PDF Projection Software Module Design

PDF projection is inherently modular. Application of the chain-rule (Section 2.2.4) breaks down complex feature extraction processes into simple steps, each of which can be embodied by a module. This provides the opportunity for highly modularized software design. The following module functionalities are defined:
  1. Feature extraction: calculating $ {\bf z}=T({\bf x})$.
  2. J-function calculation: calculating $ J({\bf x}; H_0, T)=\frac{p({\bf x}\vert H_0)}{p({\bf z}\vert H_0)}$.
  3. PDF estimation - estimating $ g({\bf z})$.
  4. PDF evaluation - evaluating $ g({\bf z})$ for some samples $ {\bf z}$.
  5. Re-sampling: computing a random sample $ {\bf x}$ from the set $ {\bf x}\in\{{\bf x}: T({\bf x})={\bf z}\}$, using uniform manifold sampling (UMS) (See Section 3.3).

There are two levels of organization of the software. At the upper level, the feature function can execute all five functionalities listed above. Feature functions can be chained together to create larger chains. Two of the functions, PDF estimation and PDF evaluation are reserved for the last feature function in a chain. It makes no sense to do PDF estimation on intermediary features.

Baggenstoss 2017-05-19