UMRgradDesc: Basic gradient descent implementation

In UMR: Unmatched Monotone Regression

Description

Basic gradient descent implementation

Usage

gradDesc(yy, grad, init, stepsize, MM, printevery, filename)

Arguments

yy	Y (response) observation vector (numeric)
grad	a function(yy, mm) where mm is same length of yy and is the previous iterate value (i.e., the estimate vector).
init	Initial value of estimate ('mm'). I.e., numeric vector of same length as yy.
stepsize	Gradient descent stepsize. Set carefully! (I often use nn^2 / 2 where nn = length(yy), or nn if gradient is 'rescaled'.)
MM	Number of iterations
printevery	integer value (generally << MM). Every 'printevery' iterations, a count will be printed and the output saved.
filename	filename (path) to save output to.

Details

Implements a very basic gradient descent. Right now stepsize is fixed.

Examples

#### Set up the gradient function 
 mysig <- 1 ##  std dev
errdist <- distr::Norm(0, sd=mysig)
modeldistname <- truedistname <- "Gauss" ## used for savefile name
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)

 ## Now run the gradient descent
savefilenameUnique <- paste("graddesc_", modeldistname, "_", truedistname,
                            "_n", nn,
                            "_", format(Sys.time(), "%Y-%m-%d-%T"), ".rsav", sep="")
print(paste("The unique save file name for this run is", savefilenameUnique))
stepsize <- nn^(1/2) ## Has to be tuned
MM <-  100 ## Total number iterations is MM * JJ 
JJ <- 2
eps <- (max(yy)-min(yy)) / (1000 * nn^(1/5) * myScale)
## print *and* SAVE every 'printevery' iterations.
## here no save occurs, printevery > MM
printevery <- 1000 
init <- yy

mmhat <- UMRgradDesc(yy=yy, grad=mygradSIR, ## from settings file
                     init=init,
                     stepsize=stepsize, MM=MM,
                     printevery=printevery,
                     filename=paste0("../saves/", savefilenameUnique))
#### some classical/matched [oracle] estimators
isoreg_std <- Iso::ufit(y=yy, x=xx, lmode=Inf)
mmhat_std = isoreg_std$y ## Isotonic regression
linreg_std <- lm(yy~xx)

UMR documentation built on Aug. 14, 2021, 9:09 a.m.