scorematchingad (version 0.1.1)

tape_smd: Build CppAD Tapes for Score Matching

Description

For a parametric model family, the function tape_smd() generates CppAD tapes for the unnormalised log-density of the model family and of the score matching discrepancy function \(A(z) + B(z) + C(z)\) (defined in scorematchingtheory). Three steps are performed by tape_smd(): first an object that specifies the manifold and any transformation to another manifold is created; then a tape of the unnormalised log-density is created; finally a tape of \(A(z) + B(z) + C(z)\) is created.

Usage

tape_smd(
  start,
  tran = "identity",
  end = start,
  ll,
  ytape,
  usertheta,
  bdryw = "ones",
  acut = 1,
  thetatape_creator = function(n) {
     seq(length.out = n)
 },
  verbose = FALSE
)

Value

A list of:

• an Rcpp_ADFun object containing a tape of the unnormalised log-density using the metric of the "end" manifold (that is the independent variable is on the end manifold).

• an Rcpp_ADFun object containing a tape of the score matching discrepancy function with the non-fixed parameters of the model as the independent variable, and the measurements on the end manifold as the dynamic parameter.

• some information about the tapes

Arguments

start

The starting manifold. Used for checking that tran and man match.

tran

The name of a transformation. Available transformations are

• ``sqrt''

• ``alr''

• ``clr''

• ``none'' or `identity'

end

The name of the manifold that tran maps start to. Available manifolds are:

• ``sph'' unit sphere

• ``Hn111'' hyperplane normal to the vector \(1, 1, 1, 1, ...\)

• ``sim'' simplex

• ``Euc'' Euclidean space

ll

An unnormalised log-density with respect to the metric of the starting manifold. ll must be either an Rcpp_ADFun object created by tape_uld() for a custom unnormalised log-density function or the name of an inbuilt function.

ytape

An example measurement value to use for creating the tapes. In the natural (i.e. start) manifold of the density function. Please ensure that ytape is the interior of the manifold and non-zero.

usertheta

A vector of parameter elements for the likelihood function. NA elements will become dynamic parameters. Other elements will be fixed at the provided value. The length of usertheta must be the correct length for the log-density - no checking is conducted.

bdryw

The name of the boundary weight function. "ones" for manifolds without boundary. For the simplex and positive orthant of the sphere, "prodsq" and "minsq" are possible - see ppi() for more information on these.

acut

A parameter passed to the boundary weight function bdryw. Ignored for bdryw = "ones".

thetatape_creator

A function that accepts an integer n, and returns a vector of n length. The function is used to fill in the NA elements of usertheta when building the tapes. Please ensure that the values filled by thetatape_creator lead to plausible parameter vectors for the chosen log-density.

verbose

If TRUE more details are printed when taping. These details are for debugging and will likely be comprehensible only to users familiar with the source code of this package.

Warning

There is no checking of the inputs ytape and usertheta.

Details

Only some combinations of start, tran and end are available because tran must map between start and end. These combinations of start-tran-end are currently available:

• sim-sqrt-sph

• sim-identity-sim

• sim-alr-Euc

• sim-clr-Hn111

• sph-identity-sph

• Euc-identity-Euc

To build a tape for the score matching discrepancy function, the scorematchingad first tapes the map from a point \(z\) on the end manifold to the value of the unnormalised log-density, where the independent variable is the \(z\), the dynamic parameter is a vector of the parameters to estimate, and the remaining model parameters are fixed and not estimated. This tape is then used to generate a tape for the score matching discrepancy function where the parameters to estimate are the independent variable.

The transforms of the manifold must be implemented in C++ and selected by name.

Currently available unnormalised log-density functions are:

• dirichlet

• ppi

• vMF

• Bingham

• FB

References

See Also

Other tape builders: tape_Hessian(), tape_Jacobian(), tape_gradoffset(), tape_logJacdet(), tape_swap(), tape_uld()

Other generic score matching tools: Windham(), cppad_closed(), cppad_search()

Examples

p <- 3
u <- rep(1/sqrt(p), p)
ltheta <- p #length of vMF parameter vector
intheta <- rep(NA, length.out = ltheta)
tapes <- tape_smd("sph", "identity", "sph", "vMF",
              ytape = u,
              usertheta = intheta,
              "ones", verbose = FALSE
              )
evaltape(tapes$lltape, u, runif(n = ltheta))
evaltape(tapes$smdtape, runif(n = ltheta), u)

u <- rep(1/3, 3)
tapes <- tape_smd("sim", "sqrt", "sph", "ppi",
              ytape = u,
              usertheta = ppi_paramvec(p = 3),
              bdryw = "minsq", acut = 0.01,
              verbose = FALSE
              )
evaltape(tapes$lltape, u, rppi_egmodel(1)$theta)
evaltape(tapes$smdtape, rppi_egmodel(1)$theta, u)