Difference between revisions of "Chun-Nam John Yu, Hofmann , Learning structural SVMs with latent variables 2009"
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where | where | ||
− | <math> h_i^*(w) = argmax_{h_ | + | <math> h_i^*(w) = argmax_{h_ \epsilon H}w.G(x_i,y_i,h)</math> |
and | and | ||
− | <math>(y_i^opt(w), hi^optopt(w)) = argmax_{(y,h) | + | <math>(y_i^opt(w), hi^optopt(w)) = argmax_{(y,h) \epsilon YxH}w.G(x_i,y,h) </math> |
− | Loss function is the difference between the pair given by prediction rule and the latent variable <math> h_i^* </math> which explains the <math> ( | + | Loss function is the difference between the pair given by prediction rule and the latent variable <math> h_i^* </math> which explains the <math> (X_i, Y_i) </math> |
Like in the case of structural svm we can derive the upper bound of this function to be | Like in the case of structural svm we can derive the upper bound of this function to be |
Revision as of 00:38, 1 October 2011
Contents
Citation
Chun-Nam John Yu and Thorsten Joachims. Learning structural SVMs with latent variables. In Proceedings of the 26th International Conference on Machine Learning,Montréal, Québec, Canada, 2009.
Online version
Summary
In this paper author talks about the use of latent variable in the structural SVM. The paper also identifies the formulation for which their exists effecient algorithm to find the local optimum using convex-concave optimization techniques. The paper argues that this is the first time latent variable are being used in large margin classifiers.Experiments were then performed in various domains of computational Biology, IR and NLP to prove the generality of the proposed method.
Method Used
This paper extends the formulation of Structured SVM given by Tsochantaridis to include a latent variable in it.
Consider set of Structed input out put pairs
The prediction rule will be:
where G is the joint feature vector that describes the relation between input and output.This paper introduces an extra latent variable h so now the prediction rule changes to
Similary extending the loss function to include latent variable will be:
where
and
Loss function is the difference between the pair given by prediction rule and the latent variable which explains the
Like in the case of structural svm we can derive the upper bound of this function to be
== Let .
The prediction rule will be
where G is the joint feature vector that describes the relation between input and output.This paper introduces an extra latent variable h so now the prediction rule changes to ==