title: Characterising the Area Under the Curve Loss Function Landscape
abstract:  One of the most common metrics to evaluate neural network classifiers is the
  area under the receiver operating characteristic curve (AUC). However, 
  optimisation of the AUC as the loss function during network
  training is not a standard procedure. Here we compare minimising the cross-entropy (CE) loss
  and optimising the AUC directly. In particular, we analyse the loss function
  landscape (LFL) of approximate AUC (appAUC) loss functions to discover
  the organisation of this solution space. We discuss various surrogates for AUC approximation and show their differences.
  We find that the characteristics of the appAUC landscape are significantly
  different from the CE landscape. The approximate AUC loss function improves
  testing AUC, and the appAUC landscape has substantially more minima, but
  these minima are less robust, with larger average Hessian eigenvalues. We provide a theoretical foundation to explain these results.
  To generalise our results, we lastly provide an overview of how the
  LFL can help to guide loss function analysis and selection. 
authors: Maximilian Paul Niroomand Conor T Cafolla John William Roger Morgan David John Wales
hIndex: Conor T Cafolla 2