Multi-Class Area Under the Minimum in Torch.

torchMAUM

This R package provides a torch efficient extension of the AUM for multi-class classification, which was created to be used as a surrogate loss for optimizing Area Under the ROC Curve (AUC) in supervised binary classification and changepoint detection problems.

Installation

if(!requireNamespace("remotes"))install.packages("remotes")
  remotes::install_github("tdhock/aum")

Usage

To extend AUM for multi-class classification , the OvR(One-Versus-Rest) approach was used , to average results , both macro and micro averages were used and there is one funtion for each averaging method( see Scikit-learn for more details and equations) Given a labels tensor:

four_labels = torch::torch_tensor(c(1,3,2,2),dtype=torch::torch_long())

and a prediction tensor:

four_pred = torch::torch_tensor(matrix(c(0.4, 0.3, 0.3,
                          0.2, 0.1, 0.7,
                          0.5,0.2,0.3,
                          0.3,0.4,0.3),
                          ncol=3,byrow=TRUE))

We could :

• Plot ROC curves using either macro or micro averaging
• Compute AUC either macro or micro
• Compute the AUM either macro or micro, micro AUM supports weighting .

ROC curves

ROC macro:

(torchMAUM::Draw_ROC_curve_macro(four_pred,four_labels))

ROC micro:

(torchMAUM::Draw_ROC_curve_micro(four_pred,four_labels))

AUC value

AUC macro:

(torchMAUM::ROC_AUC_macro(four_pred,four_labels))

torch_tensor
0.805556
[ CPUFloatType{} ]

AUC micro:

(torchMAUM::ROC_AUC_micro(four_pred,four_labels))

torch_tensor
0.734375
[ CPUFloatType{} ]

AUM values

AUM macro:

(torchMAUM::ROC_AUM_macro(four_pred,four_labels))

torch_tensor
0.0277778
[ CPUFloatType{} ]

AUM micro: The AUM micro has two variants: either weighted or unweighted . To use the weighted version we need to pass the counts of each class in the dataset to the function :

unweighted:

(torchMAUM::ROC_AUM_micro(four_pred,four_labels,counts=NULL))

torch_tensor
0.05
[ CPUFloatType{} ]

weighted:

counts=torch::torch_tensor(c(1,2,1))
(torchMAUM::ROC_AUM_micro(four_pred,four_labels,counts=counts))

torch_tensor
0.0388889
[ CPUFloatType{} ]