Difference between revisions of "Martins et al 2010"
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=== Summary === | === 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. | + | This [[Category::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 === | === Method === | ||
| − | The general loss function | + | The general loss function is: |
[[file:Martins et al 2010 Loss Function.png]] | [[file:Martins et al 2010 Loss Function.png]] | ||
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[[file:Martins et al 2010 Parameter Choices.png]] | [[file:Martins et al 2010 Parameter Choices.png]] | ||
| − | The function minimized is the | + | The function minimized is the loss function 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]] | ||
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[[file:Martins et al Regularize Coeff.png]] | [[file:Martins et al Regularize Coeff.png]] | ||
| − | The algorithm proposed | + | The online learning algorithm proposed to minimize this function is called Dual Coordinate Ascent (DCA): |
[[file:Martins et al 2010 DCA.png]] | [[file:Martins et al 2010 DCA.png]] | ||
| − | The parameters | + | The parameters can be updated using algorithm 2: |
[[file:Martins et al 2010 Alg2.png]] | [[file:Martins et al 2010 Alg2.png]] | ||
Latest revision as of 02:08, 11 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 is:
Different choices of and correspond to various well known loss functions. They are:
The function minimized is the loss function with a regularizer:
The online learning algorithm proposed to minimize this function is called Dual Coordinate Ascent (DCA):
The parameters can be updated using algorithm 2:
Experimental Result
Related Papers
MIRA CRF Softmax-margin CRFs
In progress by User:Jmflanig
