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A support Vector Method for Multivariate performance Measures

A support Vector Method for Multivariate performance Measures. Author: Thorsten Joachims (ICML’05) Presenter: Lei Tang. Motivation. Current classifier focus on error-rate, how to optimize it directly for different performance measures? Precision, recall, F-measure etc. Existing Approach.

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A support Vector Method for Multivariate performance Measures

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  1. A support Vector Method for Multivariate performance Measures Author: Thorsten Joachims (ICML’05) Presenter: Lei Tang

  2. Motivation • Current classifier focus on error-rate, how to optimize it directly for different performance measures? • Precision, recall, F-measure etc.

  3. Existing Approach • Accurately estimate the probabilities of class membership of each example. (Difficult) • Optimize tractable different variants. But for non-linear measure(F-measure), extensive CV is required. • Directly optimize the measure like ROCArea. But non on F-measure.

  4. Reformulation Sample-based Loss • Given training examples and test examples S’, our goal is to minimize • Decompose the loss function linearly: Empirical loss: Example-Based Loss

  5. SVM • Original SVM: • Multivariate SVM: Here, is a function that returns a feature vector of x,y Prediction:

  6. Problems Too many constraints!!!! N samples, k class labels, then |Y|=k^N. Do we really need to include all the constraints?

  7. Algorithm Constraint Selection

  8. Contingency Table • Still impractical!! We have to calculate • Contingency table N samples, how many different tables?

  9. Algorithm for argmax Given a table, • Exhaustive search all the possible contingency tables and get the maximum. What should the assignment be?

  10. Various Loss • F-measure: • Precision /Recall (Just look at top k data points) • Precision/Recall Break-Even Point The search space is reduced as a+b=a+c

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