Bridged Refinement for Transfer Learning

XING Dikan, DAI Wenyua, XUE Gui-Rong, YU Yong

Shanghai Jiao Tong University{xiaobao,dwyak,grxue,yyu}@apex.sjtu.edu.cn

Outline

• Motivation• Problem• Solution

– Assumption– Method– Improvement and Final Solution

• Experiment• Conclusion

Overview

• Motivation• Problem• Solution

– Assumption– Method– Improvement and Final Solution

• Experiment• Conclusion

Motivation

• Email spamming: Whether a given mail is a spam or not.

– Training Data

– Test Data

A B C D …

Z Y

Pop music

basketball basketball

football

classic music

ownerMailbox:

Motivation

• New events always occur.news in 2006, commercial or politicsnews in 2007, commercial or politics

• Solution ?– Labeling new data again and again -- costly

• Therefore, …We try to utilize those old labeled data but take the

shift of distribution into consideration.[Transfer useful information]

Overview

• Motivation• Problem• Solution

– Assumption– Method– Improvement and Final Solution

• Experiment• Some other solutions

Problem

• We want to solve a classification problem.• The set of target categories is fixed.• Main difference from traditional classification:

– The training data and test data are governed by two slightly different distributions.

• We do not need labeled data in the new test data distribution.

Illustrative Example

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sports

music+: normal mail

-: spam mail

Overview

• Motivation• Problem• Solution

– Assumption– Method– Improvement and Final Solution

• Experiment• Some other solutions

Overview

• Motivation• Problem• Solution

– Assumption– Method– Improvement and Final Solution

• Experiment• Some other solutions

Assumption

• P(c|d) doesn’t changes: Ptrain(c|d) = Ptest(c|d) Since– The set of target categories is fixed.– Each target category is definite.

• P(c|di) ~ P(c|dj), when di ~ dj.

~ means “similar”, “close to each other”• Consistency

– Mutual Reinforcement Principle

Overview

• Motivation• Problem• Solution

– Assumption– Method– Improvement and Final Solution

• Experiment• Some other solutions

Method: Refinement

• UConfc: scores of a base classifier, coarse-gained (Unrefined Confidence score of category c)

• M: adjacent matrix. Mij = 1 if di is a neighbor of dj

(then row L1 normalized).• RConfc: Refined Confidence score of category c.

• Mutual reinforcement principle yields:RConf c = α M RConfc + (1-α) UConfc

where α is a trade-off coefficient.

Method: Refinement

• Refinement can be regarded as reaching a consistency under the mixture distribution.

• Why not try to reach a consistency under the distribution of the test data?

Illustrative Example

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Overview

• Motivation• Problem• Solution

– Assumption– Method– Improvement and Final Solution

• Experiment• Some other solutions

Method: Bridged Refinement

• Bridged Refinement

– Refine towards the mixture distribution– Refine towards the target distribution.

Outline

• Motivation• Problem• Solution

– Assumption– Method– Improvement and Final Solution

• Experiment• Conclusion

Experiment

• Data set• Base classifiers• Different refinement styles• Performance• Parameter sensitivity

Experiment: Data set

• Source– SRAA

• Simulated autos (simauto)• Simulated aviation (simaviation)• Real autos (realauto)• Real aviation (realaviation)

– 20 Newsgroup• Top level categories: rec, talk, sci, comp

– Reuters-21578• Top level categories: org, places, people

Experiment: Data set

• Re-construction– 11 data sets

A2 B1 B2A1

Positive Negative

Training Data

Test Data

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Experiment: Base classifier

• Supervised – Generative model: Naïve Bayes classifier– Discriminative model: Support vector machines

• Semi-supervised:– Transductive support vector machines

Experiment: Refinement Style

• No refinement (base)• One step

– Refine directly on the test distribution (Test)– Refine on the mixture distribution only (Mix)

• Two steps– Bridged Refinement (Bridged)

Performance: On SVM

• Base• Test• Mix• Bridged

• Test (2nd) , Mix(3rd) v.s. Base (1st)• Test (2nd) v.s. Bridged (1st)：

– Different start point

Performance: NB and TSVM

Parameter: K

Whether di is regardedas a neighborof dj is decidedby checkingwhether di is in dj’s k-nearestneighbor set.

Parameter: α

Error rate Vs.Differentalpha

Convergence

The refinementformula canbe solved ina close manner or an iterativemanner.

Outline

• Motivation• Problem• Solution

– Assumption– Method– Improvement and Final Solution

• Experiment• Conclusion

Conclusion

• Task: Transfer useful information from training data to the same classification task of the test data, while training and test data are governed by two different distributions.

• Approach: Take the mixture distribution as a bridge and make a two-step refinement.

Thank youPlease ask in slow and simple English

Backup 1: Tranductive

• The boundary after either step of refinement are actually never calculated explicitly. It is hidden in the refined labels of each data points.

• I draw it in the examples explicitly is for a clearer illustration only.

Backup 2: n-step

• One important problem left unsolved by us:– How to describe a distribution

\lembda D_train + (1-\lembda) D_test ?– One solution is sampling in a generative manner.

But this makes the result depends on each random number picked up in the generative process. It may cause the solution not very stable and hard to repeat.

Backup 3: Why mutual reinforcement principle ?

• If d_j has a high confidence to be in category c, then d_i, the neigbhor of d_j should also receive a high confidence score.