Detailed Description

An implement of the dimension-independent MALA (or Inf-MALA) proposal.

This class implements the \(\infty-\)MALA proposal (and its geometry-aware version: \(\infty-\)mMALA proposal) described in Beskos et al., 2017. The proposal takes the form

\[ u^\prime = \rho u + \sqrt{1 - \rho^2} \frac{\sqrt{h}}{2} \left\{ u - K C^{-1} (u - u_0) - K \nabla \Phi \right\} + \sqrt{1-\rho} z \]

where \(u\) is the current state of the chain, \(\rho = \frac{4 - h}{4 + h}\) with \(h\) being the step size used to discretize the Langevin SDE, \(u_0\) is the prior mean, \(C\) is the prior covariance, \(\Phi\) is the negagive log likelihood (note that \(\nabla \pi_\text{post} = - C^{-1} (u - u_0) - \nabla \Phi\)), \(z\sim N(0,K)\) is a normal random variable with a strategically chosen covariance \(K\), and \(u^\prime\) is the propsed point.

Note that the above proposal is the geometry-aware version, and it is the \(\infty-\)MALA proposal when \(K = C\).

Configuration Parameters:

Parameter Key	Type	Default Value	Description
"StepSize"	double	1.0	The step size used to discrete the Langevin SDE.

Definition at line 40 of file InfMALAProposal.h.

Public Member Functions
	InfMALAProposal (boost::property_tree::ptree const &pt, std::shared_ptr< AbstractSamplingProblem > prob)

	InfMALAProposal (boost::property_tree::ptree const &pt, std::shared_ptr< AbstractSamplingProblem > prob, std::shared_ptr< muq::Modeling::GaussianBase > zDistIn)

virtual	~InfMALAProposal ()=default

Public Member Functions inherited from muq::SamplingAlgorithms::MCMCProposal
	MCMCProposal (boost::property_tree::ptree const &pt, std::shared_ptr< AbstractSamplingProblem > const &probIn)

virtual	~MCMCProposal ()=default

virtual void	Adapt (unsigned int const t, std::vector< std::shared_ptr< SamplingState >> const &state)
	Adapt the proposal after each step. More...

void	SetCommunicator (std::shared_ptr< parcer::Communicator > newcomm)

virtual void	SetBlockInd (int newBlockInd)

virtual int	GetBlockInd () const

Additional Inherited Members
Public Types inherited from muq::SamplingAlgorithms::MCMCProposal
typedef std::function< std::shared_ptr< MCMCProposal >boost::property_tree::ptree, std::shared_ptr< AbstractSamplingProblem >)>	MCMCProposalConstructor

typedef std::map< std::string, MCMCProposalConstructor >	MCMCProposalMap

Static Public Member Functions inherited from muq::SamplingAlgorithms::MCMCProposal
static std::shared_ptr< MCMCProposal >	Construct (boost::property_tree::ptree const &pt, std::shared_ptr< AbstractSamplingProblem > const &probIn)
	Static constructor for the transition kernel. More...

static std::shared_ptr< MCMCProposalMap >	GetMCMCProposalMap ()

Constructor & Destructor Documentation

◆ InfMALAProposal() [1/2]

muq::SamplingAlgorithms::InfMALAProposal::InfMALAProposal	(	boost::property_tree::ptree const &	pt,
		std::shared_ptr< AbstractSamplingProblem >	prob
	)

Construct the Inf-mMALA proposal with identity covariance for \(K\).

◆ InfMALAProposal() [2/2]

InfMALAProposal::InfMALAProposal	(	boost::property_tree::ptree const &	pt,
		std::shared_ptr< AbstractSamplingProblem >	prob,
		std::shared_ptr< muq::Modeling::GaussianBase >	zDistIn
	)

Construct the Inf-mMALA proposal with strategically chosen Gaussian distribution zDistIn for \(z\).

Definition at line 28 of file InfMALAProposal.cpp.

References rho, and stepSize.

◆ ~InfMALAProposal()

virtual muq::SamplingAlgorithms::InfMALAProposal::~InfMALAProposal ( )

virtualdefault

Member Function Documentation

◆ GetSigmaGrad()

Eigen::VectorXd InfMALAProposal::GetSigmaGrad ( std::shared_ptr< SamplingState > const & currentState ) const

protected

Returns the product of the proposal covariance times gradient of the log target density at the current state. Checks the metadata of the currentstate first to see if this has already been computed.

Definition at line 68 of file InfMALAProposal.cpp.

References muq::SamplingAlgorithms::MCMCProposal::blockInd, muq::SamplingAlgorithms::MCMCProposal::prob, and zDist.

Referenced by LogDensity(), and Sample().