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IMP Reference Guide  develop.548de65454,2020/11/26
The Integrative Modeling Platform
IMP::isd::PenalizedComplexityPrior Class Reference

Penalized complexity prior. More...

#include <IMP/isd/PenalizedComplexityPrior.h>

+ Inheritance diagram for IMP::isd::PenalizedComplexityPrior:

Detailed Description

Penalized complexity prior.

Given a parameter \(\xi\) of a model (distribution) \(f(x \mid \xi)\) with a simpler base model \(g(x)\) ( \(f(x \mid \xi=0)\) if \(\xi\) is a flexibility parameter), the Penalized Complexity (PC) prior on \(\xi\) minimizes the complexity introduced by deviation from the base model. It corresponds to an exponential distribution on the KullbackÔÇôLeibler divergence between the flexible and base models, in terms of \(\xi\).

For ease of parameterization, a 'tail event' is defined as an upper bound on an interpretable transformation \(Q(\xi)\) with tail density \(\alpha\), such that \(P(Q(\xi) > U) = \alpha\). With KL divergence defined as

\[ \mathrm{KLD}(f(x \mid \xi) || g(x)) = \int f(x \mid \xi) \log\left(\frac{f(x \mid \xi)}{g(x)}\right) dx,\]

KL divergence at \(\xi\) normalized by KL divergence at the tail

\[ D(\xi) = \frac{\mathrm{KLD}(f(x \mid \xi) || g(x))}{\mathrm{KLD}(f(x \mid \xi=Q^{-1}(U)) || g(x))} ,\]

and

\[ J(\xi) = \frac{\partial D(\xi)}{\partial \xi} ,\]

the density of the PC prior is

\[p(\xi) = \frac{-\log\alpha}{2 \sqrt{D(\xi)}} \alpha^{\sqrt{D(\xi)}} |J(\xi)|.\]

See Also
NormalSigmaPCRestraint
Note
For more details, see Simpson et al. Stat Sci. (2017) 32(1): 1. arXiv: 1403.4630
The log-density with this parameterization overflows when \(D(\xi)=0\). The value of the PC prior at the base model is unique to each case and cannot be provided by this general implementation.

Definition at line 52 of file PenalizedComplexityPrior.h.

Public Member Functions

 PenalizedComplexityPrior (double Dxi, double Jxi, double alpha, std::string name="PenalizedComplexityPrior %1%")
 Create from normalized KL divergence. More...
 
double evaluate_derivative_alpha () const
 Evaluate derivative of negative log-density wrt alpha. More...
 
double evaluate_derivative_Dxi () const
 Evaluate derivative of negative log-density wrt \(D(\xi)\). More...
 
double evaluate_derivative_Jxi () const
 Evaluate derivative of negative log-density wrt derivative of \(D(\xi)\). More...
 
double evaluate_derivative_xi (double JJxi) const
 Evaluate derivative of negative log-density wrt parameter \(\xi\). More...
 
double get_alpha () const
 Get density in tail. More...
 
double get_Dxi () const
 Get normalized KL divergence \(D(\xi)\). More...
 
double get_Jxi () const
 Get derivative of normalized KL divergence \(D(\xi)\) wrt \(\xi\). More...
 
virtual std::string get_type_name () const
 
virtual ::IMP::VersionInfo get_version_info () const
 Get information about the module and version of the object. More...
 
void set_alpha (double v)
 Set density in tail. More...
 
void set_Dxi (double v)
 Set normalized KL divergence \(D(\xi)\). More...
 
void set_Jxi (double v)
 Set derivative of normalized KL divergence \(D(\xi)\) wrt \(\xi\). More...
 
void update_sufficient_statistics (Floats Dxis, Floats Jxis)
 Update sufficient statistics with values and derivatives. More...
 
- Public Member Functions inherited from IMP::isd::OneDimensionalSufficientDistribution
 OneDimensionalSufficientDistribution (std::string name="OneDimensionalSufficientDistribution %1%")
 Constructor. More...
 
double evaluate () const
 Get negative log-density using cached sufficient statistics. More...
 
double get_density () const
 Get probability density using cached sufficient statistics. More...
 
Floats get_sufficient_statistics () const
 
void update_sufficient_statistics (Floats vs)
 Update cached sufficient statistics from data. More...
 
- Public Member Functions inherited from IMP::isd::Distribution
 Distribution (std::string name="Distribution %1%")
 
- Public Member Functions inherited from IMP::Object
virtual void clear_caches ()
 
CheckLevel get_check_level () const
 
LogLevel get_log_level () const
 
void set_check_level (CheckLevel l)
 
void set_log_level (LogLevel l)
 Set the logging level used in this object. More...
 
void set_was_used (bool tf) const
 
void show (std::ostream &out=std::cout) const
 
const std::string & get_name () const
 
void set_name (std::string name)
 

Protected Member Functions

virtual double do_evaluate () const
 
virtual Floats do_get_sufficient_statistics () const
 
virtual void do_update_sufficient_statistics (Floats Dxis)
 
virtual void do_update_sufficient_statistics (Floats Dxis, Floats Jxis)
 
- Protected Member Functions inherited from IMP::isd::OneDimensionalSufficientDistribution
virtual double do_get_density () const
 
- Protected Member Functions inherited from IMP::Object
 Object (std::string name)
 Construct an object with the given name. More...
 
virtual void do_destroy ()
 

Constructor & Destructor Documentation

IMP::isd::PenalizedComplexityPrior::PenalizedComplexityPrior ( double  Dxi,
double  Jxi,
double  alpha,
std::string  name = "PenalizedComplexityPrior %1%" 
)

Create from normalized KL divergence.

Parameters
[in]DxiNormalized KL divergence \(D(\xi)\).
[in]JxiDerivative \(J(\xi)\) of normalized KL divergence.
[in]alphaDensity in tail.
[in]nameName of prior.

Member Function Documentation

double IMP::isd::PenalizedComplexityPrior::evaluate_derivative_alpha ( ) const

Evaluate derivative of negative log-density wrt alpha.

double IMP::isd::PenalizedComplexityPrior::evaluate_derivative_Dxi ( ) const

Evaluate derivative of negative log-density wrt \(D(\xi)\).

double IMP::isd::PenalizedComplexityPrior::evaluate_derivative_Jxi ( ) const

Evaluate derivative of negative log-density wrt derivative of \(D(\xi)\).

double IMP::isd::PenalizedComplexityPrior::evaluate_derivative_xi ( double  JJxi) const

Evaluate derivative of negative log-density wrt parameter \(\xi\).

Parameters
[in]JJxiSecond derivative of normalized KL divergence wrt \(\xi\).
double IMP::isd::PenalizedComplexityPrior::get_alpha ( ) const

Get density in tail.

double IMP::isd::PenalizedComplexityPrior::get_Dxi ( ) const

Get normalized KL divergence \(D(\xi)\).

double IMP::isd::PenalizedComplexityPrior::get_Jxi ( ) const

Get derivative of normalized KL divergence \(D(\xi)\) wrt \(\xi\).

virtual ::IMP::VersionInfo IMP::isd::PenalizedComplexityPrior::get_version_info ( ) const
virtual

Get information about the module and version of the object.

Reimplemented from IMP::isd::OneDimensionalSufficientDistribution.

Definition at line 106 of file PenalizedComplexityPrior.h.

void IMP::isd::PenalizedComplexityPrior::set_alpha ( double  v)

Set density in tail.

void IMP::isd::PenalizedComplexityPrior::set_Dxi ( double  v)

Set normalized KL divergence \(D(\xi)\).

void IMP::isd::PenalizedComplexityPrior::set_Jxi ( double  v)

Set derivative of normalized KL divergence \(D(\xi)\) wrt \(\xi\).

void IMP::isd::PenalizedComplexityPrior::update_sufficient_statistics ( Floats  Dxis,
Floats  Jxis 
)

Update sufficient statistics with values and derivatives.

Definition at line 70 of file PenalizedComplexityPrior.h.


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