 |
|
IMP Reference Guide
2.18.0
The Integrative Modeling Platform
|
Penalized complexity prior. More...
#include <IMP/isd/PenalizedComplexityPrior.h>
Inheritance diagram for IMP::isd::PenalizedComplexityPrior: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 Kullback–Leibler 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
\[p(\xi) = \frac{-\log\alpha}{2 \sqrt{D(\xi)}} \alpha^{\sqrt{D(\xi)}} |J(\xi)|.\]
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 override |
| virtual ::IMP::VersionInfo | get_version_info () const override |
| 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 override |
| virtual Floats | do_get_sufficient_statistics () const override |
| virtual void | do_update_sufficient_statistics (Floats Dxis) override |
| 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 () |
| IMP::isd::PenalizedComplexityPrior::PenalizedComplexityPrior | ( | double | Dxi, |
| double | Jxi, | ||
| double | alpha, | ||
| std::string | name = "PenalizedComplexityPrior %1%" |
||
| ) |
Create from normalized KL divergence.
| [in] | Dxi | Normalized KL divergence \(D(\xi)\). |
| [in] | Jxi | Derivative \(J(\xi)\) of normalized KL divergence. |
| [in] | alpha | Density in tail. |
| [in] | name | Name of prior. |
| 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 \(\xi\).
| [in] | JJxi | Second 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 \(\xi\).
|
overridevirtual |
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 \(\xi\).
Update sufficient statistics with values and derivatives.
Definition at line 70 of file PenalizedComplexityPrior.h.