aum_linear_model_cv {aum}

aum linear model cv

Description

Cross-validation for learning number of early stopping gradient descent steps with exact line search, in linear model for minimizing AUM.

Usage

aum_linear_model_cv(feature.mat, 
    diff.dt, maxIterations = "min.aum", 
    improvement.thresh = NULL, 
    n.folds = 3, initial.weight.fun = NULL)

Arguments

feature.mat

N x P matrix of features, which will be scaled before gradient descent.

diff.dt

data table of differences in error functions, from aum_diffs_penalty or aum_diffs_binary. There should be an example column with values from 0 to N-1.

maxIterations

max iterations of the exact line search, default is number of examples.

improvement.thresh

before doing cross-validation to learn the number of gradient descent steps, we do gradient descent on the full data set in order to determine a max number of steps, by continuing to do exact line search steps while the decrease in AUM is greater than this value (positive real number). Default NULL means to use the value which is ten times smaller than the min non-zero absolute value of FP and FN diffs in diff.dt.

n.folds

Number of cross-validation folds to average over to determine the best number of steps of gradient descent.

initial.weight.fun

Function for computing initial weight vector in gradient descent.

Value

Model trained with best number of iterations, represented as a list of class aum_linear_model_cv with named elements: keep is a logical vector telling which features should be kept before doing matrix multiply of learned weight vector, weight.orig/weight.vec and intercept.orig/intercept are the learned weights/intercepts for the original/scaled feature space, fold.loss/set.loss are data tables of loss values for the subtrain/validation sets, used for selecting the best number of gradient descent steps.

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.

## simulated binary classification problem.
N.rows <- 60
N.cols <- 2
set.seed(1)
feature.mat <- matrix(rnorm(N.rows*N.cols), N.rows, N.cols)
unknown.score <- feature.mat[,1]*2.1 + rnorm(N.rows)
label.vec <- ifelse(unknown.score > 0, 1, 0)
diffs.dt <- aum::aum_diffs_binary(label.vec)

## Default line search keeps doing iterations until increase in AUM.
(default.time <- system.time({
  default.model <- aum::aum_linear_model_cv(feature.mat, diffs.dt)
}))
plot(default.model)
print(default.valid <- default.model[["set.loss"]][set=="validation"])
print(default.model[["search"]][, .(step.size, aum, iterations=q.size)])

## Can specify max number of iterations of line search.
(small.step.time <- system.time({
  small.step.model <- aum::aum_linear_model_cv(feature.mat, diffs.dt, maxIterations = N.rows)
}))
plot(small.step.model)
print(small.step.valid <- small.step.model[["set.loss"]][set=="validation"])
small.step.model[["search"]][, .(step.size, aum, iterations=q.size)]

## Compare number of steps, iterations and time. On my machine small
## step model takes more time/steps, but less iterations in the C++
## line search code.
cbind(
  iterations=c(
    default=default.model[["search"]][, sum(q.size)],
    small.step=small.step.model[["search"]][, sum(q.size)]),
  seconds=c(
    default.time[["elapsed"]],
    small.step.time[["elapsed"]]),
  steps=c(
    default.model[["min.valid.aum"]][["step.number"]],
    small.step.model[["min.valid.aum"]][["step.number"]]),
  min.valid.aum=c(
    default.model[["min.valid.aum"]][["aum_mean"]],
    small.step.model[["min.valid.aum"]][["aum_mean"]]))