UMR (version 1.1.0)

AA: Helper functions for calculating gradient of least-squares Shuffled Isotonic Regression criterion, for Laplace or for Gaussian errors

Description

Helper functions for calculating gradient of least-squares Shuffled Isotonic Regression criterion, for Laplace or for Gaussian errors

Usage

AA(yy, mm, func)
BB(mm, func)
AAfunc_Laplace_generic(dd, LL)
AAfunc_Gauss_generic(dd, sig)
BBfunc_Laplace_generic(dd, LL)
BBfunc_Gauss_generic(dd, sig)
getAAfunc_est_outer(eps, ww = 1/length(eps))
getBBfunc_est_outer(eps, ww = 1/length(eps))
BBfunc_mixGauss_generic(dd, locs, wws, sigs)
BBpfunc_mixGauss_generic(dd, locs, wws, sigs)
BBpfunc_Gauss_generic(xx, sig)
BBpfunc_Laplace_generic(xx, myLL)

Arguments

yy

Y (response) observation vector (numeric). Will apply as.vector() so it may be a matrix or array with all dimensions trivial except 1.

mm

Current (unsorted) estimate/iterate at which to compute gradient. (Length equals length of yy). Will apply as.vector() so it may be a matrix or array with all dimensions trivial except 1.

func

This is a function; should be the actual "A" or "B" function from the paper; AA and BB are just wrappers that call outer() with func(). func() should accept vector or matrix arguments.

dd

generic argument to the "A" function; usually of the form m - mmhat, where m is just some value of the regression function

LL

Double Exponential "mean" parameter: corresponding density is $exp(-|d|/LL) / (2LL)$.

sig

is standard deviation of the normal distribution.

eps

is a vector of residuals (or estimated residuals). In current coding, it should have been preprocessed to be *unique*. (If there are repeats this should be encoded in ww).

ww

is vector of weights of same length as eps, and summing to 1. Default is a weight of 1/length(eps) for each value of eps; if eps has been pre-binned then ww is the weights from binning.

locs

Vector (length LL) of mixture locations

wws

Vector (length LL, sum to 1) of mixture weights

sigs

Vector (length LL, positive) of component standard deviations ## here dd should be a matrix (usually from a call to outer())

xx

Point at which to evaluate function

myLL

is Laplace parameter.

Details

See helper functions "A" and "B" in paper.

For getAAfunc_est: returns a function(yy,mm) which is analogous to passing in an estimated 'func' argument to the AA function. (Reason to not do it that way relates to making sure matrix arguments are handled correctly.)

getBBfunc_est returns a function which as of this coding *MUST* take only a numeric vector of length 1; longer vectors will not work. Be careful! Note that ecdf objects are not intended to be stored permanently so storing functions returned by getBBfunc_est_outer or getAAfunc_est_outer may cause issues.

Examples

# NOT RUN {


 ## the "!!" de-quote (see ?partial) so e.g., can save mygradSIR for future runs.

####### gradient settings/setup for Gaussian


## set.seed(501)
library(distr)
mysig <- 1 ##  std dev
errdist <- Norm(0, sd=mysig)
mm0 <- function(xx){xx}
nn <- 300
xx <- sort(runif(n=nn, 0, 7))
yy <- mm0(xx) + errdist@r(nn)
## plot(xx,yy)

myScale <- mysig

AAfunc_Gauss <- purrr::partial(AAfunc_Gauss_generic, sig=!!mysig)
AA_Gauss <- purrr::partial(AA, func=!!AAfunc_Gauss)
BBfunc_Gauss <- purrr::partial(BBfunc_Gauss_generic, sig=!!mysig)
BB_Gauss <- purrr::partial(BB, func=!!BBfunc_Gauss)
mygradSIR <- 
    grad_SIR_Gauss <- ## just for ease of reference
        purrr::partial(grad_SIR_generic,
                       rescale=TRUE, ## factor of nn/2
                       AAfunc=!!AA_Gauss, BBfunc=!!BB_Gauss)

####### gradient settings/setup for Laplace




set.seed(501)
library(distr)
myLL <- .7 ## (1/"rate") parameter, aka "mean" parameter (except Laplace mean is 0)
errdist <- DExp(1/myLL)


nn <- 200
mm0 <- function(xx){
   (xx<=0)*0 + (0<=xx & xx<=2)*1 +
       (2<xx & xx<=3)*3 +
       (3<xx)*6
}
xx <- sort(runif(n=nn, 0, 7))
yy <- mm0(xx) + errdist@r(nn)

myScale <- myLL;

## CS settings
#'mysig <- sqrt(2) * myLL;
#' 
AAfunc_Laplace <- purrr::partial(AAfunc_Laplace_generic, LL=!!myLL)
AA_Laplace <- purrr::partial(AA, func=!!AAfunc_Laplace)
BBfunc_Laplace <- purrr::partial(BBfunc_Laplace_generic, LL=!!myLL)
BB_Laplace <- purrr::partial(BB, func=!!BBfunc_Laplace)
mygradSIR <-
    grad_SIR_Laplace <- purrr::partial(grad_SIR_generic,
                                       rescale=TRUE, ## factor of nn/2
                                      AAfunc=!!AA_Laplace, BBfunc=!!BB_Laplace)
# }