R/UMRactiveSet.R

In UMR: Unmatched Monotone Regression

## "Active Set" approach to finding (local) minima, in unlinked monotone regression.

#' @title An active set approach to minimizing objective in Unlinked Monotone
#'     Regression
#'
#' @export
#'
#' @param yy Y (response) observation vector (numeric)
#' 
#' @param grad a function(yy, mm) where mm  is the
#'     previous iterate value (i.e., the estimate vector).
#' @param CC_SIR A curvature function object (denoted "C" in the paper).   See CC_SIR_generic() and examples.
#' @param init Initial value of estimate ('mm').  Vector, length may be different than length(yy). See 'counts' input.
#' @param counts Together 'init' and 'counts' serve as the initialization; the implied initial vector is rep.int(init, counts).
#' @param stepsize Gradient descent stepsize.  
#'
#' @param MM  A number  of iterations.   May not  use them  all.  MM  is not
#'     exactly the total  number of iterations used in the  sense that within
#'     each of  MM iterations, we  will possibly run another  algorithm which
#'     may take up to MM iterations (but usually takes many fewer).
#' @param tol_end  Used as tolerance at various points .  Generally algorithm (and
#'     some subalgorithms) end once sum(abs(mm-mmprev))  < tol, or you hit MM
#'     iterations.
#'
#' @param tol_collapse Collapsing roughly equal mm values into each other.
#' 
#' @param  printevery integer  value (generally  << MM).   Every 'printevery'
#'     iterations, a count will be printed and the output saved.
#' @param filename filename (path) to save output to.
#'
#'
#' param
#' ww_y Weights (nonnegative, sum to 1) corresponding to yy.  Same length as yy.
#'
#'
#' @details  Uses first order  (gradient) for optimization, and  uses certain
#'     second   derivative  computations   to  leave   saddle  points.    See
#'     Balabdaoui, Doss, and Durot (20xx).  Note that yy and mm (i.e., number
#'     covariates) may have different length.
#' 
#'
#'
#' 

## Need think on stepsize /nny (curvature 'step')

UMRactiveSet <- function(yy,
                         ## ww_y = rep(1/length(yy), length(yy)),
                         grad,
                         CC_SIR,
                         init,
                         counts = rep(1, length(init)),
                         stepsize, MM, tol_end=1e-4, tol_collapse,
                         printevery, filename){


    ## mmprev and mmcurr_full are only used for stopping conditions
    mmprev <- rep(Inf, length(init))
    mmcurr_full <- rep(0, length(init))
    mmcurr <- init
    nnx <- sum(counts)
    nny <- length(yy)

    
    ii <- 1
    while (ii<= ceiling(sqrt(MM)) && sum(abs(mmcurr_full-mmprev))>= tol_end){
        mmprev <- rep.int(mmcurr, times=counts)
        ## mmprev <- mmcurr_full
        if ((ii %% printevery) == 0) {
            print(paste0("Completed ", ii, "th iteration."));
            save(yy,
                 ii,
                 ## mmhat_f, quantile_f,
                 ## errdist, mm0, ## model params
                 stepsize, MM,  ## algorithm params
                 ## outhist, ## waste of memory?
                 mmhat = mmcurr,
                 file=filename)
        }


        mmcurr <- gradDesc_fixed_df(yy, grad,
                                    init=mmcurr,
                                    counts=counts,
                                    stepsize=stepsize,
                                    MM=ceiling(sqrt(MM)),
                                    tol=tol_end,
                                    printevery=printevery, filename=filename)


        ## ##### Currently have two sets of code for collapsing non-unique
        ## ##### entries.  Think I only need the latter?
        

        ## ## The "collapse" non-unique entries / "activate constraints" step
        {
            ## sort needed for simplifying vector.  Unclear algorithmically if this
            ## (probabilistically) is the best thing to do or if its better to
            ## just let the length grow over time)
            neword <- order(mmcurr)
            mmcurr <- mmcurr[neword]
            counts <- counts[neword]
            mm_active <- rle(mmcurr)
            mmcurr <- mm_active$values
            metacounts <- mm_active$lengths
            inds <- cumsum(metacounts)
            pp <- length(inds)
            indsstart <- c(0, inds[-pp])+1
            countidcs <- mapply(":", indsstart, inds)
            ## accumulate counts
            counts <- sapply(countidcs, function(xx, bb){sum(bb[xx])}, counts)
        }

        
        ## ###### Group (approximately) non-unique entries
        begidx <- 1
        newidx <- 1;
        nn_i <- length(mmcurr)        
        mm_new <- counts_new <- rep(NA, nn_i)
        for (jj in 2:(nn_i+1)){
            if ((jj==nn_i+1) || ((mmcurr[jj] - mmcurr[begidx]) > tol_collapse)){
                mm_new[newidx] <- mean(mmcurr[begidx:(jj-1)])
                counts_new[newidx] <- sum(counts[begidx:(jj-1)])
                begidx <- jj
                newidx <- newidx+1
            }
        }
        nn_i  <- sum(!is.na(mm_new));
        mmcurr <- mm_new[1:nn_i]
        if (sum(counts_new[!is.na(counts_new)]) != nnx){
            print(counts_new)
            print(counts)
        }
        counts <- counts_new[1:nn_i];
       
        curv <- CC_SIR(yy=yy, mm=mmcurr,
                       ww_y=rep(1/nny, nny),
                       ww_m=counts/nnx)
        minidx <- which.min(curv)
        if (curv[minidx] >= 0)
            break;
        
        ## {
        ## negidcs <- curv<0
        ## posidcs <- !negidcs
        ## numnegs <- sum(negidcs)
        ## evens <- (1:numnegs)*2
        ## odds <- ((1:numnegs)*2)-1

        ## newmm <- rep(mmcurr[negidcs], each=2)
        ## newcounts <- rep(counts[negidcs], each=2)


        ## mmcurr <- (c(mmcurr[posidcs], newmm))
        ## ord <- order(mmcurr)
        ## ## note that the following may modify order; thus we find ord first.

        ## newmm[evens] <- newmm[evens] + sqrt(stepsize/nnx)
        ## newmm[odds] <- newmm[odds] - sqrt(stepsize/nnx)

       
        ## mmcurr <- (c(mmcurr[posidcs], newmm))
        ## mmcurr <- mmcurr[ord]  ## could be not sorted actually bc of the step taken

        ## newcounts[evens] <- floor(newcounts[evens] / 2);
        ## newcounts[odds]  <- ceiling(newcounts[odds] / 2);
        ## counts <- c(counts[posidcs], newcounts)
        ## counts <- counts[ord]

        ## if (sum(counts) != nnx){
        ##     print(newcounts)
        ##     print(counts)
        ##     stop("sum(counts) != nnx")
        ## }
        ## if (length(counts) != length(mmcurr))        {
        ##     print(counts)
        ##     print(mmcurr)
        ##     stop("length(counts) != length(mmcurr)")
        ## }

        ## }

        {
        
        ## curvlen <- length(curv)
        ## ## the following code is inefficient
        ## for (kk in 1:curvlen){
        ##     ## ## take one step in " negatively curved directions" and
        ##     ## ## then iterate
        ##     pp <- length(mmcurr)
        ##     if (curv[kk] < 0){
        ##     }
            
        ##     ## double up the minimum index
        ##     mmcurr <- c(mmcurr[1:minidx], mmcurr[minidx:pp])
        ##     counts <- c(counts[1:minidx], counts[minidx:pp])
        ##     ## take step
        ##     counts[minidx] <- floor(counts[minidx] / 2);
        ##     counts[minidx+1] <- ceiling(counts[minidx+1] / 2);
        ##     ##         stopifnot( counts[minidx])
        ##     ## mmcurr[minidx] <- mmcurr[minidx] - stepsize/nnx;
        ##     ## mmcurr[minidx+1] <- mmcurr[minidx+1] + stepsize/nnx;
        ##     mmcurr[minidx] <- mmcurr[minidx] - sqrt(stepsize/nnx);
        ##     mmcurr[minidx+1] <- mmcurr[minidx+1] + sqrt(stepsize/nnx);
            ## }

        }

        ## ## take one step in "most negatively curved direction" and
        ## ## then iterate
        pp <- length(mmcurr)
        ## double up the minimum index
        mmcurr <- c(mmcurr[1:minidx], mmcurr[minidx:pp])
        counts <- c(counts[1:minidx], counts[minidx:pp])
        ## take step
        counts[minidx] <- floor(counts[minidx] / 2);
        counts[minidx+1] <- ceiling(counts[minidx+1] / 2);
        ##         stopifnot( counts[minidx])
        ## mmcurr[minidx] <- mmcurr[minidx] - stepsize/nnx;
        ## mmcurr[minidx+1] <- mmcurr[minidx+1] + stepsize/nnx;
        mmcurr[minidx] <- mmcurr[minidx] - sqrt(stepsize/nnx);
        mmcurr[minidx+1] <- mmcurr[minidx+1] + sqrt(stepsize/nnx);


        ## for comparison with mmprev.  Not sure if this does or
        ## doesn't slow anything down (if nnx equals nny then
        ## shouldn't be dramatic slowdown).
        mmcurr_full <- rep.int(mmcurr, counts)
        ii <- ii+1                
    }

    

    
    mmord <- order(mmcurr)
    mmcurr <- mmcurr[mmord]
    counts <- counts[mmord]
    
    res <-list(mm=mmcurr,
               counts=counts,
               mm_full =rep.int(mmcurr, times=counts))
    return(res);
}