Calculate AUC in R

Question

Given a vector of scores and a vector of actual class labels  how do you calculate a single-number AUC metric for a binary classifier in the R language or in simple English    Page 9 of  AUC  a Better Measure     seems to require knowing the class labels  and here is an example in MATLAB where I don t understand   R Actual    1     Because R  not to be confused with the R language  is defined a vector but used as a function

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I found some of the solutions here to be slow and or confusing  and some of them don t handle ties correctly  so I wrote my own data table based function auc roc   in my R package mltools   library data table  library mltools   preds  lt - c  1   3   3   9  actuals  lt - c 0  0  1  1   auc roc preds  actuals     0 875  auc roc preds  actuals  returnDT TRUE     Pred CountFalse CountTrue CumulativeFPR CumulativeTPR AdditionalArea CumulativeArea 1   0 9          0         1           0 0           0 5          0 000          0 000 2   0 3          1         1           0 5           1 0          0 375          0 375 3   0 1          1         0           1 0           1 0          0 500          0 875

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You can learn more about AUROC in this blog post by Miron Kursa   https   mbq me blog augh-roc   He provides a fast function for AUROC     By Miron Kursa https   mbq me auroc  lt - function score  bool      n1  lt - sum  bool    n2  lt - sum bool    U   lt - sum rank score   bool   - n1    n1   1    2   return 1 - U   n1   n2      Let s test it   set seed 42  score  lt - rnorm 1e3  bool   lt - sample c TRUE  FALSE   1e3  replace   TRUE   pROC  auc bool  score  mltools  auc roc score  bool  ROCR  performance ROCR  prediction score  bool    auc   y values  1   auroc score  bool   0 51371668847094 0 51371668847094 0 51371668847094 0 51371668847094   auroc   is 100 times faster than pROC  auc   and computeAUC     auroc   is 10 times faster than mltools  auc roc   and ROCR  performance     print microbenchmark    pROC  auc bool  score     computeAUC score bool   score  bool      mltools  auc roc score  bool     ROCR  performance ROCR  prediction score  bool    auc   y values    auroc score  bool      Unit  microseconds                                                              expr       min                                            pROC  auc bool  score  21000 146                             computeAUC score bool   score  bool   11878 605                                     mltools  auc roc score  bool   5750 651  ROCR  performance ROCR  prediction score  bool    auc   y values  2899 573                                                auroc score  bool    236 531          lq       mean     median        uq        max neval  cld  22005 3350 23738 3447 22206 5730 22710 853  32628 347   100    d  12323 0305 16173 0645 12378 5540 12624 981 233701 511   100   c    6186 0245  6495 5158  6325 3955  6573 993  14698 244   100  b     3019 6310  3300 1961  3068 0240  3237 534  11995 667   100 ab      245 4755   253 1109   251 8505   257 578    300 506   100 a

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Without any additional packages   true Y   c 1 1 1 1 2 1 2 1 2 2  probs   c 1 0 999 0 999 0 973 0 568 0 421 0 382 0 377 0 146 0 11   getROC AUC   function probs  true Y       probsSort   sort probs  decreasing   TRUE  index return   TRUE      val   unlist probsSort x      idx   unlist probsSort ix         roc y   true Y idx       stack x   cumsum roc y    2  sum roc y    2      stack y   cumsum roc y    1  sum roc y    1           auc   sum  stack x 2 length roc y  -stack x 1 length roc y -1   stack y 2 length roc y        return list stack x stack x  stack y stack y  auc auc      aList   getROC AUC probs  true Y    stack x   unlist aList stack x  stack y   unlist aList stack y  auc   unlist aList auc   plot stack x  stack y  type    l   col    blue   xlab    False Positive Rate   ylab    True Positive Rate   main    ROC   axis 1  seq 0 0 1 0 0 1   axis 2  seq 0 0 1 0 0 1   abline h seq 0 0 1 0 0 1   v seq 0 0 1 0 0 1   col  gray   lty 3  legend 0 7  0 3  sprintf   3 3f  auc   lty c 1 1   lwd c 2 5 2 5   col  blue   title    AUC

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Calculating AUC with Metrics  package is very easy and straightforward  library Metrics   actual  lt - c 0  0  1  1  predicted  lt - c  1   3   3   9   auc actual  predicted   0 875

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As mentioned by others  you can compute the AUC using the ROCR package   With the ROCR package you can also plot the ROC curve  lift curve and other model selection measures    You can compute the AUC directly without using any package by using the fact that the AUC is equal to the probability that a true positive is scored greater than a true negative   For example  if pos scores is a vector containing a score of the positive examples  and neg scores is a vector containing the negative examples then the AUC is approximated by    gt  mean sample pos scores 1000 replace T   gt  sample neg scores 1000 replace T    1  0 7261   will give an approximation of the AUC   You can also estimate the variance of the AUC by bootstrapping    gt  aucs   replicate 1000 mean sample pos scores 1000 replace T   gt  sample neg scores 1000 replace T

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The ROCR package will calculate the AUC among other statistics   auc tmp  lt - performance pred  auc    auc  lt - as numeric auc tmp y values

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Along the lines of erik s response  you should also be able to calculate the ROC directly by comparing all possible pairs of values from pos scores and neg scores   score pairs  lt - merge pos scores  neg scores  names score pairs   lt - c  pos score    neg score   sum score pairs pos score  gt  score pairs neg score    nrow score pairs    Certainly less efficient than the sample approach or the pROC  auc  but more stable than the former and requiring less installation than the latter   Related  when I tried this it gave similar results to pROC s value  but not exactly the same  off by 0 02 or so   the result was closer to the sample approach with very high N  If anyone has ideas why that might be I d be interested

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With the package pROC you can use the function auc   like this example from the help page    gt  data aSAH   gt    gt    Syntax  response  predictor    gt  auc aSAH outcome  aSAH s100b  Area under the curve  0 7314

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Combining code from ISL 9 6 3 ROC Curves  along with  J  Won  s answer to this question and a few more places  the following plots the ROC curve and prints the AUC in the bottom right on the plot   Below probs is a numeric vector of predicted probabilities for binary classification and test label contains the true labels of the test data   require ROCR  require pROC   rocplot  lt - function pred  truth           predob   prediction pred  truth    perf   performance predob   tpr    fpr     plot perf         area  lt - auc truth  pred    area  lt - format round area  4   nsmall   4    text x 0 8  y 0 1  labels   paste  AUC     area        the reference x y line   segments x0 0  y0 0  x1 1  y1 1  col  gray   lty 2     rocplot probs  test label  col  blue     This gives a plot like this

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Currently top voted answer is incorrect  because it disregards ties  When positive and negative scores are equal  then AUC should be 0 5  Below is corrected example   computeAUC  lt - function pos scores  neg scores  n sample 100000        Args        pos scores  scores of positive observations       neg scores  scores of negative observations       n samples   number of samples to approximate AUC    pos sample  lt - sample pos scores  n sample  replace T    neg sample  lt - sample neg scores  n sample  replace T    mean 1 0  pos sample  gt  neg sample    0 5  pos sample  neg sample

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I usually use the function ROC from the DiagnosisMed package  I like the graph it produces  AUC is returned along with it s confidence interval and it is also mentioned on the graph   ROC classLabels scores Full TRUE

[r] Calculate AUC in R?

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