateSerialStatus ()

Check the status of the initialization.

void TrialState (int zero, int one, int two)

Compute the trial state from the selected particles.

void InitializeSampler (string epsfile)

Initialize the random part of the sampler from the input file.

double Logit (double x)

Logit distribution.

double InverseLogit (double q)

The inverse Logit distribution.

double Map (double x, double a, double b)

Map from finite to infinite interval.

double InverseMap (double q, double a, double b)

Map from infinite back to the finite interval.

void ResetChainStats ()

For gathering diagnostic data.

Protected Attributes

MHWidth * width

The Metropolis-Hastings width instance.

double gamma0

The default (not mode-swapping) value for the proposal direction magntiude.

double gamma

The current value of gamma.

unsigned ncount

Internal counter for mode swapping.

bool caching

Used to flag logging of each chain state.

vector< Random * > distrib

Random distribution for parameters when generating trial states.

vector< unsigned short > fail

Status vector for sampling new states.

Chain chainT

Trial Chain instance.

Uniform * unit

Unit interval variates.

bool chains_initialized

True if state values have been computed for at least the first time.

vector< double > _lower

Lower limit on values imposed by prior.

vector< double > _upper

Upper limit on values imposed by prior.

double _minw

Lower limit on weights imposed by prior.

double _maxw

Upper limit on weights imposed by prior.

unsigned int R0

State variables.

vector< unsigned char > update_flag

Does the chain need to be updated?

vector< unsigned char > update_flag1

For MPI, chains that need to be updated on each node.

vector< unsigned long > nstat0

Tally of proposals for each chain.

vector< unsigned long > nstat1

Tally of accepted proposals for each chain.

deque< vector< unsigned char > > arate

Used to compute chain acceptence rates.

int Ntot

Maximum dimension of the state vector.

vector< double > philower

Minimum allowed value for the parameter vector.

vector< double > phiupper

Maximum allowed value for the parameter vector.

int totalnum

Convergence check.

int totaltry

Friends

class boost::serialization::access

Detailed Description

Implements the Differential Evolution (DE) algorithm following the manuscript of Cajo J.

F. Ter Braak (Stat Comput 2006, 16:239-249)

Intro: Differential evolution uses parallel running Markov Chains with overdispersed initial conditions to set width of the proposal function. It, therefore, is adaptatively capable of handling nondifferentiable, nonlinear and multimodal objective functions.

Brief description: The algorithm works as follows. At each iteration, sometimes called a generation in the DE literature, new state vectors are shifted by the difference of a random selection of state vectors chosen from other chain plus a random variate chosen from a "background" distribution with unbounded support.

Parameters

The shift length is determined from the optimal estimate of the unimodal Gaussian (Roberts and Rosenthal 2001) to be:

$\gamma //! = {2.38\over\sqrt{(2d)}} //!$

where $d$ is the number of dimensions. This can be changed manually using the NewGamma member. In particular, the default value of $\gamma$ may need to be reduced from the optimal to achieve a healthy acceptence rate for proposed new states.

Input file: The fourth parameter is string value for the file containing the chain-independent random variate parameters. The first line is the distribution type followed by the width of the symmetric sampling distribution for the weight parameters. Each successive line describes specifies sampling distribution for each parameter in the mixture model and contains four values: the symmetric sampling distribution, the width, and the upper and lower limit for the parameter. The available symmetric distributions are listed in the enum Distrib.

Parameter range mapping

All finite parameters ranges $(a, b)$

may be mapped using a Logit function, e.g.

$//! q = M(x, a, b) = \log\left( {x-a\over b-x} \right) //!$

and

$//! M^{-1}(q, a, b) = {b + ae^{-q}\over 1+e^{-q}}. //!$

A standard linear mapping is better under many situations so linear mapping is the default (see SetLinearMapping).

Control methods

There are two obvious possibilities for arranging the computation.

The parallel likelihood classes should be used with parallel control only. The parallel likelihood classes LikelihoodComputationMPI and LikelihoodComputationMPITP assume that each process will enter the likelihood computation code.
A serial likelihood class should be used with serial control only. A serial likelihood computation is only entered by the process which calls it.

Diagnostic output: A call to the EnableLogging member function will cause the state of each individual chain to be logged to a separate file. The chain files will have names of the form nametag.chainlog.k where nametag is the global nametag variable and k is the chain number.

Example: See script27 in examples/Splats/parallel

Member Enumeration Documentation

enum BIE::DifferentialEvolution::Control

Parallelization type.

Enumerator:

parallel	root controls all chain updates.
serial	chains are run at each node.

enum BIE::DifferentialEvolution::Distrib

Symmetric distribution.

Enumerator:

uniform	uniform distribution centered at zero.
gaussian	Normal distribution with given sigma.
cauchy	Cauchy distribution with given scale.

Constructor & Destructor Documentation

BIE::DifferentialEvolution::DifferentialEvolution	(	int	max,
		int	ndim,
		int	number,
		string	deinit,
		BaseDataTree *	d,
		Model *	m,
		Integration *	i,
		Converge *	c,
		MixturePrior *	mp,
		LikelihoodComputation *	l,
		MCAlgorithm *	mca,
		Simulation *	last = `0`
	)

Constructor for top level invocation.

Constructor for multiple-level invocation

Member Function Documentation

void BIE::DifferentialEvolution::NewState	(	int	Mcur,
		vector< double > &	w,
		vector< vector< double > > &	p
	)			`[virtual]`

Initialize new state (override from Simulation).

Compute the state from the cardinality, weights and parameters

Reimplemented from BIE::Simulation.

void BIE::DifferentialEvolution::SetControl ( int )

Set global parameters.

Choose parallelization control (parallel=0, serial=1)

virtual void BIE::DifferentialEvolution::PrintStateDiagnostic ( ) [virtual]

override of Simulation method to provide state specific diagnostics.

Here, the method provides mixing statistics.

Reimplemented from BIE::Simulation.

void BIE::DifferentialEvolution::InitializeSampler ( string epsfile ) [protected]

Initialize the random part of the sampler from the input file.

Parameters:

epsfile

Member Data Documentation

unsigned int BIE::DifferentialEvolution::R0 [protected]

State variables.

The index of the current fiducial chain

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

/home/weinberg/src/BIE/include/DifferentialEvolution.h