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Universal Learning over Related Distributions and Adaptive Graph Transduction Erheng Zhong †, Wei Fan ‡, Jing Peng*, Olivier Verscheure ‡, and Jiangtao Ren † † Sun Yat-Sen University ‡ IBM T. J. Watson Research Center *Montclair State University 1.Go beyond transfer learning to sample selection bias and uncertainty mining 2.Unified framework 3.One single solution: supervised case

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

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3 Sample Selection Bias New York Times training (labeled) test (unlabeled) Classifier New York Times 85.5% Have a different word vector distribution August: a lot about typhoon in Taiwan September: a lot about US Open 78.5%

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Uncertainty Data Mining Training Data: –Both feature vectors and class labels contain noise (usually Gaussian) –Common for data collected from sensor network Testing data: –Feature vector contain noises

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Summary Traditional supervised learning: –Training and testing data follow the identical distribution Transfer learning: –from different domains Sample selection bias: –from same domain but distribution is different such as, missing not at random Uncertain data mining: –data contains noise In other words: in all three cases, training and testing data are from different distributions. Traditionally, each problem is handled separately.

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Main Challenge Could one solve these different but similar problems under a uniform framework? With the same solution? Universal Learning

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is the subsets of X that are the support of some hypothesis in a ﬁxed hypothesis space ([Blitzer et al, 2008] The distance between two distributions ([Blitzer et al, 2008]

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How to Handle Universal Learning? Most traditional classifiers could not guarantee the performance when training and test distributions are different. Could we find one classifier under weeker assumption? Graph Transduction?

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Advantage of Graph Transduction Weaker assumption that the decision boundary lies on the low density regions of the unlabeled data. Two-Gaussians vs. Two-arcs

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Just Graph Transduction? Sample Selection: which samples? “Un-smooth label”(more examples in low density region) and “class imbalance” problems ([Wang et al, 2008]) may mislead the decision boundary to go through the high density regions. Bottom part closest red square More red square than blue square

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Maximum Margin Graph Transduction In margin-terms, unlabeled data with low margin are likely misclassiﬁed! Bad sample Good sample

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Main Flow Predict the labels of unlabeled data Lift the unlabeled data margin Maximize the unlabeled data margin

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Properties Adaptive Graph Transduction can be bounded Training error in terms of approximating the ideal hypothesis Error of the ideal hypothesis Emprical distance between training and test distribution

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Properties If one classiﬁer has larger unlabeled data margin, it will make the training error smaller (recall last theorem) Average ensemble is likely to achieve larger margin

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Experiment – Data Set Transfer Learning –Reuters: 21758 Reuters news articles –SyskillWebert: HTML source of web pages plus the ratings of a user on those web pages First fill up the “GAP”, then use knn classifier to do classification Reuters org org.subA org.subB place place.subA place.subB 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

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Experiment – Data Set Sample Selection Bias Correction –UCI data set: Ionosphere, Diabetes, Haberman, WDBC 1.Randomly select 50% of the features, and then sort the data set according to each selected features; 2.we attain top instances from every sorted list as training set; Feature 1 Feature 2 Uncertainty Mining –Kent Ridge Biomedical Repository: high dimensional, low sample size (HDLSS) Generate two different Gaussian Noises and add them into training and test set

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Experiment -- Baseline methods Original graph transduction algorithm ([Zhu, 2005]) –Using the entire training data set –Variation: choosing a randomly selected sample whose size is equal to the one chosen by MarginGraph CDSC: transfer learning approach ([Ling et al, 2008]) –find a mapping space which optimizes over consistency measure between the out-domain supervision and in- domain intrinsic structure BRSD-BK/BRSD-DB: bias correction approach ([Ren et al, 2008]) –discover structure and re-balance using unlabeled data

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Performance--Transfer Learning

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Perform best on 5 of 6 data sets!

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Performance--Sample Selection Bias Accuracy: Best on all 4 data sets! AUC: Best on 2 of 4 data sets.

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Performance--Uncertainty Mining Accuracy: Best on all 4 data sets! AUC: Best on all 4 data sets!

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Margin Analysis MarginBase is the base classiﬁer of MarginGraph in each iteration. LowBase is a “minimal margin classiﬁer” which selects samples for building a classiﬁer with minimal unlabeled data margin. LowGraph is the averaging ensemble of LowBase.

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Maximal margin is better than minimal margin Ensemble is better than any single classiﬁers

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Conclusion Cover different formulations where the training and test set are drawn from related but different distributions. Flow –Step-1 Sample selection -- Select labeled data from different distribution which could maximize the unlabeled data margin –Step-2 Label Propagation -- Label the unlabeled data –Step-3 Ensemble -- Further lift the unlabeled data margin Code and data available from http://www.cs.columbia.edu/~wfan http://www.cs.columbia.edu/~wfan

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