Margin-infused relaxed algorithm

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Margin-infused relaxed algorithm (MIRA)[1] is a machine learning algorithm, an online algorithm for multiclass classification problems. It is designed to learn a set of parameters (vector or matrix) by processing all the given training examples one-by-one and updating the parameters according to each training example, so that the current training example is classified correctly with a margin against incorrect classifications at least as large as their loss.[2] The change of the parameters is kept as small as possible.

A two-class version called binary MIRA[1] simplifies the algorithm by not requiring the solution of a quadratic programming problem (see below). When used in a one-vs.-all configuration, binary MIRA can be extended to a multiclass learner that approximates full MIRA, but may be faster to train.

The flow of the algorithm[3][4] looks as follows:

Algorithm MIRA
  Input: Training examples 
  Output: Set of parameters 
   ← 0,  ← 0
  for  ← 1 to 
    for  ← 1 to 
       ← update  according to 
    end for
  end for
  • "←" denotes assignment. For instance, "largestitem" means that the value of largest changes to the value of item.
  • "return" terminates the algorithm and outputs the following value.

The update step is then formalized as a quadratic programming[2] problem: Find , so that , i.e. the score of the current correct training must be greater than the score of any other possible by at least the loss (number of errors) of that in comparison to .


  1. ^ a b Crammer, Koby; Singer, Yoram (2003). "Ultraconservative Online Algorithms for Multiclass Problems". Journal of Machine Learning Research. 3: 951–991. 
  2. ^ a b McDonald, Ryan; Crammer, Koby; Pereira, Fernando (2005). "Online Large-Margin Training of Dependency Parsers" (PDF). Proceedings of the 43rd Annual Meeting of the ACL. Association for Computational Linguistics. pp. 91–98. 
  3. ^ Watanabe, T. et al (2007): "Online Large Margin Training for Statistical Machine Translation". In: Proceedings of the 2007 Joint Conference on Empirical Methods in Natural Language Processing and Computational Natural Language Learning, 764–773.
  4. ^ Bohnet, B. (2009): Efficient Parsing of Syntactic and Semantic Dependency Structures. Proceedings of Conference on Natural Language Learning (CoNLL), Boulder, 67–72.

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