ROChange {penaltyLearning}

ROC curve for changepoints

Description

Compute a Receiver Operating Characteristic curve for a penalty function.

Usage

ROChange(models, predictions, 
    problem.vars = character())

Arguments

models

data.frame describing the number of incorrect labels as a function of log(lambda), with columns min.log.lambda, max.log.lambda, fp, fn, possible.fp, possible.fn, etc. This can be computed via labelError(modelSelection(...), ...)$model.errors – see examples.

predictions

data.frame with a column named pred.log.lambda, the predicted log(penalty) value for each segmentation problem.

problem.vars

character: column names used to identify data set / segmentation problem.

Value

named list of results:

roc

a data.table with one row for each point on the ROC curve

thresholds

two rows of roc which correspond to the predicted and minimal error thresholds

auc.polygon

a data.table with one row for each vertex of the polygon used to compute AUC

auc

numeric Area Under the ROC curve

aum

numeric Area Under Min(FP,FN)

aum.grad

data.table with one row for each prediction, and columns hi/lo bound for the aum generalized gradient.

Author(s)

Toby Dylan Hocking

Examples

  library(penaltyLearning)
  library(data.table)

  data(neuroblastomaProcessed, envir=environment())
  ## Get incorrect labels data for one profile.
  pid <- 11
  pro.errors <- neuroblastomaProcessed$errors[
    profile.id==pid][order(chromosome, min.log.lambda)]
  dcast(pro.errors, n.segments ~ chromosome, value.var="errors")
  ## Get the feature that corresponds to the BIC penalty = log(n),
  ## meaning log(penalty) = log(log(n)).
  chr.vec <- paste(c(1:4, 11, 17))
  pid.names <- paste0(pid, ".", chr.vec)
  BIC.feature <- neuroblastomaProcessed$feature.mat[pid.names, "log2.n"]
  pred <- data.table(pred.log.lambda=BIC.feature, chromosome=chr.vec)
  ## edit one prediction so that it ends up having the same threshold
  ## as another one, to illustrate an aum sub-differential with
  ## un-equal lo/hi bounds.
  err.changes <- pro.errors[, {
    .SD[c(NA, diff(errors) != 0), .(min.log.lambda)]
  }, by=chromosome]
  (ch.vec <- err.changes[, structure(min.log.lambda, names=chromosome)])
  other <- "11"
  (diff.other <- ch.vec[[other]]-pred[other, pred.log.lambda, on=.(chromosome)])
  pred["1", pred.log.lambda := ch.vec[["1"]]-diff.other, on=.(chromosome)]
  pred["4", pred.log.lambda := 2, on=.(chromosome)]
  ch.vec[["1"]]-pred["1", pred.log.lambda, on=.(chromosome)]
  result <- ROChange(pro.errors, pred, "chromosome")
  library(ggplot2)
  ## Plot the ROC curves.
  ggplot()+
    geom_path(aes(FPR, TPR), data=result$roc)+
    geom_point(aes(FPR, TPR, color=threshold), data=result$thresholds, shape=1)

  ## Plot the number of incorrect labels as a function of threshold.
  ggplot()+
    geom_segment(aes(
      min.thresh, errors,
      xend=max.thresh, yend=errors),
      data=result$roc)+
    geom_point(aes((min.thresh+max.thresh)/2, errors, color=threshold),
               data=result$thresholds,
               shape=1)+
    xlab("log(penalty) constant added to BIC penalty")

  ## Plot area under Min(FP,FN).
  err.colors <- c(
    "fp"="red",
    "fn"="deepskyblue",
    "min.fp.fn"="black")
  err.sizes <- c(
    "fp"=3,
    "fn"=2,
    "min.fp.fn"=1)
  roc.tall <- melt(result$roc, measure.vars=names(err.colors))
  area.rects <- data.table(
    chromosome="total",
    result$roc[0<min.fp.fn])
  (gg.total <- ggplot()+
     geom_vline(
       xintercept=0,
       color="grey")+
     geom_rect(aes(
       xmin=min.thresh, xmax=max.thresh,
       ymin=0, ymax=min.fp.fn),
       data=area.rects,
       alpha=0.5)+
     geom_text(aes(
       min.thresh, min.fp.fn/2,
       label=sprintf(
         "Area Under Min(FP,FN)=%.3f ",
         result$aum)),
       data=area.rects[1],
       hjust=1,
       color="grey50")+
     geom_segment(aes(
       min.thresh, value,
       xend=max.thresh, yend=value,
       color=variable, size=variable),
       data=data.table(chromosome="total", roc.tall))+
     scale_size_manual(values=err.sizes)+
     scale_color_manual(values=err.colors)+
     theme_bw()+
     theme(panel.grid.minor=element_blank())+
     scale_x_continuous(
       "Prediction threshold")+
     scale_y_continuous(
       "Incorrectly predicted labels",
       breaks=0:10))

  ## Add individual error curves.
  tall.errors <- melt(
    pro.errors[pred, on=.(chromosome)],
    measure.vars=c("fp", "fn"))
  gg.total+
    geom_segment(aes(
      min.log.lambda-pred.log.lambda, value,
      xend=max.log.lambda-pred.log.lambda, yend=value,
      size=variable, color=variable),
      data=tall.errors)+
    facet_grid(chromosome ~ ., scales="free", space="free")+
    theme(panel.spacing=grid::unit(0, "lines"))+
    geom_blank(aes(
      0, errors),
      data=data.table(errors=c(1.5, -0.5)))

  print(result$aum.grad)
  if(interactive()){#this can be too long for CRAN.
    ## Plot how Area Under Min(FP,FN) changes with each predicted value.
    aum.dt <- pred[, {
      data.table(log.pen=seq(0, 4, by=0.5))[, {
        chr <- paste(chromosome)
        new.pred.dt <- data.table(pred)
        new.pred.dt[chr, pred.log.lambda := log.pen, on=.(chromosome)]
        with(
          ROChange(pro.errors, new.pred.dt, "chromosome"),
          data.table(aum))
      }, by=log.pen]
    }, by=chromosome]
    bounds.dt <- melt(
      result$aum.grad,
      measure.vars=c("lo", "hi"),
      variable.name="bound",
      value.name="slope")[pred, on=.(chromosome)]
    bounds.dt[, intercept := result$aum-slope*pred.log.lambda]
    ggplot()+
      geom_abline(aes(
        slope=slope, intercept=intercept),
        size=1,
        data=bounds.dt)+
      geom_text(aes(
        2, 2, label=sprintf("directional derivatives = [%d, %d]", lo, hi)),
        data=result$aum.grad)+
      scale_color_manual(
        values=c(
          predicted="red",
          new="black"))+
      geom_point(aes(
        log.pen, aum, color=type),
        data=data.table(type="new", aum.dt))+
      geom_point(aes(
        pred.log.lambda, result$aum, color=type),
        shape=1,
        data=data.table(type="predicted", pred))+
      theme_bw()+
      theme(panel.spacing=grid::unit(0, "lines"))+
      facet_wrap("chromosome", labeller=label_both)+
      coord_equal()+
      xlab("New log(penalty) value for chromosome")+
      ylab("Area Under Min(FP,FN)
using new log(penalty) for this chromosome
and predicted log(penalty) for others")
  }