ppi_cW: Quickly Generate a Vector of Windham Exponents for the PPI...

In scorematchingad: Score Matching Estimation by Automatic Differentiation

Quickly Generate a Vector of Windham Exponents for the PPI Model

Description

These functions help to quickly generate a set of Windham exponents for use in ppi_robust() or Windham(). Rows and columns of A_L and b_L corresponding to components with strong concentrations of probability mass near zero have non-zero constant tuning exponent, and all other elements have a tuning constant of zero. All elements of \beta have a tuning exponent of zero.

The function ppi_cW_auto() automatically detects concentrations near zero by fitting a PPI distribution with A_L=0 and b_L=0 (i.e. a Dirichlet distribution) with the centred log-ratio transformation of the manifold.

Usage

ppi_cW(cW, ...)

ppi_cW_auto(cW, Y)

Arguments

cW	The value of the non-zero Windham tuning exponents.
...	Values of TRUE or FALSE in the same order of the components specifying that a component has probability mass concentrated near zero.
Y	A matrix of observations

Details

The Windham robustifying method involves weighting observations by a function of the proposed model density \insertCitewindham1995roscorematchingad. \insertCitescealy2024ro;textualscorematchingad found that only some of the tuning constants should be non-zero: the tuning exponents corresponding to \beta should be zero to avoid infinite weights;and to improve efficiency any rows or columns of A_L corresponding to components without concentrations of probability mass (i.e. outliers can't exist) should have exponents of zero. \insertCitescealy2024ro;textualscorematchingad set the remaining tuning exponents to a constant.

Value

A vector of the same length as the parameter vector of the PPI model. Elements of A_L will have a value of cW if both their row and column component has probability mass concentrated near zero. Similarly, elements of b_L will have a value of cW if their row corresponds to a component that has a probability mass concentrated near zero. All other elements are zero.

References

\insertAllCited

Examples

Y <- rppi_egmodel(100)$sample
ppi_cW_auto(0.01, Y)
ppi_cW(0.01, TRUE, TRUE, FALSE)

scorematchingad documentation built on April 4, 2025, 12:15 a.m.