Speed comparison

Neuroblastoma data

Consider the neuroblastoma data. There are 3418 labeled examples. If we consider subsets, how long does it take to compute the AUM and its directional derivatives?

data(neuroblastomaProcessed, package="penaltyLearning")
library(data.table)
nb.err <- data.table(neuroblastomaProcessed$errors)
nb.err[, example := paste0(profile.id, ".", chromosome)]
nb.X <- neuroblastomaProcessed$feature.mat
(N.pred.vec <- as.integer(10^seq(1, log10(nrow(nb.X)), by=0.5)))
#> [1]   10   31  100  316 1000 3162
if(requireNamespace("atime")){
  aum.pL.list <- atime::atime(
    N=N.pred.vec,
    setup={
      N.pred.names <- rownames(nb.X)[1:N]
      N.diffs.dt <- aum::aum_diffs_penalty(nb.err, N.pred.names)
      pred.dt <- data.table(example=N.pred.names, pred.log.lambda=0)
    },
    penaltyLearning={
      roc.list <- penaltyLearning::ROChange(nb.err, pred.dt, "example")
    },
    aum={
      aum.list <- aum::aum(N.diffs.dt, pred.dt$pred.log.lambda)
    })
  plot(aum.pL.list)
}
#> Loading required namespace: atime
#> Loading required namespace: directlabels
#> Warning in grid.Call.graphics(C_polygon, x$x, x$y, index): semi-transparency is
#> not supported on this device: reported only once per page

From the plot above we can see that both packages have similar asymptotic time complexity. However aum is faster by orders of magnitude.

R implementation

In this section we show a base R implementation of aum.

diffs.df <- data.frame(
  example=c(0,1,1,2,3),
  pred=c(0,0,1,0,0),
  fp_diff=c(1,1,1,0,0),
  fn_diff=c(0,0,0,-1,-1))
pred.log.lambda <- c(0,1,-1,0)
microbenchmark::microbenchmark("C++"={
  aum::aum(diffs.df, pred.log.lambda)
}, R={
  thresh.vec <- with(diffs.df, pred-pred.log.lambda[example+1])
  s.vec <- order(thresh.vec)
  sort.diffs <- data.frame(diffs.df, thresh.vec)[s.vec,]
  for(fp.or.fn in c("fp","fn")){
    ord.fun <- if(fp.or.fn=="fp")identity else rev
    fwd.or.rev <- sort.diffs[ord.fun(1:nrow(sort.diffs)),]
    fp.or.fn.diff <- fwd.or.rev[[paste0(fp.or.fn,"_diff")]]
    last.in.run <- c(diff(fwd.or.rev$thresh.vec) != 0, TRUE)
    after.or.before <-
      ifelse(fp.or.fn=="fp",1,-1)*cumsum(fp.or.fn.diff)[last.in.run]
    distribute <- function(values)with(fwd.or.rev, structure(
      values,
      names=thresh.vec[last.in.run]
    )[paste(thresh.vec)])
    out.df <- data.frame(
      before=distribute(c(0, after.or.before[-length(after.or.before)])),
      after=distribute(after.or.before))
    sort.diffs[
      paste0(fp.or.fn,"_",ord.fun(c("before","after")))
    ] <- as.list(out.df[ord.fun(1:nrow(out.df)),])
  }
  AUM.vec <- with(sort.diffs, diff(thresh.vec)*pmin(fp_before,fn_before)[-1])
  list(
    aum=sum(AUM.vec),
    deriv_mat=sapply(c("after","before"),function(b.or.a){
      s <- if(b.or.a=="before")1 else -1
      f <- function(p.or.n,suffix=b.or.a){
        sort.diffs[[paste0("f",p.or.n,"_",suffix)]]
      }
      fp <- f("p")
      fn <- f("n")
      aggregate(
        s*(pmin(fp+s*f("p","diff"),fn+s*f("n","diff"))-pmin(fp, fn)),
        list(sort.diffs$example),
        sum)$x
    }))
}, times=10)
#> Unit: microseconds
#>  expr      min       lq      mean   median       uq      max neval cld
#>   C++   592.00   594.68   651.496   632.54   653.08   896.16    10  a 
#>     R 42077.68 42186.36 46758.920 43509.78 47050.16 63950.32    10   b

It is clear that the C++ implementation is several orders of magnitude faster.

Synthetic data

library(data.table)
max.N <- 1e6
(N.pred.vec <- as.integer(10^seq(1, log10(max.N), by=0.5)))
#>  [1]      10      31     100     316    1000    3162   10000   31622  100000
#> [10]  316227 1000000
max.y.vec <- rep(c(0,1), l=max.N)
max.diffs.dt <- aum::aum_diffs_binary(max.y.vec)
set.seed(1)
max.pred.vec <- rnorm(max.N)
if(requireNamespace("atime")){
  aum.sort.list <- atime::atime(
    N=N.pred.vec,
    setup={
      N.diffs.dt <- max.diffs.dt[1:N]
      N.pred.vec <- max.pred.vec[1:N]
    },
    dt_sort={
      N.diffs.dt[order(N.pred.vec)]
    },
    R_sort_radix={
      sort(N.pred.vec, method="radix")
    },
    R_sort_quick={
      sort(N.pred.vec, method="quick")
    },
    aum_sort={
      aum.list <- aum:::aum_sort_interface(N.diffs.dt, N.pred.vec)
    })
  plot(aum.sort.list)
}
#> Warning: Transformation introduced infinite values in continuous y-axis
#> Transformation introduced infinite values in continuous y-axis
#> Transformation introduced infinite values in continuous y-axis
#> Warning in grid.Call.graphics(C_polygon, x$x, x$y, index): semi-transparency is
#> not supported on this device: reported only once per page