1. Cross Domain Distribution Adaptation via Kernel Mapping Erheng Zhong † Wei Fan ‡ Jing Peng* Kun Zhang # Jiangtao Ren † Deepak Turaga ‡ Olivier Verscheure ‡ † Sun Yat-Sen University ‡ IBM T. J. Watson Research Center *Montclair State University # Xavier University of Lousiana

2. Standard Supervised Learning New York Times training (labeled)‏ test (unlabeled)‏ Classifier 85.5% New York Times

3. In Reality …… New York Times training (labeled)‏ test (unlabeled)‏ Classifier 64.1% New York Times Labeled data not available! Reuters

4. Domain Difference->Performance Drop traintest NYT New York Times Classifier 85.5% Reuters NYT ReutersNew York Times Classifier 64.1% ideal setting realistic setting

5. Synthetic Example

7. Main Challenge  Motivation Both the marginal and conditional distributions between target-domain and source-domain could be significantly different in the original space!! How to get rid of these differences? Could we find other feature spaces? Could we remove those useless source-domain data?

8. Main Flow Kernel Discriminant Analysis

9. Kernel Mapping

10. Instances Selection

11. Ensemble

12. Properties Kernel mapping can reduce the difference of marginal distributions between source and target domains. [Theorem 2] Cluster-based instances selection can select those data from source domain with similar conditional probabilities. [Cluster Assumption] Error rate of the proposed approach can be bounded; [Theorem 3] Ensemble can further reduce the transfer risk. [Theorem 4] Both the target and source domain data follow appropriate Gaussian distributions in a Gaussian RKHS. It assumes that if two point x1 and x2 are close in the intrinsic geometry of q(x), then the conditionals r(y|x1) and r(y|x2) are similar.

13. Experiment – Data Set Reuters 21758 Reuters news articles 20 News Groups 20000 newsgroup articles SyskillWebert HTML source of web pages plus the ratings of a user on those web pages from 4 different subjects All of them are high dimension (>1000)! First fill up the “GAP”, then use knn classifier to do classification 20 News groups (Reuters) comp comp.sys comp.graphics rec rec.sport rec.auto Target-Domain Source-Domain First fill up the “GAP”, then use knn classifier to do classification SyskillWebert Target-Domain Sheep Biomedical Bands- recording Source-Domain Goats

14. Experiment -- Baseline methods Non-transfer single classifiers Transfer learning algorithm TrAdaBoost. Base classifiers: K-NN SVM NaiveBayes

15. Experiment -- Overall Performance Dataset 1~9 kMapEnsemble -> 24 win, 3 lose!

16. Conclusion Domain transfer when margin and conditional distributions are different between two domains. Flow Step-1 Kernel mapping -- Bring two domains ’ marginal distributions closer; Step-2 Cluster-based instances selection -- Make conditional distribution transferable; Step-3 Ensemble – Further reduce the transfer risk. Code and data available from the authors.