@TechReport{Uricar-CAK-2012-46,
  IS = { zkontrolovano 15 Jan 2013 },
  UPDATE  = { 2012-10-01 },
  author =       {U{\v{r}}i{\v{c}}{\'{a}}{\v{r}}, Michal and 
                  Franc, Vojt{\v{e}}ch},
  title =        {Bundle Method for Structured Output Learning},
  institution =  {Department of Cybernetics, Faculty of Electrical Engineering,
                  Czech Technical University},
  address =      {Prague, Czech Republic},
  year =         {2012},
  month =        {September},
  type =         {Research Report},
  number =       {K333--46/12, CTU--CMP--2012--20},
  pages =        {17},
  figures =      {3},
  authorship =   {50-50},
  psurl =        {[Uricar-TR-2012-20.pdf]},
  project =      {1M0567, FP7-ICT-247525 HUMAVIPS, TACR TE01020197, SGS12/187/OHK3/3T/13},
  annote =       {Discriminative methods for learning structured
    output classifiers have been gaining popularity in recent years
    due to their successful applications in fields like computer
    vision, natural language processing or bio-informatics. Learning
    of the structured output classifiers leads to solving a convex
    minimization problem which is not tractable by standard
    algorithms. A significant effort has been put to development of
    specialized solvers among which the Bundle Method for Risk
    Minimization (BMRM) [Teo et al., 2010] is one of the most
    successful. The BMRM is a simplified variant of bundle methods
    well known in the filed of non-smooth optimization. The simplicity
    of the BMRM is compensated by its reduced efficiency. In this
    paper, we propose several improvements of the BMRM which
    significantly speeds up its convergence. The improvements involve
    i) using the prox-term known from the original bundle methods, ii)
    starting optimization from a non-trivial initial solution and iii)
    using multiple cutting plane model to refine the risk
    approximation. Experiments on real-life data show that the
    improved BMRM converges significantly faster achieving speedup up
    to a factor of 10 compared to the original BMRM. The proposed
    method has become a part of the SHOGUN Machine Learning Toolbox
    [Sonnenburg et al., 2010]. },
  keywords =     {Regularized risk minimization, Structured Output SVM, 
                  Bundle methods, BMRM},
}