en>Awaterl: Small clarification.

2013-10-19T06:35:31Z

Small clarification.

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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.

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			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]]

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2012-06-01T06:29:46Z

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en>Awaterl: Small clarification.

75.139.239.118: /* Attack against truncated version */