Importance Weighted Active Learning

1. Importance Weighted Active Learning by Alina Beygelzimer, Sanjoy Dasgupta and John Langford (ICML 2009) Presented by Lingbo Li ECE, Duke University September 25, 2009

2. Outline • Introduction • The Importance Weighting Skeleton • Setting the rejection threshold • Label Complexity • Implementing IWAL • Conclusion

3. Introduction • Active learning At each step t, a learner receives an unlabeled point , and decide whether to query its label . Hypothesis space is , where Z is prediction space. Loss function • Drawback from earlier work: not consistent • PAC-convergence guarantee active learning 1) only 0-1 loss function; 2) internal use of generalization bounds. • Importance weighted approach 1) non-adaptive; 2) asymptotic. • Motivation Using importance weighting to build a consistent binary classifier under general loss functions, which removes sampling bias and improves label complexity.

4. The Importance Weighting Skeleton • The expected loss • The importance weighted estimate of the loss at time T then • IWAL algorithms are consistent, if does not equal zero.

5. Setting the rejection threshold • To do the minimization over instead of where • IWAL performs never worse than supervised learning.

6. Label Complexity – upper bound Previous work of active learning has been done only on the 0-1 loss with the number of queries of ; For arbitrary loss functions with the similar conditions, the number of queries is

7. Label Complexity – lower bound Lower bound is increased.

8. linear separators; logistic loss; MNIST data set of handwritten digits with 3’s and 5’s as two classes; 1000 exemplars for training; another 1000 for testing; Use PCA to reduce dimensions; Optimistic bound of Active learning performs similar to supervised learning with only less than 1/3 of the labels queried. Implementing IWAL (1)

9. Implementing IWAL (2) bootstrapping scheme binary and multiclass classification loss MNIST dataset

10. Conclusion • IWAL is a consistent algorithm, which can be implemented with flexible losses. • Label complexity is theoretical provided with substantial improvement. • Practical experiments approve this.