Difference between revisions of "Martins et al 2010"

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[[file:Martins et al 2010 Parameter Choices.png]]
 
[[file:Martins et al 2010 Parameter Choices.png]]
  
The function they minimize is the empirical risk with a regularizer:
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The function minimized is the empirical risk with a regularizer:
  
 
[[file:Martins et al 2010 Learning Problem.png]]  [[file:Martins et al Relarizer.png]]
 
[[file:Martins et al 2010 Learning Problem.png]]  [[file:Martins et al Relarizer.png]]
  
 
[[file:Martins et al Regularize Coeff.png]]
 
[[file:Martins et al Regularize Coeff.png]]
 +
 +
The algorithm proposed in the paper is called Dual Coordinate Ascent (DCA):
 +
 +
[[file:Martins et al 2010 DCA.png]]
 +
 +
The parameters are updated using algorithm 2:
 +
 +
[[file:Martins et al 2010 Alg2.png]]
  
 
=== Experimental Result ===
 
=== Experimental Result ===

Revision as of 21:12, 1 October 2011

Citation and Online Link

A. F. T. Martins, K. Gimpel. N. A. Smith, E. P. Xing, P. M. Q. Aguiar, M. A. T. Figueiredo, 2010. Aggressive Online Learning of Structured Classifiers. Technical report CMU-ML-10-109.

Summary

This paper generalizes the loss function of CRFs, structured SVMs, structured perceptron, and Softmax-margin CRFs into a single loss function, and then derives an online learning algorithm that can be used to learn with that more general loss function. For the hinge loss, the learning algorithm reduces to MIRA.

Method

The general loss function they use is:

Martins et al 2010 Loss Function.png

Different choices of and correspond to various well known loss functions. They are:

Martins et al 2010 Parameter Choices.png

The function minimized is the empirical risk with a regularizer:

Martins et al 2010 Learning Problem.png Martins et al Relarizer.png

Martins et al Regularize Coeff.png

The algorithm proposed in the paper is called Dual Coordinate Ascent (DCA):

Martins et al 2010 DCA.png

The parameters are updated using algorithm 2:

Martins et al 2010 Alg2.png

Experimental Result

Related Papers

MIRA CRF Softmax-margin CRFs

In progress by User:Jmflanig