@article{JMLR:v14:zhao13a,
  author  = {Ming-Jie Zhao and Narayanan Edakunni and Adam Pocock and Gavin Brown},
  title   = {Beyond Fano's Inequality: Bounds on the Optimal F-Score, BER, and Cost-Sensitive Risk and Their Implications},
  journal = {Journal of Machine Learning Research},
  year    = {2013},
  volume  = {14},
  number  = {32},
  pages   = {1033--1090},
  url     = {http://jmlr.org/papers/v14/zhao13a.html}
}