Finite-sample Analysis of M-estimators using Self-concordance

  title={Finite-sample Analysis of M-estimators using Self-concordance},
  author={Dmitrii Ostrovskii and F. Bach},
  journal={arXiv: Statistics Theory},
  • Dmitrii Ostrovskii, F. Bach
  • Published 2018
  • Mathematics
  • arXiv: Statistics Theory
  • We demonstrate how self-concordance of the loss can be exploited to obtain asymptotically optimal rates for M-estimators in finite-sample regimes. We consider two classes of losses: (i) canonically self-concordant losses in the sense of Nesterov and Nemirovski (1994), i.e., with the third derivative bounded with the $3/2$ power of the second; (ii) pseudo self-concordant losses, for which the power is removed, as introduced by Bach (2010). These classes contain some losses arising in generalized… CONTINUE READING
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