Importance Weighted Active Learning

by

Alina Beygelzimer, Sanjoy Dasgupta and John Langford

(ICML 2009)

Presented by Lingbo LiECE, Duke University

September 25, 2009

Outline

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

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.

tx Xty Y :{ : }H h X Z

: [0, )l Z Y

The Importance Weighting Skeleton

X Y

• The expected loss

• The importance weighted estimate of

the loss at time T

then

• IWAL algorithms are consistent, if does not equal zero.

tp

Setting the rejection threshold

H

• To do the minimization over instead of

where• IWAL performs never worse than

supervised learning.

tHH

Label Complexity – upper bound

2( log )O T dT T 2( log )O T d T

2( log )O T dT T

Previous work of active learning has been done only on the 0-1 loss with the number of queriesof ; For arbitrary loss functions with the similar conditions, the number of queries is

Label Complexity – lower boundLower bound is increased.

Implementing IWAL (1)• 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 (2)bootstrapping schemebinary and multiclass classification loss MNIST dataset

tp

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.