aum_line_search {aum}

aum line search

Description

Exact line search using a C++ STL map (red-black tree) to implement a queue of line intersection events. If number of rows of error.diff.df is B, and number of iterations is I, then space complexity is O(B) and time complexity is O( (I+B)log B ).

Usage

aum_line_search(error.diff.df, 
    feature.mat, weight.vec, 
    pred.vec = NULL, 
    maxIterations = nrow(error.diff.df), 
    feature.mat.search = feature.mat, 
    error.diff.search = error.diff.df, 
    maxStepSize = -1)

Arguments

error.diff.df

aum_diffs data frame with B rows, one for each breakpoint in example-specific error functions.

feature.mat

N x p matrix of numeric features.

weight.vec

p-vector of numeric linear model coefficients.

pred.vec

N-vector of numeric predicted values. If NULL, feature.mat and weight.vec will be used to compute predicted values.

maxIterations

max number of line search iterations, either a positive integer or "max.auc" or "min.aum" indicating to keep going until AUC decreases or AUM increases.

feature.mat.search

feature matrix to use in line search, default is subtrain, can be validation

error.diff.search

aum_diffs data frame to use in line search, default is subtrain, can be validation

maxStepSize

max step size to explore.

Value

List of class aum_line_search. Element named "line_search_result" is a data table with number of rows equal to maxIterations (if it is positive integer, info for all steps, q.size column is number of items in queue at each iteration), otherwise 1 (info for the best step, q.size column is the total number of items popped off the queue).

Author(s)

Toby Dylan Hocking <[e-mail]> [aut, cre], Jadon Fowler [aut] (Contributed exact line search C++ code)

Examples

if(require("data.table"))setDTthreads(1L)#for CRAN check.

## Example 1: two binary data.
(bin.diffs <- aum::aum_diffs_binary(c(0,1)))
if(requireNamespace("ggplot2"))plot(bin.diffs)
bin.line.search <- aum::aum_line_search(bin.diffs, pred.vec=c(10,-10))
if(requireNamespace("ggplot2"))plot(bin.line.search)

if(requireNamespace("penaltyLearning")){

  ## Example 2: two changepoint examples, one with three breakpoints.
  data(neuroblastomaProcessed, package="penaltyLearning", envir=environment())
  nb.err <- with(neuroblastomaProcessed$errors, data.frame(
    example=paste0(profile.id, ".", chromosome),
    min.lambda,
    max.lambda,
    fp, fn))
  (nb.diffs <- aum::aum_diffs_penalty(nb.err, c("1.1", "4.2")))
  if(requireNamespace("ggplot2"))plot(nb.diffs)
  nb.line.search <- aum::aum_line_search(nb.diffs, pred.vec=c(1,-1))
  if(requireNamespace("ggplot2"))plot(nb.line.search)
  aum::aum_line_search(nb.diffs, pred.vec=c(1,-1)-c(1,-1)*0.5)

  ## Example 3: all changepoint examples, with linear model.
  X.sc <- scale(neuroblastomaProcessed$feature.mat)
  keep <- apply(is.finite(X.sc), 2, all)
  X.subtrain <- X.sc[1:50,keep]
  weight.vec <- rep(0, ncol(X.subtrain))
  (diffs.subtrain <- aum::aum_diffs_penalty(nb.err, rownames(X.subtrain)))
  nb.weight.search <- aum::aum_line_search(
    diffs.subtrain,
    feature.mat=X.subtrain,
    weight.vec=weight.vec, 
    maxIterations = 200)
  if(requireNamespace("ggplot2"))plot(nb.weight.search)

  ## Stop line search after finding a (local) max AUC or min AUM.
  max.auc.search <- aum::aum_line_search(
    diffs.subtrain,
    feature.mat=X.subtrain,
    weight.vec=weight.vec,
    maxIterations="max.auc")
  min.aum.search <- aum::aum_line_search(
    diffs.subtrain,
    feature.mat=X.subtrain,
    weight.vec=weight.vec,
    maxIterations="min.aum")
  if(require("ggplot2")){
    plot(nb.weight.search)+
      geom_point(aes(
        step.size, auc),
        data=data.table(max.auc.search[["line_search_result"]], panel="auc"),
        color="red")+
      geom_point(aes(
        step.size, aum),
        data=data.table(min.aum.search[["line_search_result"]], panel="aum"),
        color="red")
  }

  ## Alternate viz with x=iteration instead of step size.
  nb.weight.full <- aum::aum_line_search(
    diffs.subtrain,
    feature.mat=X.subtrain,
    weight.vec=weight.vec, 
    maxIterations = 1000)
  library(data.table)
  weight.result.tall <- suppressWarnings(melt(
    nb.weight.full$line_search_result[, iteration:=1:.N][, .(
      iteration, auc, q.size,
      log10.step.size=log10(step.size),
      log10.aum=log10(aum))],
    id.vars="iteration"))
  if(require(ggplot2)){
    ggplot()+
      geom_point(aes(
        iteration, value),
        shape=1,
        data=weight.result.tall)+
      facet_grid(variable ~ ., scales="free")+
      scale_y_continuous("")
  }

  ## Example 4: line search on validation set.
  X.validation <- X.sc[101:300,keep]
  diffs.validation <- aum::aum_diffs_penalty(nb.err, rownames(X.validation))
  valid.search <- aum::aum_line_search(
    diffs.subtrain,
    feature.mat=X.subtrain,
    weight.vec=weight.vec, 
    maxIterations = 2000,
    feature.mat.search=X.validation,
    error.diff.search=diffs.validation)
  if(requireNamespace("ggplot2"))plot(valid.search)

  ## validation set max auc, min aum.
  max.auc.valid <- aum::aum_line_search(
    diffs.subtrain,
    feature.mat=X.subtrain,
    weight.vec=weight.vec,
    maxIterations="max.auc",
    feature.mat.search=X.validation,
    error.diff.search=diffs.validation)
  min.aum.valid <- aum::aum_line_search(
    diffs.subtrain,
    feature.mat=X.subtrain,
    weight.vec=weight.vec,
    maxIterations="min.aum",
    feature.mat.search=X.validation,
    error.diff.search=diffs.validation)
  if(require("ggplot2")){
    plot(valid.search)+
      geom_point(aes(
        step.size, auc),
        data=data.table(max.auc.valid[["line_search_result"]], panel="auc"),
        color="red")+
      geom_point(aes(
        step.size, aum),
        data=data.table(min.aum.valid[["line_search_result"]], panel="aum"),
        color="red")
  }

  ## compare subtrain and validation
  both.results <- rbind(
    data.table(valid.search$line_search_result, set="validation"),
    data.table(nb.weight.search$line_search_result, set="subtrain"))
  both.max <- rbind(
    data.table(max.auc.valid$line_search_result, set="validation"),
    data.table(max.auc.search$line_search_result, set="subtrain"))
  ggplot()+
    geom_vline(aes(
      xintercept=step.size, color=set),
      data=both.max)+
    geom_point(aes(
      step.size, auc, color=set),
      shape=1,
      data=both.results)

}