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'''Margin Infused Relaxed Algorithm (MIRA)'''<ref name="crammer-singer2003"> | |||
{{cite journal | |||
| last1 = Crammer | first1 = Koby | |||
| last2 = Singer | first2 = Yoram | |||
| year = 2003 | |||
| title = Ultraconservative Online Algorithms for Multiclass Problems | |||
| journal = [[Journal of Machine Learning Research]] | |||
| volume = 3 | |||
| pages = 951–991 | |||
| url = http://jmlr.csail.mit.edu/papers/v3/crammer03a.html | |||
}} | |||
</ref> 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 (machine learning)|margin]] against incorrect classifications at least as large as their loss.<ref name="mcdonald-etal2005"> | |||
{{cite conference | |||
| last1 = McDonald | first1 = Ryan | |||
| last2 = Crammer | first2 = Koby | |||
| last3 = Pereira | first3 = Fernando | |||
| title = Online Large-Margin Training of Dependency Parsers | |||
| booktitle = Proceedings of the 43rd Annual Meeting of the ACL | |||
| publisher = [[Association for Computational Linguistics]] | |||
| date = 2005 | |||
| pages = 91–98 | |||
| url = http://aclweb.org/anthology-new/P/P05/P05-1012.pdf }} | |||
</ref> The change of the parameters is kept as small as possible. | |||
A two-class version called '''binary MIRA'''<ref name="crammer-singer2003"/> simplifies the algorithm by not requiring the solution of a [[quadratic programming]] problem (see below). When used in an [[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<ref>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.</ref><ref>Bohnet, B. (2009): ''Efficient Parsing of Syntactic and Semantic Dependency Structures''. Proceedings of Conference on Natural Language Learning (CoNLL), Boulder, 67-72.</ref> looks as follows: | |||
{{Algorithm-begin|name=MIRA}} | |||
'''Input:''' Training examples <math>T = \{x_i, y_i\}</math> | |||
'''Output:''' Set of parameters <math>w</math> | |||
<math>i</math> ← 0, <math>w^{(0)}</math> ← 0 | |||
'''for''' <math>n</math> ← 1 '''to''' <math>N</math> | |||
'''for''' <math>t</math> ← 1 '''to''' <math>|T|</math> | |||
<math>w^{(i+1)}</math> ← update <math>w^{(i)}</math> according to <math>\{x_t, y_t\}</math> | |||
<math>i</math> ← <math>i + 1</math> | |||
'''end for''' | |||
'''end for''' | |||
'''return''' <math>\frac{\sum_{j=1}^{N \times |T|} w^{(j)}}{N \times |T|}</math> | |||
{{Algorithm-end}} | |||
The update step is then formalized as a [[quadratic programming]]<ref name="mcdonald-etal2005"/> problem: Find <math>min\|w^{(i+1)} - w^{(i)}\|</math>, so that <math>score(x_t,y_t) - score(x_t,y')\geq L(y_t,y')\ \forall y'</math>, i.e. the score of the current correct training <math>y</math> must be greater than the score of any other possible <math>y'</math> by at least the loss (number of errors) of that <math>y'</math> in comparison to <math>y</math>. | |||
==References== | |||
<!--- See [[Wikipedia:Footnotes]] on how to create references using <ref></ref> tags which will then appear here automatically --> | |||
{{Reflist}} | |||
==External links== | |||
*[https://github.com/jihelhere/adMIRAble adMIRAble] - MIRA implementation in C++ | |||
*[https://code.google.com/p/miralium/ Miralium] - MIRA implementation in Java | |||
*[https://cwiki.apache.org/confluence/display/MAHOUT/Online+Passive+Aggressive MIRA implementation] for [[Apache Mahout|Mahout]] in [[Hadoop]] | |||
[[Category:Classification algorithms]] | |||
Latest revision as of 08:35, 19 October 2013
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 an 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:
Input: Training examples Output: Set of parameters
← 0, ← 0 for ← 1 to for ← 1 to ← update according to ← end for end for return
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 .
References
43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.
External links
- adMIRAble - MIRA implementation in C++
- Miralium - MIRA implementation in Java
- MIRA implementation for Mahout in Hadoop
- ↑ 1.0 1.1
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You can view that web-site... ccleaner free download - ↑ 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.
- ↑ Bohnet, B. (2009): Efficient Parsing of Syntactic and Semantic Dependency Structures. Proceedings of Conference on Natural Language Learning (CoNLL), Boulder, 67-72.